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Partial credit guarantee and trade credit in an emission-dependent supply chain with capital constraint
Transportation Research Part E 135 (2020) 101859
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Transportation Research Part E journal homepage: www.elsevier.com/locate/tre
Partial credit guarantee and trade credit in an emission-dependent supply chain with capital constraint Song Xu, Lei Fang
T
⁎
Business School, Nankai University, 94 Weijin Road, Nankai District, Tianjin 300071, PR China
ARTICLE INFO
ABSTRACT
Keywords: Emission-dependent supply chain Capital constraint Partial credit guarantee Trade credit Emission reduction investment
This study investigates a supply chain financing (SCF) system with one supplier and one emission-dependent and capital-constrained manufacturer. Unlike the traditional SCF, the manufacturer borrows two loans to execute the ordering decision and make a low-carbon investment, respectively. We derive the equilibrium strategies of the supply chain members under partial credit guarantee (PCG) and a combination of trade credit and PCG and compare with that under a benchmark (well-funded manufacturer). There exists a unique coefficient of credit guarantee for the supplier to decide whether to provide a trade credit. Numerical studies and extension are discussed to obtain more managerial implications.
1. Introduction The greenhouse effect has a significant negative influence on global sustainable development, such as a rise in the sea level and natural disasters. Excessive carbon emissions primarily contribute to the greenhouse effect. Therefore, an increasing number of countries and organizations have taken efforts to curb carbon emissions through carbon emission trading (Du et al., 2013) and environmental tax (Chan et al., 2018), among others. However, the carbon emissions trading mechanism is more effective than compulsory regulations (e.g., environmental tax) in curbing carbon emissions (Hua et al., 2011; Tang et al., 2015). According to the carbon emissions trading mechanism (Du et al., 2015), the manufacturers obtain respective emission caps allocated by the government. The emission permit plays an important role for the manufacturers’ production, because the manufacturers need to submit enough emission permits to regulatory body (i.e., compliance) after production. If the total amount of carbon emissions exceeds the emission cap, the manufacturers are required to buy emission permits from the emissions trading market to emit extra carbon. Alternatively, the manufacturers can sell the surplus emission permits to obtain extra revenue. Generally speaking, larger enterprises have greater advantages to invest in emission reduction improvement. For example, H&M, Marks & Spencer, and Levis, which are fashion apparel manufacturing enterprises, have adopted new emission reduction technologies to minimize their carbon emissions (Li and Li, 2016; Yang et al., 2017). However, some small and medium-sized enterprises (SMEs) also have motivations to invest in emission reduction improvement because of pressures from the environmental regulations and consumer preference. For example, about 40% of Chinese factories has been shut down because of their substandard emission inspected by environmental bureau officials (Nace, 2017). Additionally, according to the case study of Korean manufacturing SMEs (Lee, 2009), one of the most important drivers for the SMEs adopting environmental improvement is to comply with stringent environmental regulations. Another case study based on 202 SMEs (Meath et al. 2016) demonstrates that implementing emission reduction investment can reduce the environmental cost and improve the competition of the enterprises. Furthermore, consumers
⁎
Corresponding author. E-mail addresses: [email protected] (S. Xu), [email protected] (L. Fang).
https://doi.org/10.1016/j.tre.2020.101859 Received 20 February 2019; Received in revised form 22 January 2020; Accepted 25 January 2020 1366-5545/ © 2020 Elsevier Ltd. All rights reserved.
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
with higher low-carbon awareness possess the willingness to pay more for low-carbon products (Zhu and He, 2017). However, manufacturers, especially small and medium enterprises (SMEs), usually face capital constraints, which worsen when they invest in emission reduction technologies. Therefore, manufacturers need to seek financing sources to execute their operational decisions and emission reduction investments. For example, Industrial and Commercial Bank of China has offered 100 billion yuan to help capitalconstrained SMEs to invest in carbon reduction investments (Sohu Finance, 2013). Additionally, supply chain finance is considered effective in enabling the SMEs to overcome capital constraints and improving the performance of entire supply chains (Yan et al., 2016; Ni et al., 2017; Li et al., 2018). While external bank credit financing (BCF) is popular among capital-constrained manufacturers, the low-level of creditworthiness and collateral of capital -constrained manufacturers limits their direct access to BCF (Gao et al., 2018). Usually, the capital-constrained manufacturers should obtain a partial credit guarantee (PCG) from their suppliers to approach banks for BCF (Yan et al., 2016). This can be attributed to the fact that even if the capital-constrained SMEs fail to repay and approach bankruptcy, the suppliers will bear the responsibility of partially paying the outstanding amount to the bank. Note that the PCG will bring great risk to the supplier. However, if the supplier rejects to provide the guarantee for the manufacturer to obtain loans, the transaction between the supplier and manufacturer might not be able to continue. Furthermore, it is also beneficial for the supplier to improve sales when the manufacturer makes low-carbon investment to attract more consumers with low-carbon awareness. Moreover, even if the supplier undertakes the guarantee risk from the manufacturer, he will make the decision to maximize own expected profit. Trade credit financing (TCF) is another popular financing scheme that supports capital-constrained supply chains (Chen and Wang, 2012; Jing et al., 2012; Kouvelis and Zhao, 2012; Yang and Bridge, 2018). Under TCF, the upstream supplier charges an interest on the delayed payment to the capital-constrained manufacturer. Despite the provision under TCF, an emission-dependent manufacturer seeks another loan through PCG in order to invest in emission reduction technologies. Therefore, we consider two financing schemes for the emission-dependent and capital-constrained manufacturer. Under the PCG scheme, the manufacturer borrows all the funds through PCG to execute the ordering decision and make the emission reduction investment. Under a combination of TCF and PCG (TPCG) scheme, the manufacturer places an order from the supplier through TCF and borrows capital for emission reduction investment from the bank through PCG. According to a report conducted by SWITCH-Asia Network Facility (Agster et al. 2016), some large leading enterprises can provide guarantees to help their up- and downstream SME partners to obtain loans from the banks and improve the environmental performance. Additionally, Taixiang Wood Industry Corporation (China Green Times, 2019), which acts as a core enterprise in a forestry supply chain, provided the guarantee to help his downstream SME manufacturers to obtain green loans from Guangdong Sihui Bank of Agriculture and Commerce. Furthermore, there exist account receivables for the Taixiang after offering trade credit to his downstream SMEs. Finally, six downstream SMEs obtained 5.3 million guarantee green loan and trade credit to execute low-carbon investments and operational decisions. Therefore, we consider PCG and TPCG financing schemes for a capital-constrained manufacturer. These two financing schemes give rise to the following research questions: 1. Which equilibrium strategies are adopted by the supply chain’s members under a benchmark scenario (i.e., well-funded manufacturer), PCG, and TPCG financing schemes, respectively? 2. How does the coefficient of credit guarantee impact the financing equilibrium? Does the supplier always prefer to provide TCF to the manufacturer? 3. How do other important parameters, such as the emission cap, consumer low-carbon awareness, and unit price of emission permit, impact the equilibrium strategies and profits of the supply chain’s members? To address the above questions, we consider a two-echelon supply chain with one supplier and one emission-dependent and capital-constrained manufacturer under the cap-and-trade regulation. The manufacturer borrows loans to execute the ordering decision and make the emission reduction investment through PCG or TPCG. Subsequently, the manufacturer processes the products and sells them to consumers with a low-carbon awareness. We derive the equilibrium strategies of the supply chain’s members under the two financing schemes, and compare with that under a benchmark i.e., well-funded manufacturer. We discuss the impact of the different coefficients of credit guarantee on financing equilibrium and conduct numerical studies to analyze the impact of other important parameters. Additionally, we extend this study to discuss the endogenous interest rates under PCG and TPCG, respectively. The contributions of this study are summarized as follows. We formulate a two-stage Stackelberg game of an emission-dependent supply chain under PCG and TPCG financing schemes and derive the equilibrium strategies of the supply chain’s members. Under the benchmark scenario, the emission cap allocated by the government ceases to influence the decisions of the well-funded manufacturer. Under the two financing schemes, given the interest rate and the wholesale price, an increase in the emission cap negatively influences the optimal ordering quantity determined by the manufacturer. Additionally, when compared to the benchmark scenario, under the two financing schemes, the capital-constrained manufacturer places a larger ordering quantity but invests less in emission reduction. On the supplier’s side, we observe that a trade-off between additional revenue and potential loss occurs when the manufacturer faces bankruptcy, according to different coefficients of credit guarantee. When the coefficient of credit guarantee is within a relatively low range, the supplier expresses reluctance to provide TCF to the capital-constrained manufacturer. This result is contrary to literature (Cao et al., 2019) suggesting that the supplier will always make more profit under TCF than that under BCF. The remaining parts of this paper are organized as following. Section 2 summarizes the relevant literature. Section 3 describes the model and presents the notations used in this study. Section 4 derives the equilibrium strategies of the supply chain’s members under the benchmark scenario, PCG, and TPCG schemes, respectively. Section 5 presents a comparative analysis under the three scenarios. Section 6 carries out numerical studies to analyze the influence of some important parameters. Section 7 extends this study to discuss 2
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S. Xu and L. Fang
the endogenous interest rates under PCG and TPCG, respectively. Finally, Section 8 presents the conclusion and limitations of this study. 2. Literature review This study is related to the following two streams of literature: the emission-dependent supply chains and supply chain finance. We will review the related literature and highlight the differences between this study and existing literature. The emission-dependent supply chain focuses on the production and inventory of a firm under the cap-and-trade regulation. For example, Dobos (2005) analyzed the effect of emission permits on the production and inventory strategies of a firm under the capand-trade system, based on the dynamic Arrow-Karlin model. Extending Dobos’s (2005) model, Li and Gu (2012) further considered the impact of tradable emission permits with banking on a firm’s production and inventory decisions. Li et al. (2013a, 2013b) investigated the impact of the emission trading scheme on the dynamic decision-making of generation companies (GENCOs), under a multimarket environment comprising the electricity, fuel, and carbon markets. However, this study focuses on the operational decision and low-carbon investment of the capital-constrained manufacturer, under a different multimarket environment comprising the emission trading market and the supply chain financing market. In recent years, emphasis has been given to extending the literature on a firm regulated by the cap-and-trade system to an emission-dependent supply chain. For example, Du et al. (2013, 2015) investigated the impact of the emission cap on equilibrium strategies of a supply chain consisting of one emission-dependent manufacturer and one emission permit supplier. Xu et al. (2017a) considered production and pricing decisions in an emission-dependent supply chain in which an upstream manufacturer, under the cap-and-trade regulation, produces two products based on make-to-order production. Yang et al. (2017) explored pricing and carbon emission reduction decisions in two competitive and emission-dependent supply chains with vertical and horizontal cooperation. Some studies (Jaber et al., 2013; Glock and Kim, 2015; Xu et al., 2016; Xu et al., 2017b) investigated different contracts that can be used to achieve two-level supply chain coordination under cap-and-trade regulation. Apart from considering competition or coordination in emission-dependent supply chains, Xia et al. (2018) integrated reciprocal preferences and the consumer with a lowcarbon awareness into an emission-dependent supply chain and analyzed its impact on the decisions and performances of the supply chain’s members. Furthermore, Li et al. (2017) investigated centralized and decentralized supply chain models with a carbon-sensitive demand and compared the optimal decisions of the production quantity and emission reduction effort under absolute-cap and intensity-cap regulations. Daryantoa et al. (2019) explored the impact of emission cost, deterioration, and variable transportation cost on a three-echelon supply chain with a supplier, a third-party logistics service provider, and a buyer. However, the above literature assumes that the supply chain’s members have sufficient capital to execute optimal decisions regarding operation and emission reduction investment. In practice, a manufacturer, especially an SME, is vulnerable to capital constraint. Therefore, to fill this research gap, we consider a capital-constrained and emission-dependent manufacturer who requires two loans to execute the decisions of ordering quantity and emission reduction investment, respectively. Another stream of literature related to this study is supply chain finance. In this domain, the two popular financing schemes BCF and TCF for the capital-constrained supply chain members are highlighted in several studies, such as Dada and Hu (2008), Chen and Wang (2012), Kouvelis and Zhao (2011), and Yang and Birge (2018). For example, Zhang et al. (2018) assumed that a manufacturer offers trade credit to the capital-constrained retailer, by integrating customer balking and asymmetric market information. Unlike the traditional TCF, Tsao (2017) showed that providing trade credit to customers leads to default risk, for an uncertain and credit-period dependent demand; they also discussed who (supplier or retailer) should implement big data analytics to mitigate default risk in the supply chain. Devalkar and Krishnan (2019) focused on the role of TCF in addressing the supplier’s moral hazard problems and how to coordinate the supply chain. Kouvelis and Zhao (2017) investigated the impact of credit ratings on operational and financial decisions of a capital-constrained supply chain. The capital-constrained retailer can obtain short-term financings via both bank loans and trade credits, while the capital-constrained supplier can decide the operational decisions through bank loans and/or an early payment contract. Furthermore, Lee et al., (2017) employed a dyadic panel data set to explore the impact of TCF on different types of competition between supply chain members and firm performance, while Wu et al., (2019) considered quantitative modelling to discuss the role of TCF on inventory competition between two asymmetric retailers. Additionally, some studies have focused on conducting a comparison between BCF and TCF, such as Jing et al. (2012), Jing and Seidmann (2014), Kouvelis and Zhao (2012), and Cai et al. (2014). In this context, it must be noted that capital-constrained enterprise with low trustworthiness face difficulties in directly obtaining loans from the bank. Some studies assumed that the capital-constrained supply chain’s members obtain loans from other financing schemes, such as third-party logistics firms (Chen and Cai, 2011; Wang et al., 2019b), peer-to-peer lending platform (Gao et al., 2018), and electronic business platform (Wang et al., 2019a). Furthermore, some studies assumed that core enterprises with enough capital in the supply chain provide a PCG, enabling capital-constrained SMEs to obtain the loans from banks. For example, Yan et al. (2016) designed a PCG contract for a capital-constrained supply chain and analyzed equilibrium financing strategies and coordination conditions for the PCG contract. Li et al. (2018) extended the study by Yan et al. (2016) and explored two financing strategies—PCG and TCF—for a supply chain comprising one risk-averse supplier and one risk-neutral retailer with capital constraint. They characterized the preference of two financing strategies with different coefficients of credit guarantee and riskaversion degree. However, the above literature ignored the impact of cap-and-trade regulation on the operational, greening, and financing decisions of capital-constrained supply chains. In recent years, some studies have focused on emission-dependent supply chains with capital constraints. For example, Wu et al. (2018) examined a green supply chain financing system comprising one manufacturer and one capital-constrained retailer. However, they considered that the upstream manufacturer had sufficient capital for low-carbon 3
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Table 1 Summary of the literature about supply chain finance. Existing work Dada and Hu (2008) Chen and Wang (2012) Zhang et al., (2018) Devalkar and Krishnan (2019) Wu et al. (2019) Lee et al. (2018) Jing and Seidmann (2014) Jing et al. (2012) Kouvelis and Zhao (2012) Kouvelis and Zhao (2017) Cao and Yu (2018) Yan et al. (2016) Li et al. (2018) Wu et al., (2018) Cao et al. (2019) This study
Cap-and-trade regulation
Yes
Yes Yes
Financing schemes
Uses of loans
BCF TCF TCF TCF TCF TCF BCF/TCF BCF/TCF/BCF + TCF BCF/TCF BCF + TCF/Early payment contract TCF PCG PCG/TCF BCF/TCF BCF/TCF PCG/TPCG
Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Low-carbon investment + ordering
investment, and hence ignored capital constraints for this investment. Furthermore, they ignored the influence of the cap-and-trade regulation on the decisions of supply chain members. Cao and Yu (2018) investigated that both the manufacturer and retailer are under the cap-and-trade regulation, and the manufacturer provides TCF contract for a capital-constrained retailer. They designed a general contract to achieve supply chain coordination under the cap-and-trade regulation. We summarize the differences between this study and existing literature in Table 1. The most closely related literature to this study is Cao et al. (2019); they compared two financing schemes—BCF and TCF—for a downstream manufacturer who is emission-dependent and capital constraint. They assumed that the manufacturer borrowed only one loan for ordering decision and discussed whether investments in carbon abatement has an impact on the financing equilibrium. However, they ignored the fact that the manufacturer may need another loan for emission reduction investments. The differences between this and Cao et al.’s study (2019) are summarized as follows. On the one hand, we assume that the capital-constrained manufacturer needs two loans for the ordering decision and emission reduction investment, respectively. On the other one hand, we assume that the supplier will provide a PCG contract for the emission-dependent and capital-constrained manufacturer because it is difficult for the manufacturer to directly obtain loan from a bank. We find that when the coefficient of credit guarantee is within a relatively low range, the supplier expresses reluctance to provide TCF to the capital-constrained manufacturer. The result is contrary to that of Cao et al. (2019). 3. Model description We consider a supply chain comprising one supplier and one emission-dependent manufacturer, under the cap-and-trade regulation. The manufacturer purchases raw products from the supplier and, subsequently, sells the products to the consumers with a low-carbon awareness after processing. The manufacturer buys emission permits from the emission trading market if the manufacturer’s total amount of carbon emissions exceeds the emission cap allocated by the government. Alternatively, the manufacturer can sell the surplus emission permits to earn extra revenue. Furthermore, the consumers with a low-carbon awareness exhibit willingness to pay more for low-carbon products (Zhu and He, 2017). This drives the rational manufacturer to invest in the improvement of emission reduction to reduce emission and attract more consumers. Note that carbon emission reduction investment is a long-term investment activity, but the enterprises usually divide the long-term investment into several short-term programs. For example, Fujitsu (2012) completed the fifth short-term program of emission reduction in earlier 2012 and moved to the sixth stage of environmental improvement. In this study, we considered a single-period supply chain problem with a downstream manufacturer who intends to invest in one of short-term programs of emission reduction. However, the manufacturer usually faces capital constraints either when ordering from the supplier or investing in emission reduction. In this study, we consider two financing schemes for the capital-constrained manufacturer—PCG and TPCG. Under the former scheme, with the assistance offered in the form of the supplier’s PCG, the manufacturer borrows all the capital needed from the bank to execute decisions regarding procurement and emission reduction investment. Under the latter scheme, the manufacturer obtains the following two loans: one loan is borrowed through TCF for obtaining raw products before processing, and the other loan is borrowed from the bank through PCG to invest in emission reduction. The framework of the emission-dependent supply chain financing system is shown in Fig. 1. We also set a benchmark wherein the manufacturer has sufficient capital to execute the ordering decision and make the emission reduction investment. The demand will be influenced by the consumers’ willingness to buy low-carbon products and by other uncertain events or factors. Thus, the demand function is characterized as D = e + (Cao et al., 2019), where denotes the consumer low-carbon awareness; e denotes the level of emission reduction, represents the stochastic factor and follows a distribution in the range of [0, + ) . F ( ) and f ( ) represent cumulative distribution function and probability density function, respectively. Let h ( ) = f ( ) F ( ) be the failure rate (Jing et al., 2012), which increases with . 4
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
Bank
Government
Int
ere
r (λ
Credit guarantee
λ
Supplier
Low-carbon Investment
)
st r
ate
Emission cap
G
Wholesale price w
Manufacturer
Order quantity Q ion iss em n e f o tio c vel Le redu
Sell
Unit price
p =1
Consumers
Buy
Emission Trading Market
Fig. 1. The framework of an emission-dependent supply chain financing system.
Without the loss of generality, we present the following assumptions: (1) The manufacturer has no initial capital. This assumption can simplify the complex derivation and make the results more obvious in this study. It is also widely used in the literature of capital-constrained supply chain (Jing and Seidmann, 2014; Chen, 2015; Jing et al., 2012; Cao et al., 2019). (2) The retail price is fixed and normalized to 1 (Cai et al., 2014; Chen and Wang, 2012). For simplification, the processing cost of the manufacturer is normalized to zero (Yang et al., 2017). (3) All parameters are common knowledge for the bank, supplier, and manufacturer (Kouvelis and Zhao, 2012). Furthermore, similar to Li et al., (2018), we assume that the two interest rates under PCG and TPCG are fixed at the same value. This might occur that the interest rates are purely determined by the industrial benchmark (Kouvelis and Zhao, 2012). We will discuss the impact of difference between the two interest rates on the selection of financing schemes in Sub-section 6.1. In addition, we will relax the assumption of fixed interest rates to discuss the endogenous interest rates in Section 7. For easier representation, the notations throughout this study are summarized in Table 2. The subscript ‘‘i = b ’’ represents the parameters under benchmark, ‘‘i = 1’’ refers to the parameters under PCG, and the subscript ‘‘i = 2 ’’ denotes the parameters under TPCG. 4. Financing equilibrium under two financing schemes 4.1. Benchmark scenario In this section, we consider a benchmark wherein an emission-dependent manufacturer has sufficient capital to execute the Table 2 Notations. Parameters
Definitions
Di ri
Demand of the products Interest rate Consumer low-carbon awareness Stochastic factor of demand Cost coefficient of the emission reduction investment Unit price of the emission permit Initial emission of the per unit of the product Emission cap allocated by the government Coefficient of credit guarantee Cost of the supplier Bankruptcy threshold Probability density function Cumulative distribution function
v pe G cs Ai f (·) F (·) h (·) s i m i
Decision variables wi Qi ei
Failure rate, h (·) = f (·) F (·) Profit of the supplier Profit of the manufacturer
Wholesale price Ordering quantity Level of emission reduction
5
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
optimal ordering decision and make a low-carbon investment. The transaction between the manufacturer and supplier is based on the wholesale price contract. We employ the backward induction approach to derive the equilibrium strategies of the two supply chain participants. The emission-dependent manufacturer places an order Qb with the supplier, according to the wholesale price wb , and sells to the low-carbon awareness consumers after processing. Under the cap-and-trade regulation, the manufacturer may obtain extra revenue from selling surplus carbon permits. This motivates the manufacturer to make an emission reduction investment. This investment is a one-off short-term program to reduce the total amount of carbon emissions (Cao et al., 2019); thus, the total cost of the investment is 2 characterized as veb (Zhu and He, 2017; Yang et al., 2017). At the end of period, the manufacturer will obtain the revenue 2 min[Db , Qb] pe ( Qb G eb). Therefore, the manufacturer, who acts as a Stackelberg follower, decides the ordering quantity Qb and the level eb of emission reduction, and the expected profit of the manufacturer can be written as: m b
= E min[Db , Qb]
pe ( Qb
G
eb )
wb Qb
veb2 2
(1)
The supplier who acts as a Stackelberg leader determines the wholesale price according to the best response of the manufacturer. cs Qb . We can obtain the following lemma. The expected profits of the supplier can be written as bs = wb Qb Lemma 1. When the emission-dependent manufacturer has sufficient capital, the optimal ordering quantity and the level of emission reduction p + (1 pe wb ) eb)[1 QbN h (QbN eb)] = pe + cs and eb = e are F (QbN , respectively. The optimal wholesale price under the v benchmark is wb = F (QbN eb) pe . It is obvious that the optimal ordering quantity Qb and the level eb of emission reduction are closely related to the unit price of the emission permit pe , the initial emission , and the consumer low-carbon awareness . Additionally, Qb and eb decrease with the wholesale price; however, it will not be influenced by the emission cap G. The benchmark is similar with that of a capital-constrained downstream member who borrows the loan from a competitive bank (Wu et al., 2018). However, the findings of this scenario are different from the results of the benchmark considered in this study. On the one hand, they considered that the upstream member made the emission reduction investment and simultaneously determined the wholesale price and level of the emission reduction. On the other hand, they ignored the impact of the cap-and-trade regulation on the optimal decisions of the supply chain’s members. 4.2. Financing equilibrium under PCG Under PCG, the manufacturer borrows all the capital needed from the bank through the PCG from the supplier. Given the interest rate r1 and credit guarantee , the supplier first charges a wholesale price w1 for the manufacturer. Subsequently, the manufacturer, who acts as a Stackelberg follower, simultaneously, determines the ordering quantity Q1 and the level e1 of emission reduction. We employ the backward induction approach to derive the equilibrium strategies of the supplier and manufacturer. 4.2.1. Manufacturer’s problem under PCG We assume that the manufacturer has no initial capital to execute the ordering decision and make the emission reduction investment (Cao et al., 2019). This assumption can simplify the complex derivation and make the results more obvious in this study. Additionally, it is widely employed in other literature about capital-constrained supply chains (Jing and Seidmann, 2014; Chen, 2015; Jing et al., 2012). Furthermore, we present a numerical experiment with considering initial capital of the manufacturer (as shown in Fig. A.11 in the Appendix A) to justify that the main result continues to hold. The manufacturer borrows the loan
(
L1 = w1 Q1 +
ve12 2
) from a bank, with a coefficient
of credit guarantee from the supplier. When the demand is realized, the
emission-dependent manufacturer buys or sells the emission permits on the emission trading market according to the total carbon emissions ( Q1 e1) and emission cap G allocated by government. At the end of the selling season, the manufacturer obtains the revenue min[D1, Q1] pe ( Q1 e1 G ) and repays the loan and interest L1 (1 + r1) to the bank. However, the manufacturer faces bankruptcy and pays the revenue earned to the bank in the case of a failure to repay the loan and interest. Therefore, the expected profit of the manufacturer under PCG is characterized as follows: m 1
= E min[D1, Q1]
pe ( Q1
e1
G)
w1 Q1 +
ve12 (1 + r1) 2
+
The retail price should exceed the margin cost, that is, [w1 (1 + r1) + pe ] ruptcy threshold of the manufacturer.
(2)
1. Lemma 2 is presented to demonstrate the bank-
Lemma 2. Under PCG, the manufacturer will be able to repay the loan and the interest to the bank, and hence not face bankruptcy, if the realized demand D1 = e1 + variable should satisfy
A1
is no less than A1 = pe ( Q1
e1
(
G ) + w1 Q1 +
e1 .
ve12 2
) (1 + r ) , namely, the minimum realized random 1
The bankruptcy threshold A1 plays an important role in characterizing the profit functions of the supply chain’s members under PCG and in simplifying the analysis procedure (Wang et al., 2019a). Additionally, it also significantly impacts the endogenous interest rate, which we will discuss in sub-section 7.1. 6
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S. Xu and L. Fang
According to Lemma 2, we present the following proposition to show the manufacturer’s optimal decisions of ordering quantity and the level of emission reduction. Proposition 1. Under PCG, given the wholesale price w1, (1) the optimal ordering quantity and the level of emission reduction determined by [w1 (1 + r 1) + pe ] + pe e1 ) = [w1 (1 + r1) + pe ] F (A1 e1 ) and e1 = the manufacturer should satisfy F (Q1 , respectively; (2) the v (1 + r 1 ) optimal ordering quantity Q1 and the level e1 of emission reduction decrease with the wholesale price w1, and (3) the optimal ordering quantity Q1 decreases with the emission cap G. However, the level e1 of emission reduction is not influenced by the emission cap G. The proofs are presented in the Appendix A. Proposition 1 demonstrates that the manufacturer should consider the wholesale price, the unit price of the emission permit, and the initial emission of per unit of the product when determining the optimal ordering quantity. When determining the optimal level of emission reduction, the manufacturer should consider the wholesale price, the coefficient of the emission reduction investment, and the interest rate but without considering the ordering quantity. Proposition 1 also demonstrates a straightforward managerial insight that the manufacturer will make conservative decisions on the optimal ordering quantity and the level of emission reduction, when the supplier charges a higher wholesale price. However, it is interesting to note that the manufacturer will make a radical decision regarding the ordering quantity when the government allocates a lower emission cap. According to Lemma 2, if the government provides a lower emission cap, the bankruptcy probability of the manufacturer will increase. Given the interest rate and wholesale price, the additional bankruptcy risk will be borne by the bank or by the supplier, not by the manufacturer. Therefore, the manufacturer should exploit this factor and place a larger order to maximize own expected profit. 4.2.2. Supplier’s problem under PCG
(
The manufacturer borrows the loan L1 = w1 Q1 +
ve12 2
) from the bank with a PCG from the supplier and, subsequently, pays w Q 1
1
to the supplier to procure an optimal quantity of raw products before processing. Therefore, the supplier can obtain the profit (w1 cs ) Q1 if the revenue of the manufacturer can cover the loan and interest. However, when the manufacturer faces bankruptcy at the end of the selling season, the supplier bears the responsibility of partially repaying the loan [L1 (1 + r1) + pe ( Q1 e1 G ) min(D1, Q1)] to the bank. Therefore, the profit of the supplier is shown as follows: s 1
w1 Q1 w1 Q1
=
cs Q1 cs Q1
E {[L1 (1 + r1) + pe ( Q1
e1
if + min (D1, Q1)]}
G)
A1
e1 if A1
e1 >
0
(3)
The feasible region of the wholesale price determined by the supplier should satisfy the following constraints. First, in the e1 ) of the entire supply chain must exceed the marginal cost (cs + pe ) . As decentralized supply chain, the marginal revenue F (Q1 e1 ) is increasing with w1. The minimum wholesale price should satisfy (Q1 e1 ) is decreasing with w1, we can obtain that F (Q1 e1 ) = (cs + pe ) or Q1 = F 1 (cs + pe ) + e1 . According to Proposition 1, the optimal ordering quantity the equation F (Q1 [w1 (1 + r1) + pe ] F (Q1 e1 ) = [w1 (1 + r1) + pe ] F (A1 e1 ) ; should satisfy thus, we have
Q1 = F F
1
1
cs + pe
cs + pe w1 (1 + r 1) + pe
ve1 2 (1 + r 1 ) 2
+ pe (e1 + G )
w1 (1 + r 1) + pe
+ pe (e1 + G )
ve1 2 (1 + r 1 ) 2
+ e1 . w1 is the smaller root of [w1 (1 + r1) + pe ][F
1 (c s
+ pe ) + e1 ]=
+ e1 . Furthermore, the unit retail price set by the manufacturer should be larger than
the unit cost of procurement and carbon emission 1
[w1 (1 + r1) + pe ], and the wholesale price must obtain
1
pe
(1 + r 1 )
w1 .
= w1
Lemma 3. Under PCG, the feasible region of the wholesale price should be in the range of [w1, w1 ]. The supplier decides the optimal wholesale price to pursuit the maximum profit, we derive the first order of Eq. (3), and have
1 d 1s = dw1 h (Q1 where (w1) = Proposition w1
w1 =
w1 w^1
[w1 (1 + r1) + pe ] Q1 h (A1 e1 )
1 (w1)
+
e1 )
[w1 (1 + r1) + pe ] h (A1
2 (w1)
+
2. Under PCG, if (w1) 1
3 (w1) .
e1 )
The equations of
given
the
best
× [1
(w1)]
1 (w1) ,
2 (w1) ,
response
of
(4)
and
the
3 (w1)
are shown in Proof of Proposition 2.
manufacturer’s
decisions,
. The unique wholesale price w1 is implied by (w1) =
if
(w1 )
if
(w1) < 1 and (w1 ) > 1
1
the
1 (w1)
+
wholesale 2 (w1)
+
price
3 (w1)
is
= 1,.
Proposition 2 demonstrates that, under PCG, the wholesale price determined by the supplier heavily depends on sensitivity coefficient (w1) ; this reflects the sensitivity coefficient of the ordering quantity with respect to the wholesale price w1. If the send s
0 (because (w1) is increasing with w1, see Proof of Proposition 2). The sitivity coefficient (w1) 1, we have (w1) 1 and dw1 1 managemental implication is that the ordering quantity decided by the manufacturer would be very sensitive to the wholesale price. In other words, if the supplier intends to set a slight high wholesale price, the manufacturer would significantly reduce his ordering quantity. The profit of the supplier will also decrease with reduced product sales. Therefore, the supplier should set the lowest wholesale price in order to prevent the manufacturer’s ordering quantity from decreasing significantly. However, when (w1 ) 1, we have
(w1)
1 and
d 1s
dw1
0 . It indicates that the ordering quantity determined by the manufacturer will be little sensitive to the 7
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wholesale price. Thus, the supplier can set the highest wholesale price without worrying about reduced product sales. When (w1) < 1 and (w1 ) > 1, the supplier should set a unique wholesale price to achieve the maximum profit. 4.3. Financing equilibrium under TPCG Under TPCG, the manufacturer obtains the following two loans: one loan is borrowed through TCF for obtaining raw products before processing, and the other loan is borrowed from the bank through PCG to invest in emission reduction. Given the coefficient of credit guarantee and interest rate r2 , the supplier provides a TCF to the manufacture and charges a wholesale price w2 . Subsequently, the manufacturer, who acts as a Stackelberg follower, simultaneously, decides the ordering quantity Q2 and the level e2 of emission reduction. We also employ the backward induction approach to derive the equilibrium strategies of the supplier and manufacturer. 4.3.1. Manufacturer’s problem under TPCG The supplier who acts as a Stackelberg leader decides postponed wholesale price w2 under TPCG. Note that the postponed wholesale price w2 is the only contract variable under trade credit, because it can be consisted of a wholesale cash price w and an associated interest rate rT , i.e. w2 w (1 + rT ) . This assumption is in line with other literature of trade credit in supply chains (e.g. Cao et al. 2019; Jing et al. 2012). Subsequently, the manufacturer determines the ordering quantity Q2 of the raw products and the level of 2 emission reduction e2 . The total cost of emission reduction investment is characterized as ve2 . To execute the emission reduction 2
2
investment, the manufacturer can borrow the loan ve2 from a bank through a PCG from supplier. When the demand is realized, the 2 emission-dependent manufacturer will buy or sell the emission permits on the emission trading market according to the total carbon emissions ( Q2 e2) and emission cap G. At the end of the selling season, if the manufacturer fails to repay to the bank and supplier, the manufacturer will face bankruptcy. Therefore, the expected profit of the manufacturer can be written as: m 2
= E min(D2 , Q2)
pe ( Q2
e2
G)
w2 Q2
ve22 (1 + r2) 2
+
(5)
Lemma 4. Under TPCG, the manufacturer will not face bankruptcy, when the realized demand D2 = e2 +
A2 = w2 Q2 +
ve 22 (1 2
+ r2 )
pe (G + e2
Q2) , namely, the minimum realized random variable should satisfy
is no less than
A2
e2 .
Similar to Lemma 2, the bankruptcy threshold A2 also plays an important role in characterizing the profit functions of the supply chain’s members under TPCG and in simplifying the analysis procedure (Wang et al., 2019a). Additionally, in sub-section 7.2, we will discuss the relationship between the bankruptcy threshold A2 and the endogenous interest rate under TPCG. We have written the following proposition to show the manufacturer’s optimal ordering quantity and the level of emission reduction. Lemma 5. Under TPCG, given the postponed wholesale price w2 , the optimal ordering quantity and the level of emission reduction should [w 2 + pe ] + pe e2 ) = [w2 + pe ] F (A2 e2 ) and e2 = satisfy F (Q2 , respectively. v (1 + r ) 2
Lemma 5 shows that the optimal ordering quantity and the level of emission reduction under TPCG are similar with that under PCG. The optimal ordering quantity determined by the manufacture will be influenced by the wholesale price, the unit price of the emission permit, and the initial emission of per unit of the product. The optimal level of emission reduction decreases with the wholesale price, the coefficient of emission reduction investment, and the interest rate; however, it is independent of the ordering quantity. 4.3.2. Supplier’s problem under TPCG Under TPCG, the manufacturer obtains two loans from the supplier and bank, respectively. At the end of the selling season, if the manufacturer earns sufficient revenue to repay loans to the supplier and bank, then the supplier will also obtain a revenue w2 Q2 . However, if the manufacturer faces bankruptcy, then there will be two situations because of the sequence of the repayment to the supplier and bank. We assume that the bankrupt manufacturer repays to the bank, before repaying the remaining revenue to the e2 G )] of supplier (Yang and Birge, 2018; Ivashina and Iverson, 2014). In the first situation, the revenue [min(D2 , Q2 ) pe ( Q2 the
manufacturer
is
large
enough
to
cover
the
bank’s
ve 2
loan
and
interest
ve2 2 (1 2
+ r2)
(i.e.,
min(D2 , Q2 ) b2 = 22 (1 + r2) + pe ( Q2 e2 G ) ); however, it fails to meet the repayment obligation to the supplier. As a result, the supplier only obtains min(D2 , Q2 ) b2 . In the second situation, the revenue of the manufacturer fails to cover the loan and interest from the bank; hence, the manufacturer uses the entire revenue to repay the bank loan, and the supplier fails to obtain any revenue from the manufacturer. Additionally, the supplier has the responsibility to repay a part of the loan and interest [b2 min(D2 , Q2 )] to the bank. Therefore, the profit of the supplier under TPCG can be written as: s 2
=
w2 Q2 cs Q2 E min(D2 , Q2 ) cs Q2 [b2
b2 cs Q2 Emin (D2 , Q2 )]
if + if A2 if b2
A2 e2 > e2 >
e2 b2 0
e2 (6)
The constraints of the feasible region of the postponed wholesale price under TPCG are similar to that under PCG. First, the 8
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e2 ) of the entire supply chain must exceed the marginal cost (cs + pe ) in the decentralized supply chain. marginal revenue F (Q2 e2 ) increases with w2 . The minimum wholesale price should satisfy the e2 ) decreases with w2 , we can find that F (Q2 As (Q2 e2 ) = (cs + pe ) or Q2 = F 1 (cs + pe ) + e2 . According to Proposition 3, the optimal ordering quantity should equation F (Q2 satisfy F (Q2
e2 ) = [w2 + pe ] F (A2
the smaller root of [w2 + pe ][F
1 (c s
e2 ) ; thus, we have [w2 + pe ] Q2 = F 1
+ pe ) + e2 ] = F
cs + pe
cs + pe
ve2 2 (1 + r 2 ) 2
+ pe (e2 + G )
w 2 + pe
ve2 2 (1 + r 2 ) 2
+ pe (e2 + G )
w 2 + pe
1
+ e2 . w2 is
+ e2 . Furthermore, the unit retail price
set by the manufacturer must exceed the unit cost of procurement and carbon emission 1 wholesale price can be written as w2 = 1 pe .
(w2 + pe ) , and thus the maximum
Lemma 6. Under TPCG, the feasible region of the postponed wholesale price should be in the range of [w2, w2 ]. As the supplier decides the optimal wholesale price to obtain the maximum profit, we derive the first order of Eq. (6) and have
1 d 2s = dw2 h (Q2 where
(w 2 ) =
Proposition w2
w2 =
w2 w^ 2
[w2 + pe ] Q2 h (A2 e2 )
+
3 (w 2 ) .
Under TPCG, (w 2 ) 1
given
1 (w 2 )
3. if
+
e2 )
[w2 + pe ] h (A2
2 (w 2 )
if
(w 2 )
if
(w2) < 1 and
e2 )
× (1
The equations of the
best
(w2 )) 1 (w 2 ) ,
response
of
(7) 2 (w 2 ) ,
and
the
. The unique w2 is implied by
1
3 (w 2 )
are shown in Proof of Proposition 3.
manufacturer’s
(w 2 ) =
1 (w 2 )
decisions,
+
2 (w 2 )
+
the
wholesale
3 (w 2 )
price
is
= 1.
(w 2 ) > 1
Proposition 3 shows that, under TPCG, the wholesale price is heavily dependent on sensitivity coefficient (w1) ; this reflects the sensitivity coefficient of the ordering quantity with respect to the wholesale price w2 . The sensitivity coefficient of the ordering d s
0 . The result quantity under TPCG is similar with that of Proposition 2 under PCG. When (w2 ) 1, we have (w2 ) 1 and dw2 2 indicates that the ordering quantity determined by the manufacturer is little sensitive to the wholesale price. Therefore, to earn more profit, the supplier can set the highest wholesale price without worrying about reduced product sales. However, when (w2 ) 1, we d s
0 . The result reveals that the ordering quantity is very sensitive to the wholesale price. If the supplier have (w2 ) 1 and dw2 2 intends to set a slight high wholesale price, the profit of the supplier will also significantly decrease because of reduced product sales. Therefore, the supplier should set the lowest wholesale price to prevent the manufacturer’s ordering quantity from decreasing significantly. When (w2 ) < 1 and (w2 ) > 1, the supplier will set a unique optimal wholesale price. 5. Comparative analysis To get more managerial insights, we assume that the stochastic factor of demand follows an exponential distribution with mean y, which is similar to Yan et al. (2019). We compare the optimal ordering decision and emission reduction investment under the three situations (i.e., benchmark and two financing schemes), and derive the following Proposition 4. Proposition 4. Assume that the stochastic factor of the demand follows an exponential distribution with mean y. We get that (1) e1 e2 eb and Qb eb and Qb Q1 Q2 if w2 w1 (1 + r1) ; (2) e2 < e1 Q2 < Q1 if w2 > w1 (1 + r1) . Proposition 4 shows that when the supplier charges a lower wholesale price under TPCG (w2 w1 (1 + r1) ), the manufacturer will exhibit willingness to improve the optimal ordering quantity and the level of emission reduction under TPCG than that under PCG. Otherwise, the manufacturer will make the opposite decisions. The reason is that if the supplier expresses willingness to provide a trade credit and sets a lower wholesale price under TPCG, then the manufacturer will face relatively less risk of bankruptcy and make more radical decisions regarding the optimal ordering quantity and the level of emission reduction. It is interesting to note that the capital-constrained manufacturer will invest less in the emission reduction and place a large order under the two financing schemes, when compared to that under the benchmark scenario. The capital-constrained manufacturer has a limited responsibility to repay the loans and interest in the case of bankruptcy. Hence, the manufacturer will make a radical decision regarding the ordering quantity, even if the bankruptcy probability increases. However, the optimal level of emission reduction is heavily dependent on the wholesale price and interest rates. As the supplier charges higher wholesale prices under the two financing schemes than that under the benchmark scenario, the manufacturer will take a more conservative decision regarding the optimal level of emission reduction. Proposition 5. Assume that the stochastic factor of demand follows an exponential distribution with mean y. In this case, there exists a unique coefficient of credit guarantee 0 < < 1 such that the supplier prefers to provide PCG for the manufacturer when 0 < < but < 1. prefers to provide TPCG when Proposition 5 shows that the supplier will set different wholesale prices to induce the manufacturer to choose a PCG or a TPCG financing scheme according to the different coefficients of credit guarantee. There exists a trade-off between the additional revenue and the potential loss if the manufacturer faces bankruptcy. We can obtain the managerial insight that if the coefficient of credit guarantee is within a lower range (0 < < ), the supplier would not provide trade credit and set a wholesale price to induce the manufacturer to borrow all the capital from the bank. The reason is that the supplier will have lesser responsibility to cover the 9
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potential loss from outstanding amount under the PCG financing scheme. Otherwise ( < < 1), the supplier should exhibit willingness to provide trade credit. Note that the supplier undertakes greater risk from the manufacturer under TPCG than that under PCG. However, the risks for the supplier under PCG would become close to that under TPCG, when coefficient of credit guarantee is within a higher range. Then, although the supplier undertakes a bit higher risk under TPCG, he will obtain a risk premium because of providing trade credit for the manufacturer. Therefore, when coefficient of credit guarantee is within a higher range, the supplier should choose to provide trade credit guarantee to maximize own expected profit. In Section 6, we will conduct two numerical experiments to analyze the impact of some important factors under the benchmark, PCG, and TPCG financing schemes. Furthermore, we will discuss the impact of the endogenous interest rates in Section 7. 6. Numerical study To show the robustness of the results in the numerical studies, we assume that the stochastic factor of demand follows two different distributions, that is, an exponential distribution (Yan et al., 2016) and a uniform distribution (Li et al., 2018), and both their means are set as 10. We obtain similar results with the two different distributions. To save space, the results of the impact of coefficient of credit guarantee with uniform distribution are presented in the Appendix A (see Figs. A.1–A.6). The main parameters are set based on real-word industrial data and prior literature. Specifically, the Fiji SME credit guarantee scheme (Asian Development Bank, 2016) was implemented by Reserve Bank of Fiji to promote the local business industry in 2012, and the maximum interest rate was set as 10% per year. Therefore, the interest rates in this study are set as r1 = r2 = 0.1. Additionally, in dairy industry, around 1.5 kg CO2e will be emitted to produce one kg milk (Flysjö, 2012). Thus, the initial carbon emission of per unit product is set as = 1.5 kg. Furthermore, more than 40 countries have been implementing carbon pricing policies, and the range of carbon pricing varies from one to 130 $ per ton (Gomez, 2019). Therefore, the unit price of the emission permit is set as pe = 0.13 $ per kg. Moreover, referring to prior literature of emission-dependent supply chain (Wang et al., 2016), we set the same ratio of cost coefficient of lowcarbon investment to unit production cost (i.e., v cs = 300 ): cs = 0.15 and v = 45. 6.1. The impact of coefficient of credit guarantee and emission cap In this sub-section, we will discuss the impact of the coefficient of credit guarantee and emission cap G on the equilibrium strategies of the supply chain’s members. The consumer low-carbon awareness is set as = 15. We can obtain wb (G = 3) = 0.45, Qb (G = 3) = 6.17, and eb (G = 3) = 0.12 . Apparently, the wholesale price wb (G = 3) = 0.45 under the benchmark scenario is less than that under the two financing schemes (see Fig. 2). Furthermore, Fig. 2 demonstrates that the optimal wholesale price increases with the coefficient of credit guarantee but decreases with the emission cap allocated by the government. The reason is that the supplier bears a higher bankruptcy risk from the manufacturer with a higher coefficient of credit guarantee. Hence, the supplier will raise the wholesale price to balance the bankruptcy risk from the manufacturer. When the government allocates a higher emission cap for the manufacturer, the manufacturer places a relatively small order (see Fig. 3). Therefore, the supplier will decrease the wholesale price to induce the manufacturer to place a larger order. When the coefficient of credit guarantee is within a higher range, the wholesale price w2 set by the supplier under TPCG is lower than w1 (1 + r1) under PCG. It means that when the supplier is required to provide a very high credit guarantee, he will undertake more risk under PCG than that under TPCG. Therefore, the supplier prefers to provide trade credit and sets a lower wholesale price under TPCG. Figs. 3 and 4 respectively show that the optimal ordering quantity and the level of emission reduction decrease with the coefficient of credit guarantee. The reason is that the supplier raises the wholesale price to balance the bankruptcy risk from the manufacturer with a higher coefficient of credit guarantee. In addition, the results demonstrate that the optimal decisions of the
Fig. 2. Optimal wholesale price under different coefficients of credit guarantee and emission caps (Exponential distribution). 10
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Fig. 3. Optimal ordering quantity under different coefficients of credit guarantee and emission caps (Exponential distribution).
Fig. 4. Optimal level of emission reduction under different coefficients of credit guarantee and emission caps (Exponential distribution).
manufacturer heavily depend on the wholesale price determined by the supplier. The optimal ordering quantity and the level of emission reduction under TPCG are higher than that under PCG when w2 w1 (1 + r1) , and the result is consistent with Proposition 4. Furthermore, the optimal ordering quantity Qb (G = 3) = 6.17 under the benchmark scenario is less than that under PCG and TPCG. The reason is that the manufacturer has limited responsibility to repay loans and interest. Hence, the capital-constrained manufacturer will make a radical decision regarding the ordering quantity, when compare to that under the benchmark scenario.
Fig. 5. The profit of supplier under different coefficients of credit guarantee and emission caps (Exponential distribution). 11
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Fig. 6. The profit of the manufacturer under different coefficients of credit guarantee and emission caps (Exponential distribution).
Fig. 5 demonstrates that the profit of the supplier decreases with the coefficient of credit guarantee under the two financing schemes. For the supplier, there exists a trade-off between the additional revenue from TCF and the potential loss when the manufacturer faces bankruptcy. Specifically, if the coefficient of credit guarantee is less than the threshold, the supplier will express reluctance to provide trade credit to the manufacturer. The result is consistent with Proposition 5. Furthermore, it is worth noting that when the government provides a higher emission cap G, the supplier would be easier in a better position to change the decision with regards to providing a trade credit to the manufacturer. The reason is that, with an increase in the emission cap, the capitalconstrained manufacturer would make a more conservative decision regarding the ordering quantity. Consequently, the supplier would face a lower risk from the manufacturer under TPCG; additionally, the supplier would be in a better position to earn additional profit by providing trade credit. Fig. 6 shows that the profit of the manufacturer decreases with the coefficient of credit guarantee under the PCG and TPCG financing schemes. The result indicates that the manufacturer has a lower bargaining power when the coefficient of credit guarantee increases. The manufacturer might be squeezed by the supplier, because the supplier can set a higher wholesale price and earn more risk premiums. Furthermore, it is worth noting that the profit of the manufacturer bm(G = 3) = 1.43 under the benchmark scenario is larger than that under the two financing schemes. The reason is that the capital-constrained manufacturer seeks credit guarantee from the supplier in order to obtain loans from the bank. Therefore, the supplier will determine a higher wholesale price (see Fig. 2) to squeeze the manufacturer. Fig. 7 demonstrates that the tendency of the profit generated by the entire supply chain is similar to that generated by the supplier (see Fig. 5), who acts as a Stackelberg leader and has a greater bargaining power in the supply chain financing (SCF) system. Therefore, the supplier has a significant influence on the profit of the entire supply chain. The profit of the entire supply chain increases with the emission cap G provided by the government under TPCG. The reason is that, given the higher emission cap, the supplier has lower responsibility for bankruptcy risk from the manufacturer. Additionally, the supplier would be in a better position to earn additional profits by providing trade credit. However, when the credit guarantee is within a relatively low range, the profit of the entire supply chain would decrease with the emission cap under PCG. The supplier bears a lower risk from the manufacture under
Fig. 7. The profit of entire supply chain under different coefficients of credit guarantee and emission caps (Exponential distribution). 12
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Fig. 8. Impact of difference between r1 and r2 on unique coefficient r2 = 0.1
of credit guarantee. Note: r12 = r1
r2 , r1 = 0.06, 0.08, 0.1, 0.12, 0.14 , and
PCG than that under TPCG with a lower credit guarantee. Furthermore, the manufacturer determines a higher ordering quantity, and thus the supplier earns a larger profit with lower emission cap under PCG. As we assume that the interest rates are fixed at the same value under PCG and TPCG, we further discuss the impact of the difference between r1 and r2 on the unique coefficient of credit guarantee. As shown in Fig. 8, the unique coefficient of credit guarantee is decreasing when the difference between the interest rates increases. The result indicates that with the increasing of the differences between r1 and r2 , the supplier would be easier in a better position to change the decision with regards to providing a trade credit to the manufacturer. The reason might be that compared with fixed interest rate under TPCG, the supplier undertakes more risk with the increasing of interest rate under PCG. 6.2. Impact of the consumer low-carbon awareness and the unit price of the emission permit In this sub-section, we will discuss the impact of the consumer low-carbon awareness and the unit price of the emission permit on the equilibrium strategies of the supply chain’s members. This section will also discuss their expected profits. The emission cap and the coefficient of credit guarantee are set as G = 3 and = 0.8, respectively. The results of the benchmark are shown in Appendix A (see Table A1). It is interesting to note that the wholesale price increases with the consumer low-carbon awareness under the benchmark scenario but decreases under PCG and TPCG financing schemes (see Fig. 9). As the consumer low-carbon awareness increases, the manufacturer exhibits willingness to procure a large order from the supplier. In this case, the supplier faces a lower bankruptcy risk from the manufacturer and sets a lower wholesale price. Additionally, the wholesale price decreases with the unit price of emission permit under the two financing schemes. The reason might be that the government usually allocates a lower emission cap, and the manufacturer makes a conservative decision on ordering quantity with increasing of unit price of emission permit (see Fig. 10). Therefore,
Fig. 9. Optimal wholesale price under the scenario comprising different consumer low-carbon awareness and unit prices of the emission permit.
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Fig. 10. Optimal ordering quantity under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit.
the supplier charges a lower wholesale price when unit price of emission permit increases. According to Figs. 10 and 11, we find that both the ordering quantity and the level of emission reduction increase with the consumer low-carbon awareness under the benchmark scenario (see Table A1), PCG, and TPCG. This is because the demand increases with the consumer low-carbon awareness, and the manufacturer improves the level of emission reduction and places a larger order. However, the level of emission reduction under the benchmark scenario is larger than that under PCG and TPCG. These results are consistent with Proposition 4. It is worth noting that when the consumer low-carbon awareness is within a relatively low range, an increase in the unit price of emission permit leads to raise the level of emission reduction. Alternatively, the increasing unit price of emission permit will reduce the level of emission reduction. The reason might be that when the consumer low-carbon awareness is within a relatively low range and the unit price is higher, the manufacturer will place a lower order and raise the level of emission reduction to reduce the cost of emission. According to Fig. 12, we find that the profit of the supplier increases with the consumer low-carbon awareness under the benchmark scenario (see Table A1) and two financing schemes. The reason is that the market demand increases with the consumer low-carbon awareness and the manufacturer orders more raw products from the supplier. Furthermore, the profit of the supplier under the TPCG financing scheme is always higher than that under the PCG financing scheme, this is because we assume that the coefficient of PCG is within a higher range (i.e., = 0.8). The result is consistent with Proposition 5 and Fig. 7. Moreover, Fig. 12 demonstrates that the lower the unit prices of emission permit, the higher profit of the supplier. The reason might be that the manufacturer has greater motivation to place a larger order when the unit prices of emission permit decreases. As a result, the supplier can set a higher wholesale price to earn more profit from the manufacturer. Fig. 13 shows that the profit of the manufacture increases with consumer low-carbon awareness under the two financing schemes and the benchmark scenario (see Table A1). The profit of the manufacturer under the benchmark scenario is higher than that under the two financing schemes. The result is consistent within Sub-section 6.1. Furthermore, an increase in the consumer low-carbon awareness motivates the manufacturer to select TPCG. The reason might be that with the increasing of the consumer low-carbon awareness, the bankruptcy risk of the manufacturer decreases. The supplier can obtain more profits from the TCF risk premiums. As a result, the supplier would set the wholesale price to induce the manufacturer to select TPCG, when the consumer low-carbon
Fig. 11. Optimal level of emission reduction under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit. 14
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Fig. 12. The profit of the supplier under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit.
Fig. 13. The profit of the manufacturer under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit.
awareness is within a larger range. Fig. 14 demonstrates that the tendency of the profit generated by the entire supply chain is similar with that generated by the supplier (see Fig. 13) because the supplier acts as a Stackelberg leader in the SCF system. Therefore, the decision of the supplier has a significant influence on the profit of the entire supply chain.
Fig. 14. The profit of entire supply chain under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit. 15
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7. Extension: Endogenous interest rate Apart from the scenario of the fixed interest rate determined by the industrial benchmark, there might exist another scenario that interest rate is decided by the bank. Therefore, we further discuss that the bank acts as a Stackelberg leader and charges two interest rates for the manufacturer under the PCG and TPCG schemes, respectively. We assume that the capital market is perfect, and the bank occupies a competitively priced (Zhou and Groenevelt, 2008; Yan et al., 2016; Bi et al., 2018). Then, we demonstrate the impact of endogenous interest rates on the profits of supplier. 7.1. Bank’s problem under PCG To reduce the potential loss, the bank requires the supplier to provide a credit guarantee for the manufacturer. According to the best responses of the supplier and manufacturer, the bank charges an interest rate r1 for the manufacturer under PCG. At the end of the selling period, if the manufacturer earns enough revenue to repay loan obligation, then the bank will obtain the loan and interest L1 (1 + r1) . However, if the revenue of the manufacturer cannot cover L1 (1 + r1) , then the manufacturer will be e1 G )] to the bank. Additionally, the supplier has the responsibility required to repay the entire revenue [min(D1, Q1 ) pe ( Q1 to repay [A1 min(D1, Q1 )] to the bank because of providing a credit guarantee . As we assume that the bank is in a competitive capital market, the loan L1 is equal to the expected revenue of the bank, as shown below:
L1 = E min{L1 (1 + r1), [min(D1, Q1 )
pe ( Q1
e1
G )] + [A1
(8)
(D1, Q1 )]}
We derive the Proposition 6 to show the optimal decision of the bank. Proposition 6. Under PCG, given the coefficient of credit guarantee and the best response of supplier and manufacturer, the optimal interest rate charged by the bank is characterized as r1 =
A e1 ) 0 1 F (x ) dx . L1
(1
Proposition 6 demonstrates that the optimal interest rate charged by the bank is heavily dependent on the loan size L1 , the coefficient of credit guarantee, and the bankruptcy threshold A1 of the manufacturer. When the supplier provides no credit guarantee, that is, = 0 , the optimal decisions of the capital-constrained manufacturer become identical to that of the manufacturer with sufficient capital. The result is similar to that in the prior literature (Kouvelis and Zhao, 2012; Jing et al., 2012; Chen, 2015). However, when the supplier provides full credit guarantees, that is, = 1, the bank will not face any bankruptcy risk from the manufacturer and charge no interest rate because of a perfectly competitive banking market. 7.2. Bank’s problem under TPCG 2
Under TPCG, the bank provides a loan ve2 to the manufacturer and charges an interest rate r2 based on the best responses of the 2 manufacturer and the supplier. It must be noted that, under TPCG, the bank prioritizes collection of the outstanding amount (Yang and Birge, 2018; Ivashina and ve 2 e2 G ) of the manufacturer cannot cover 22 (1 + r2) , then the Iverson, 2014). Therefore, if the revenue min(D2 , Q2 ) pe ( Q2 manufacturer will use the entire revenue to repay the loan amount and interest. However, the supplier cannot collect any liquidation [b2 min(D2 , Q2 )] to the bank, where from the manufacturer, and has the responsibility to repay
b2 =
ve 2 2 (1 2
+ r2) + pe ( Q2
e2
G).
2
As we assume that the bank is in a competitive capital market, the loan ve2 is equal to the expected revenue of the bank, shown as 2 below:
ve2 2
2
= E min
ve2 2 (1 + r2), min(D2 , Q2 ) 2
pe ( Q2
e2
G ) + [b2
min(D2 , Q2 )]
(9)
We have the following proposition to show the optimal decision of the bank. Proposition 7. Under TPCG, given the coefficient interest rate charged by the bank is r2 =
(1
b ) 02
of credit guarantee and the best response of the supplier and manufacturer, the optimal
e2
ve 2 2 2
F (x ) dx
. 2
Proposition 7 demonstrates that the optimal interest rate under TPCG is heavily dependent on the loan size ve2 and coefficient 2 of credit guarantee. However, different from that under PCG, the optimal interest rate is not directly influenced by the bankrupt threshold A2 of the manufacturer. The reason is that the bank prioritizes the collection of the outstanding amount. As a result, the ve 2 bank only focuses on the expected revenue of the manufacturer for procuring the loan amount and interest 22 (1 + r2) .
16
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Fig. 15. The optimal interest rates under different coefficients of credit guarantee.
7.3. Comparison analysis under endogenous interest rates In this section, we discuss the influence of endogenous interest rates on the profits of supplier under PCG and TPCG. Due to the limited space, we put other results (e.g. the optimal decisions of the supplier and manufacturer) in the Appendix A (see Figs. A.7–A.10). The parameters are set the same as the numerical study in Section 6.1 and G = 3. Fig. 15 demonstrates that the optimal interest rate decreases with coefficient of credit guarantee under PCG, because bank would transfer more risk to the supplier. However, under TPCG, an increase in the credit guarantee leads to raise the interest rate and, 0.5), the supplier has a weaker subsequently, to decrease. When credit guarantee range increases in a relatively low (0 < dominant and would set a higher wholesale price to hedge the risk from the manufacturer (see Fig. A.7). Thus, the manufacturer has to make a more conservative decision on the ordering quantity and level of emission reduction under TPCG (see Figs. A.8 and A.9) The demand might be significantly decreasing with credit guarantee, when the consumers have higher low-carbon awareness and the level of emission reduction is decreasing. Therefore, the bank would set a higher interest rate. Alternatively (0.5 < < 1), the bank would transfer more risk to the supplier. However, the supplier has a greater dominant and would set a lower wholesale price to induce the manufacturer to place a larger order and invest more on emission reduction. Thus, the bank would bear less risk and set a lower interest rate. Especially, when = 1, the bank would transfer the entire risk to the supplier, thus setting no interest rate under PCG and TPCG. According to Fig. 16, it is obvious that the profit of the supplier is heavily dependent on the interest rate decided by the bank. The tendency of the profit generated by the supplier is completely opposite to that of the optimal interest rate under PCG and TPCG. The profit of the supplier increases with the credit guarantee under PCG. The reason is that, with an increase in the credit guarantee, the bank transfers the risk to the supplier and charges a lower interest rate for the manufacturer under PCG. As a result, the supplier may have greater bargaining power on wholesale price to extract the amount from the manufacturer and earn more profit. However, under TPCG, an increase in the credit guarantee leads to a decrease in the profit of the supplier and, subsequently, to an 0.5), the bank charges a higher interest rate, increase. When the credit guarantee is increasing within a relatively low range (0 <
Fig. 16. The profit of the supplier with endogenous interest rates. 17
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and the supplier has a lower bargaining power and bears a higher bankruptcy risk from the manufacturer. As a result, the supplier might set a higher wholesale price (see Fig. A.7) to keep the manufacturer from making a radical decision regarding operations (see Figs. A.8 and A.9). Alternatively (0.5 < < 1), the bank would charge a lower interest rate, and the supplier would have a greater bargaining power and earn more profit from the manufacturer. When = 1, the profit of the supplier under TPCG would be identical to that under PCG because the supplier would face the entire bankruptcy risk from the manufacturer under PCG and TPCG. Fig. 16 also shows that the profit of the supplier under PCG is higher than that under TPCG, when the credit guarantee is within a middle range. However, the supplier exhibits willingness to provide TCF to the manufacturer, when the credit guarantee is within a relatively higher range. Therefore, the main insights of fixed interest rates in Proposition 5 continue to hold. 8. Conclusion This study investigates an SCF system with one supplier and one capital-constrained and emission-dependent manufacturer under the cap-and-trade regulation. We consider PCG and TPCG financing schemes for the manufacturer to execute the decisions regarding the emission reduction investment and the order quantity. We derive the equilibrium strategies of the supply chain’s members under the two financing schemes, and compare with that under a benchmark i.e., the manufacturer has enough capital. Additionally, we relax the assumption of fixed interest rates under the two financing schemes and find that the main insights of fixed interest rates continue to hold. According to the results of the analysis, we find that the optimal ordering quantity and the level of emission reduction will not be influenced by the emission cap under the benchmark scenario. However, under PCG and TPCG, given the wholesale price, the optimal ordering quantity decreases with the emission cap. Furthermore, we find that the wholesale price determined by the supplier is heavily dependent on the sensitivity of the ordering quantity under the two financing schemes. Additionally, the capital-constrained manufacturer will place a large order, but invest less in the emission reduction, under the two financing schemes when compared to that under the benchmark. According to a different credit guarantee, there exists a trade-off for the supplier between the additional revenue and the potential loss when the manufacturer faces bankruptcy. Specifically, if the credit guarantee is within a relatively low range, the supplier will not exhibit willingness to provide TCF to the manufacturer. According to the results of the numerical study, we find that the supplier can obtain more profit under the two financing schemes than that under the benchmark scenario. However, the capital-constrained manufacturer would earn less profit. The reason is that the supplier will squeeze the manufacturer by determining a higher wholesale price. This is because the bank would require the capitalconstrained manufacturer to obtain credit guarantee from the supplier. Additionally, the adoption of PCG or TPCG will bear the same outcome for the manufacturer when the consumer low-carbon awareness is within a relatively low range. However, there are a few limitations in this study that need attention. For example, finance leasing is another popular financing scheme that is considered by the emission-dependent and capital-constrained enterprise. It is possible to derive some managerial insights when the capital-constrained enterprise selects finance leasing or other financing schemes. Furthermore, in practice, the manufacturer expresses reluctance to share information to the upstream supplier. We can consider the information asymmetry between the supply chain’s members to extend this study. CRediT authorship contribution statement Song Xu: Conceptualization, Methodology, Writing - original draft, Investigation. Lei Fang: Supervision, Writing - review & editing, Funding acquisition. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgement This work was supported by the National Natural Science Foundation of China [grant No.71671095]. Appendix A Proof of Lemma 1. Under benchmark, the expected profit of the manufacturer can be written as: m b
= E min(Db , Qb) + pe (G + eb =Qb
Qb 0
eb
Qb )
F (x ) dx + pe (G + eb
Qb )
We first take the first and second derivatives of d2 bm dQb2
=
f (Qb
we can obtain:
veb2 2
wb Qb
wb Qb m b
veb2 2
(A.1)
with respect to the ordering quantity Qb :
eb) , respectively. Then, taking the first and second derivative of d bm deb
= F (Qb
eb) + pe
veb and
d2 bm deb2
=
2f
(Qb 18
eb )
m b
d bm dQb
= F (Qb
eb)
(pe + wb) and
with respect to the level eb of emission reduction,
v , respectively. Furthermore, differentiating
m b
Qb
with
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang 2 m b
respect to the level eb of emission reduction, we can obtain:
eb) > 0 . As
det H (Qb, eb) = vf (Qb definite, and
m b
m b
Qb
eb). Then, we can obtain the determinant
= f (Qb
Qb deb
< 0 and det H (Qb, eb) > 0 , we verify that the Hessian matrix H (Qb, eb) is a negative
is a joint concave in Qb and eb . Then, the optimal ordering quantity and the level of emission reduction should satisfy: p + (1
p
w )
b e F (Qb eb) = pe + wb and eb = e . v eb) pe written and have cs Qb . We plug wb = F (QbN The expected profit of the supplier can be written as: bs = wb Qb s eb) pe cs ) QbN . Then, we take the first derivatives of bs with respect to QbN , shown as b (QbN ) = (F (QbN
d bs
dQbN
= (F (QbN
F (QbN
eb)
eb)[1
pe
cs )
eb) . Therefore, the optimal ordering quantity is Qb = QbN , where should satisfy
QbN f (QbN
eb)] = pe + cs , and the optimal wholesale price is wb = F (QbN
QbN h (QbN
eb )
pe . □
Proof of Proposition 1. Under PCG, the expected profit of the manufacturer can be written as:
{
= E min(~ + e1, Q1)
m 1
=Q1
pe ( Q1
e1
(w Q + ) (1 + r ) + p (G + e 1
ve12 2
1
1
(w Q + ) (1 + r ) }
G)
e
1
=1
Q1 2 m 1 Q12
=
w1 (1 + r1)
f ( Q1
pe
e1 )[h (Q1
e1)
m 1
=
ve1 (1 + r1) + pe + F (Q1
=
v (1 + r1)
e1 2 m 1 e12
= v (1 + r1)
2f
( Q1
Furthermore, differentiating 2 m 1
Q1 e1
= f (Q1
m 1
Q1
(A.3)
e1)
(A.4)
e1)]
with respect to the level e1 of emission reduction, we can obtain:
e1) + [ve1 (1 + r1)
e1 )[ h (Q1 m 1
e1)
e1)
e1) + [ve1 (1 + r1)
F (Q1
(A.2)
with respect to the ordering quantity Q1:
[w1 (1 + r1) + pe ] h (A1
Then, taking the first and second derivatives of
+
1
e1) + [w1 (1 + r1) + pe ] F (A1
[w1 (1 + r1) + pe ]2 f (A1
e1)
= F ( Q1
F (Q1
m 1
ve12 2
Q1 e1 F (x ) dx A1 e1
Q1)
1
(1) We first take the first and second derivatives of m 1
1
pe
pe
] F (A1
]2 f (A1
[ve1 (1 + r1)
e1)
(A.5)
e1) pe
] h (A1
(A.6)
e1)]
with respect to the level e1 of emission reduction, we can obtain:
e1) + [ve1 (1 + r1)
pe
][w1 (1 + r1) + pe ] f (A1
e1)
(A.7)
Then, we can obtain the determinant det H (Q1, e1) :
det H (Q1, e1) = v (1 + r1 ) F (Q1
e1)[h (Q1
e1)
[w1 (1 + r1) + pe ] h (A1
(A.8)
e1)] > 0
2 m 1 Q12
< 0 and det H (Q1, e1) > 0 , we verify that the Hessian matrix H (Q1, e1) is a negative definite, and As and e1. Then, the optimal ordering quantity and the level of emission reduction should satisfy: F (Q1
e1) = [w1 (1 + r1) + pe ] F (A1
F (Q1
e1) = [
ve1 (1 + r1) + pe ] F (A1
m 1
is joint concave in Q1 (A.9)
e1)
(A.10)
e1)
The optimal level e1 of emission reduction can be rewritten as e1 = (2) Taking the derivative of e1 with respect to w1, we have creases with the wholesale price.
de1 dw1
=
v
[w1 (1 + r 1) + pe ] + pe v (1 + r 1 )
.
< 0 . Therefore, the optimal level of emission reduction de-
According to Eq. (A.9), taking the first-order derivation of Q1 with respect to w1, we have:
dQ1 = dw1 If
1 h (Q1
2
v
1 (1 + r1 ) [w1 (1 + r1) + pe ] h (Q1
[w1 (1 + r 1) + pe ] Q1 h (A1 e1 )
e1 )
[w1 (1 + r 1) + pe ] h (A1
e1 )
[w1 (1 + r1) + pe ] Q1 h (A1 e1 )
e1 )
[w1 (1 + r1) + pe ] h (A1
is larger than zero, then we can obtain
Kouvelis and Zhao (2012), Chen and Cai 1 [w1 (1 + r1) + pe ] Q1 h (A1 e1 ) > 1 Q1 h (Q1 e1 ) > 1
(A.11)
e1 ) dQ1 dw1
< 0 . As 1
Q1 h (Q1 ) > 0 has been proofed in
(2011), and Gao et al., (2018), dQ Q1 h (Q1 ) > 0 . Therefore, we can obtain dw1 < 0 . 1
19
we
have
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
(3) Taking the first-order derivation of Q1 with respect to G, we have:
pe h (A1
dQ1 = dG h (Q1
e1 )
e1 )
[w1 (1 + r1) + pe ] h (A1
e1 )
<0
(A.11)
It is obvious that given the wholesale price, e1 will not be influenced by the carbon quota G allocated by the government. In addition, we can also obtain other intuitive result. Under PCG, given the wholesale price the optimal ordering quantity Q1 and the level e1 of emission reduction decrease with the wholesale price w1. de Taking the derivative of e1 with respect to w1, we have dw1 = v < 0 . Therefore, the optimal level of emission reduction decreases 1 with the wholesale price. According to Eq. (A.9), taking the first-order derivation of Q1 with respect to w1, we have:
If
1
1 (1 + r1 ) [w1 (1 + r1) + pe ] h (Q1
2
dQ1 = dw1
v
[w1 (1 + r 1) + pe ] Q1 h (A1 e1 ) e1 ) [w1 (1 + r 1) + pe ] h (A1 e1 )
h (Q1
[w1 (1 + r1) + pe ] Q1 h (A1 e1 )
e1 )
[w1 (1 + r1) + pe ] h (A1
is larger than zero, then we can obtain
Kouvelis and Zhao (2012), Chen and Cai 1 [w1 (1 + r1) + pe ] Q1 h (A1 e1 ) > 1 Q1 h (Q1 e1 ) > 1
(A.12)
e1 ) dQ1 dw1
< 0 . As 1
Q1 h (Q1 ) > 0 has been proofed in
(2011), and Gao et al., (2018), we dQ Q1 h (Q1 ) > 0 . Therefore, we can obtain dw1 < 0 . □
have
1
Proof of Proposition 2. Under PCG, the expected profit of the supplier can be rewritten as: s 1
= (w1 Q1 A1
+
cs Q1 )[1 e1
c1 Q1
cs Q1 )
A1
d 1s
s 1 dQ1
=
dw1
Q1 dw1
=[w1
+
cs
s 1 de1
= where 3 (w1)
(w1) = =
v
We d (A1 e1 ) dw1
e1
+
1
1 (w1)
cs ) [h (Q1 1
have
+
+
e1 )]
e1 )
Additionally, we take the derivative
dQ1 dw1
de
e1 ) dw1 + Q1
[Q1 (1 + r1) + pe ] F (A1
1
3 (w1) ,
× [1 in
which e1 )]
(A.14) 1 (w1)
e1 ) Q 1
0.
Furthermore, e1 )
[w1 (1 + r 1) + pe ] h (A1 e1 ) [1 Q1 h (Q1 e1 )] of 1 [w1 (1 + r 1) + pe ] Q1 h (A1
Q1 h (Q1
[ (1 + r1 ) Q1 h (A1
h (Q1
e1 ) =
<0 , and (A1
dh (Q1 d (Q1
e1 ) =
e1 ) , e1 )
e1 )
h (A1
d (A1 e1 ) dw1
e1 )[Q1
dh (A1 d (A1
= (1 + r1 ) Q1
2 (w1)
as
e1 )
=
Therefore, we can obtain
e1 )
(1 + r1 ) F (A1
[w1 (1 + r1) + pe ] Q1 h (A1 e1 ) Q1 + Q1 h (A2 ) =
with
and
w1
(i.e.,
e1 )] is increasing with w1.
e1 )]
e2 )[Q2 d (Q1 e1 ) dw1
e1 )
[w1 (1 + r 1) + pe ] h (A1
e1 ) + [w1 (1 + r1) + pe ] Q1 h (A1 2
(1 + r 1 ) F (A1 e1 )][1 Q1 h (Q1 e1 )] , 1 [w1 (1 + r 1) + pe ] Q1 h (A1 e1 )
decreases
e1)
e1 )
e2 ] ]] × [1
e1 )][Q1
< 0.
(w1 ) > 0 . Furthermore, we have
20
e1 ] > 0
Q1 h (Q1
1 (1 + r1 ) [w1 (1 + r 1) + pe ] h (Q1
=
e1 ) > (Q1 e1 ) > Q1 and obtain the following inequality We have (A1 numerator> [1 Q1 h (Q1 e1 )] × [ h (Q1 e1 ) + [w1 (1 + r1) + pe ] h (A1 e1 )] Q1 + [ Q1 h (Q1
[1
with respect to w2 . The denominator of the derivative is obviously
e1 ) dQ e1 , Q1 = dw1 , (Q1 e1 ) 1 1 [w1 (1 + r 1) + pe ] Q1 h (A1
h (Q1
(A1
< 0 ), we have that [1
e1 ] ] × [1
[w1 (1 + r1) + pe ][h (A1
e1 ) =
=
(w1 cs )(1 + r 1 ) , [w1 (1 + r 1) + pe ]
.
larger than zero, and the numerator can be written as: numerator=[ h (Q1
e1 )
(w1)]
[w1 (1 + r 1) + pe ] Q1 h (A1
h (Q1
min(D1, Q1 ) dF (x )
w1
[w1 (1 + r 1) + pe ] Q1 h (A1 e1 ) pe (1 + r 1 ) 1 (w1) = [w1 (1 + r 1) + p ]2 > e
= (1 + r1 ) Q1
Q1)
with respect to w1, we have
[w1 (1 + r 1) + pe ] h (A1
1
pe (G + e1
1
s 1
] F (A1
2 (w1)
e1 )
) (1 + r )
(A.13)
[w1 (1 + r1) + pe ] F (A1 pe
ve1 2 2
F (x ) dx
[w1 (1 + r 1) + pe ] Q1 h (A1 e1 ) e1 ) [w1 (1 + r 1) + pe ] h (A1 e1 )
h (Q1
2 (w 1
s 1
+
e1 dw1
[ve1 (1 + r1) 1
1
0
Taking the first derivative of
e1 )]
(w Q
w1 Q1
0
= (w1 Q1
F (A1
.
e1 )]
, where
[w1 (1 + r1) + pe ] Q1 h (A1 e1 ) e1 ) [w1 (1 + r 1) + pe ] h (A1 e1 )
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
3
2Q 1
(w ) =
× >
2Q 1
{
2 (w e1 ) [w1 (1 + r 1) + pe ] Q1 h (A1 e1 )] 1 cs ) Q1 [h (Q1 e1 ) 1 [w1 (1 + r 1) + pe ] Q1 h (A1 vQ1 2
1 cs ) vQ1
{[w1 (1 + r 1) + pe ]Q1 h (A1
e1 )[Q1 e1 ] ] [h (Q1 e1 )] [w1 (1 + r1) + pe ] Q1 h (A1
[1
2 (w
+
1
e1 )} e1 )
[w1 (1 + r 1) + pe ] Q1 h (A1
[h (Q1
1
1
e1 ) [w1 (1 + r 1) + pe ] Q1 h (A1 e1 )] e1 ) [w1 (1 + r 1) + pe ] Q1 h (A1
}
.
2 (w
2 (w e1 ) [w1 (1 + r 1) + pe ] Q1 h (A1 e1 )] c ) e )[Q e ]] [h (Q 1 cs ) Q1 [h (Q1 + vQ1 s [1 [w (1 +1 r ) +1p ] Q1 h (A1 e )] e1 ) 1 [w1 (1 + r 1) + pe ] Q1 h (A1 vQ1 2 1 1 1 1 1 1 e 2 (w h (Q1 e1 ) (1 + r 1 ) 1 cs ) > 1 > 0 e1 )] [1 [w1 (1 + r 1) + pe ] Q1 h (A1 vQ1 2 [w1 (1 + r 1) + pe ]
Therefore, we can obtain that (w1) =
1 (w1)
+
2 (w1)
+
3 (w1)
increases with w1.
When (w1) > 1, we find that (w1 ) > (w1) > (w1) > 1 . In this situation, we can obtain that
d 1s dw1
< 0 , the optimal wholesale d s
price is w1 = w1. In addition, when (w1 ) < 1, we have that (w1) < (w1) < (w1 ) < 1 . In this situation, we can obtain that dw1 > 0 ; the optimal wholesale price is w1 = w1 . When (w1) < 1 and (w1 ) > 1, we have strates that there exists a unique wholesale price w1 when (w1) = 1. □
d 1s
dw1 w = w 1 1
< 0 and
1
d 1s
dw1 w = w 1 1
> 0 , which demon-
Proof of Lemma 5. Under TPCG, the expected profit of the manufacturer can be written as: m 2
{
= E min(D2 , Q2 ) =Q2
pe ( Q2
ve22 (1 2
w 2 Q2
G
+ r2)
e2)
pe ( Q2
G
d =1 dQ2
d 2 2m dQ2 2
=
w2
pe
F (Q 2
ve2 (1 + r2) + pe + F (Q2
d 2 2m = de2 2
2f
v (1 + r2)
(Q 2
Furthermore, differentiating 2
m 2
Q2 e2
= f (Q 2
F (x ) dx
(A.15)
e2)
(A.16) (A.17)
m 2
with respect to the level e2 of emission reduction, we can obtain:
e2) + [ve2 (1 + r2)
e2) + [ve2 (1 + r2)
m 2
+
e2)
Then, taking the first and second derivatives of
d 2m = de2
}
with respect to the ordering quantity Q2 :
m 2
e2) + [w2 + pe ] F (A2
e2) + [w2 + pe ]2 f (A2
f (Q 2
+ r2)
Q 2 e2 A2 e 2
e2)
We first take the first and second derivatives of m 2
ve 22 (1 2
w2 Q2
pe
] F (A2
]2 f (A2
pe
e2)
(A.18)
e2)
(A.19)
with respect to the level e2 of emission reduction, we can obtain:
Q2
e2 ) + [w2 + pe ][ve2 (1 + r2)
pe
] f (A2
e2)
(A.20)
Then, we can obtain the determinant det H (Q2, e2) :
det H (Q2, e2) = v (1 + r2 ) F (Q2
e2)[h (Q2
e2 )
[w2 + pe ] h (A2
e2 )] > 0
d 2m
As dQ < 0 and det H (Q2, e2) > 0 , we verify that the Hessian matrix H (Q2 , e2) is a negative definite, and 2 and e2 . Then, the optimal ordering quantity and the level of emission reduction should satisfy:
F (Q 2
e2 ) = [w2 + pe ] F (A2
m 2
is joint concave in Q2 (A.21)
e2 )
[w2 + pe ] + pe
e2 =
(A.22)
v (1 + r2 )
Proof of Proposition 3. The expected profit of the supplier under TPCG can be rewritten as: s 2
= (w2 Q2
A2
cs Q2 )
b2
Taking the first derivative of d 2s dw 2
=
s 2 dQ2 Q2 dw 2
=[w2
+
cs
s 2 de 2 e2 dw 2
As
dQ2 dw 2
=
v (1 + r 2 )
s 2,
F (x ) dx
pe
b2
e2
0
F (x ) dx
(A.23)
we have
s 2
w2
(w2 + pe ) F (A2
+[ [ve2 (1 + r2 ) 2
+
e2 e2
e2 ) + (1
] F (A2
1 1 [w 2 + pe ] h (Q2
e2 ) + (1
[w 2 + pe ] Q2 h (A2 e2 )
) pe F (b2
e2 )]
)[ve2 (1 + r2) e2 )
[w 2 + pe ] h (A2
e2 )
and
de2 dw 2
21
=
dQ2 dw 2
pe v (1 + r 2 )
] F ( b2 ,
d 2s dw 2
de
e2 )] dw2 + Q2 F (A2 2
can be rewritten as
e2 )
(A.24)
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
1 d 2s = dw2 h (Q2 where 3 (w 2 )
(w 2 ) = =
2 (w
2
[w2 + pe ] Q2 h (A2 e2 )
1 (w 2 )
cs )
Similar to (w2) = 1 (w2 ) +
+
2 (w 2 )
w 2 2 (1 ) F (b 2 v (1 + r 2 )
2
e2 )
[w2 + pe ] h (A2
+
× (1
in which
3 (w 2 )
e2 ) [h (Q2 [1
e2 )
e2 )
1 (w 2 )
[w 2 + pe ] h (A2
[w 2 + pe ] Q2 h (A2
(w1) = proofing (w2 ) + 3 (w2 ) > 0 .
1
(w2 ))
(w1) +
=
e2 )]
e2 )]
2
(w 2
(w1) +
(A.25) cs ) + (1
) pe F (b2
e2 )
[w 2 + pe ]
.
in
(w1) > 0
3
,
2 (w 2 )
=
[1 Q2 h (Q2 e2 )] F (A2 e2 ) [1 [w 2 + pe ] Q2 h (A2 e 2 )]
Proposition
2,
we
also
and have
d s
When (w2 ) > 1, we have that (w2 ) > (w2) > (w2 ) > 1 . In this situation, we can obtain that dw2 < 0 , and the optimal 2 wholesale price is w2 = w2 . Additionally, when (w2 ) < 1, we have that (w2 ) < (w2 ) < (w2 ) < 1 . In this situation, we can obtain that d 2s dw 2
w2= w 2
d 2s
> 0 ; the optimal wholesale price is w2 = w2 . When
dw 2
(w2 ) < 1 and
> 0 , that demonstrates that there exists an unique wholesale price w2 when
(w2 ) > 1, we have
d 2s
dw 2 w = w 2 2
< 0 and
(w1) = 1. □
Proof of Proposition 4. We employ the proof by contradiction to indicate wb < w1 (1 + r1) . The minimum wholesale price under PCG e1 ) w1= w1 (QbN eb) . We should satisfy F (Q1 e1 ) w1= w1 = (cs + pe ) (wb + pe ) = F (QbN eb) . Therefore, we have (Q1 e1 ) w1= w1 = Q1 (cs + pe ). assume wb w1 (1 + r1) . We can rewrite the equation of minimum wholesale price under PCG as Q1 F (Q1 Taking the first order of the equation with respect to Q1, we have d (Q1 F (Q1 e1)) dQ1 = F (Q1 e1 )[1 Q1 h (Q1 e1 )] w1= w1 = cs + pe . The optimal ordering quantity under benchmark can be written as F (QbN eb)[1 QbN h (QbN eb)] = pe + cs . eb)[1 QbN h (QbN eb)]. As we assume wb w1 (1 + r1) , we e1 )[1 Q1 h (Q1 e1 )] w1= w1 = F (QbN Therefore, we have F (Q1 can further obtain However, the result contradicts with that F (Q1 e1 ) w1= w1 > F (QbN eb ) . F (Q1 e1 ) w1= w1 = (cs + pe ) (wb + pe ) = F (QbN eb ) . Therefore, we can obtain wb < w1 (1 + r1) . The proof of wb < w2 is similar with that of wb < w1 (1 + r1) , and we omit here. Finally, we can obtain eb > e1 and eb > e2 . Q1 . Similar to Jing et al., (2012), we can rewrite the equation of the optimal ordering quantity Then, we intend to proof Qb e1 ) is a unimodal function in Q1 F (Q1 e1 ) = Q1 [w1 (1 + r1) + pe ] F (A1 e1 ) . As the assumption of failure rate, Q1 F (Q1 [D1, D1]. Thus, there exist a unique Q1, and Q1 F (Q1 e1 ) is increasing in [D1, Q1], but decreasing in [Q1, D1]. As d [Q1 F (Q1 e1)] dQ1 = F (Q1 e1 )[1 Q1 h (Q1 e1)], we have [1 Q1 h (Q1 e1)] = 0 Furthermore, when w1 (1 + r1) + pe = 1, 1 pe G = 0 based on assumption of the optimal ordering quantity with exponential distribution we have 2 ve1 2 (1 + r1) pe e1
Q1 [1
(Q1
1
y ln[w1 (1 + r1) + pe ] + 2 ve1 2 (1 + r1)
[w1 (1 + r1) + pe ]] =
e1 ) = Q1 [w1 (1 + r1) + pe ] F [Q1 [w1 (1 + r1) + pe ]
dQ1 dw1 < 0 ,
we
have
[1
QbN h (QbN
eb)] =
e1 ] pe + cs
F (QbN
pe e1
pe G ,
and
then
obtain
e1)] = 0
we,
Q1 F
. Therefore, we have Q1 = Q1 = Q1 when w1 (1 + r1) + pe = 1. As
eb)
=0 and [1
Q1 (w1 ) h (Q1 (w1)
and
thus
Q2 is similar with that of Qb Q1 , and we omit here. Q1 = Q1 (w1) QbN . The proof of Qb [w1 (1 + r 1) + pe ] + pe [w 2 + pe ] + pe e = According to e1 = and , we consider two scenarios w2 w1 (1 + r1) and w2 > w1 (1 + r1) 2 v (1 + r 1 ) v (1 + r 2 ) to discuss the comparison of the optimal decisions of the manufacturer under different financing schemes. If w2 w1 (1 + r1) , we have e1 e2 because we assume r1 = r2 . Then, we intend to verify Q2 > Q1 . We assume that the stochastic factor of demand follows an exponential distribution with mean y. The optimal ordering quantities under PCG and TPCG can be rewritten as 1 1 Q1 [1 [w1 (1 + r1) + pe ]] = y ln[w1 (1 + r1) + pe ] + 2 ve1 2 (1 + r1) pe e1 pe G and Q2 [1 (w2 + pe )] = y ln[w2 + pe ] + 2 ve2 2 (1 + r2) 1 ve 2 (1 2 2
+ r2)
pe e2
pe e2 .
pe G , respectively. When w2 = w1 (1 + r1) = w2 , we transfer to compare The
derivative
of
1 ve 2 (1 2 2
+ r1)
pe e2
with
pe e1
pe G
respect
to
e2
is
larger
1 ve 2 (1 2 1
+ r1)
than
zero,
pe e1
that
and
is,
1 v (1 + r2 ) e2 pe = [w2 + pe ] = v (1 + r1 ) e1 pe > 0 . We find that 2 vx 2 (1 + r1) pe x is increasing with x . As e1 < e2 , we can Q 2 ( w 2 ) > Q1 . obtain Q2 pe = [w2 + pe ] = v (1 + r1 ) e1 pe . The derivative of When w2 = w1 (1 + r1) = w2 , we have v (1 + r2 ) e2 1 ve 2 (1 + r2) pe e2 pe G e2 with respect to e2 is less than zero, that is, ve2 (1 + r2) pe = [w2 + pe ] < 0 . Therefore, we 2 2
pe G e2 < 2 ve1 2 (1 + r1) can obtain 2 ve2 2 (1 + r2) pe e2 that of w2 w1 (1 + r1) , and we omit here. □ 1
1
e1 . The proof of scenario w2 > w1 (1 + r1) is similar to
d 2s (w 2 , )
b2
= 0 d we intend to proof Case 1. s 2
e2
F (x ) dx < 0 . Therefore, both s s = 0 and 1 ( ) > 2 ( ) when
s 1 (w1 , s 2( ) >
d 1s (w1 , )
e1
F (x ) dx < 0 and
) and 2s (w1 , ) are monotonically decreasing with s = 1. □ 1 ( ) when
[0, 1]. Then,
Proof of Proposition 5. By the Envelope Theorem (Varian, 1992, p. 490), we have
d
= 0 . The profit of the supplier under PCG and TPCG can be rewritten as
= (w2 Q2 cs Q2 ) mean y, we have
A2
b2
e2 e2
A1
=
0
s 1
= (w1 Q1
cs Q1 ) and
F (x ) dx , respectively. As the stochastic factor of demand follows an exponential distribution with
22
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang s 12
s 1
=
s 2
=(w1
cs ) Q1
=cs (Q2
A2 e2 b2 e2
As x > ln x , we have
) when
s 2(
) >
Case 2.
A2 e2 b2 e2
cs ) Q2 + A2
Q1 ) + w1 Q1
> w 1 Q1
s 1 (
(w 2
e2
w1 Q1 y
F (x ) dx = y
w1 Q1 y
e
b2
y
F (x ) dx
e2
b2
e2
F (x ) dx
A2
e
A2
+e
y
e2
y
e2
e
> ln
= 0.
(
b2
y
e2
(A.26)
w1 Q1 y
)+
b2
e2
ln 1
y
e
= 1. The profits of the supplier under PCG and TPCG can be rewritten as A2
w 2 Q2 y
s 1
> 0 . Therefore, we can obtain
= (w1 Q1
A1
cs Q1 )
0
e2
e1
F (x ) dx
= (w2 Q2 cs Q2 ) F (x ) dx , respectively. We first employ the proof by contradiction to indicate w1 (1 + r1) w2 and 0 s s = 1, and then proof = 1. We have when We assume w1 (1 + r1) w2 when 2 ( = 1) > 1 ( = 1) . s Q2 1 s s s Q1 Q2 <0 = F (Q1 e1 ) cs pe and because and 2 (Q 2 w 2 ) 2 (Q 2 w 2 ) 1 (Q1 w1 ) , w Q s 2
2
s
s 2 (Q2
s 1 (Q1
w2 )
w1 ) = (w 2
s 2(
= 1) > 1
2
s
= (w2 + pe ) F (A2
Q2
and
s 2 (Q 2
(1 + r2 ) A1 0
e1
pe x
w2 )
s 2 (Q1
e2
F (x ) dx
0
s 2 (Q 2
pe G .
pe e2
e2 )
cs
Given
pe = F (Q2
w2 ) = [w1 (1 + r1)
the
e2 )
cs ] Q1
0
F (x ) dx . Therefore, we can obtain
s 2 (Q 2
w2 )
s 2
F (x ) dx = w1 Q2 r1 > 0
= (w2 Q2
wholesale
w2)
w2 when A2
cs Q2 )
e2
0
price
(w1 (1 + r 1) + pe ) Q1 + 12 ve2 2 (1 + r 2) pe e2
s 2 (Q 2
e1
0
w2 ,
(A.27)
= 1. Then, we
F (x ) dx , where we
can
pe > 0 . When w2 = w1 (1 + r1) = w2 , we have Q2 (w2 )
cs
x is decreasing with x, we can obtain that
pe G
A1
cs ) Q1
w1 ) . Therefore, we have w1 (1 + r1)
s 1 (Q1
w2 )
(w 1
= 1) . Similar to Cao et al. (2019), we first discuss
s 1 (
A2 = (w2 + pe ) Q2 + 2 ve2 2 (1 + r2 )
obtain
A2
cs ) Q2
The result the result contradicts with that
intend to proof
1
pe > 0 hold. However, when w1 (1 + r1) = w 2 , we have Q1 = Q2 (w 2 ), e1 = e2 (w 2 ), and
> 0 and Q2 = F (Q2 e2 ) cs 2 A1 = A2 (w 2 ) , thus obtaining
pe G
e2
F (x ) dx .
(w1 (1 + r 1) + pe ) Q1 + 12 ve 2 2 (1 + r 2) pe e 2
0 s 1 (Q1
w1 ) and
s 2(
) >
s 1 (
pe G
) when
e2
As
Q1 1 vx 2 2
F (x ) dx is less than
= 1.
Proof of Proposition 6. Under PCG, the equation of the bank’s problem is shown as follows:
L1 = E min{L1 (1 + r1), [min(~ + e1 , Q1 ) =
+ A1
L1 (1 + r1 ) dF (x ) +
e1
= L1 (1 + r1)
(1
A1
)
e1
0
A1
e1
0
pe ( Q1
(1
e1
G )] + [A1
) D1 + A1
pe ( Q1
e1
min(~ + e1 , Q1 )]} G ) dF (x )
F (x ) dx
(A.28)
Therefore, the optimal interest rate charged by the bank under PCG can be written as r1 =
A ) 0 1
(1
L1
e1 F (x ) dx
□
Proof of Proposition 7. Under TPCG, the equation of the bank’s problem is shown as follows: ve2 2 2
= Emin =
=
b2 0 ve2 2
2
{
e2
ve2 2 (1 2
(1
(1 + r2)
+ r2 ), min (~ + e2 , Q2 ) ) D2 (1
pe ( Q2 )
b2 0
e2 e2
pe ( Q2
e2
G ) + b2 dF (x ) +
G ) + [b2 + b2 e2
ve2 2 (1 2
min (~ + e2 , Q2 )]
}
+ r2 ) dF (x )
F (x ) dx
(A.29)
Therefore, under TPCG, the optimal interest rate charged by the bank can be written as r2 =
(1
b e2 ) 02 F (x ) dx . ve 2 2 2
□
Figs. A.1-A.6 show the impact of coefficient of credit guarantee on the optimal decisions and profits of the supply chain members with uniform distribution. The results are similar with those of exponential distribution, as shown in main text. Figs. A.7–A.9 demonstrate the optimal decisions of the supplier and manufacturer with endogenous interest rates. Fig. A.10 shows the profits of the manufacturer with endogenous interest rates under PCG and TPCG. Compared with Proposition 5 and Fig. 5, Fig. A.11 demonstrates that the main result continues to hold, thus justifying the assumption of no initial capital of the manufacturer (see Table A1).
23
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
Fig. A1. Optimal wholesale price under different coefficients of credit guarantee and emission caps (Uniform distribution).
Fig. A2. Optimal ordering quantity under different coefficients of credit guarantee and emission caps (Uniform distribution).
Fig. A3. Optimal level of emission reduction under different coefficients of credit guarantee and emission caps (Uniform distribution).
24
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
Fig. A4. The profit of supplier under different coefficients of credit guarantee and emission caps (Uniform distribution).
Fig. A5. The profit of the manufacturer under different coefficients of credit guarantee and emission caps (Uniform distribution).
Fig. A6. The profit of entire supply chain under different coefficients of credit guarantee and emission caps (Uniform distribution).
25
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
Fig. A7. The optimal wholesale price with endogenous interest rates.
Fig. A8. The optimal ordering quantity with endogenous interest rates.
Fig. A9. The optimal level of emission reduction with endogenous interest rates.
26
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
Fig. A10. The profit of manufacturer with endogenous interest rates.
Fig. A11. The profit of supplier with considering the manufacturer’s insufficient initial capital (set as 1). Table A1 The results of the benchmark under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit. Consumer low-carbon awareness
Wholesale price
Ordering quantity
Level of emission reduction
Profit of the supplier
Profit of the manufacturer
Profit of the entire supply chain
10 ( pe = 0.13 ) 12 14 16 18 20
0.4643 0.4654 0.4664 0.4674 0.4683 0.4692
5.9882 6.3063 6.6831 7.1184 7.6125 8.1640
0.0786 0.0934 0.1082 0.1229 0.1376 0.1521
1.1548 1.2081 1.2710 1.3435 1.4256 1.5169
1.8826 1.9891 2.1147 2.2594 2.4232 2.6060
3.0374 3.1972 3.3857 3.6029 3.8488 4.1229
10 ( pe = 0.12 ) 12 14 16 18 20
0.4681 0.4694 0.4706 0.4718 0.4730 0.4741
6.1164 6.4411 6.8250 7.2686 7.7724 8.3355
0.0809 0.0962 0.1114 0.1265 0.1415 0.1564
1.1854 1.2412 1.3068 1.3824 1.4681 1.5635
1.9459 2.0571 2.1882 2.3393 2.5104 2.7014
3.1313 3.2983 3.4950 3.7217 3.9784 4.2649
10 ( pe = 0.11) 12 14 16 18 20
0.4719 0.4733 0.4748 0.4762 0.4776 0.4789
6.2467 6.5775 6.9685 7.4211 7.9339 8.5092
0.0831 0.0989 0.1145 0.1300 0.1454 0.1607
1.2182 1.2763 1.3447 1.4237 1.5128 1.6127
2.0106 2.1264 2.2632 2.4208 2.5993 2.7987
3.2287 3.4028 3.6079 3.8445 4.1121 4.4114
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References Agster, R., Eisinge, F., Cochu, A., 2016. Enabling SME access to finance for sustainable consumption and production in Asia: An overview of finance trends and barriers in China. Available at: http://www.switch-asia.eu/fileadmin/user_upload/Publications/2016/Green_Fina nce_Study_-_2016_-_China.pdf (Accessed date: December 10th, 2019). Asian Development Bank, 2016. Credit guarantees challenging their role in improving access to finance in the Pacific region. Available at: https://www.adb.org/sites/ default/files/publication/ 203871/credit-guarantees.pdf (Accessed date: January 20th, 2020). Bi, G., Fei, Y., Yuan, X., Wang, D., 2018. Joint operational and financial collaboration in a capital-constrained supply chain under manufacturer collateral. Asia-Pac. J. Oper. Res. https://doi.org/10.1142/S0217595918500100. Cai, G., Chen, X., Xiao, Z., 2014. The roles of bank and trade credits: Theoretical analysis and empirical evidence. Prod. Oper. Manage. 23 (4), 583–598. Cao, E., Yu, M., 2018. Trade credit financing and coordination for an emission-dependent supply chain. Comput. Ind. Eng. 119, 50–62. Cao, E., Du, L., Ruan, J., 2019. Financing preferences and performance for an emission-dependent supply chain: Supplier vs. bank. Int. J. Prod. Econ. 208, 383–399. Chan, H.L., Choi, T.M., Cai, Y.J., Shen, B., 2018. Environmental taxes in newsvendor supply chains: A mean-downside-risk analysis. IEEE Transactions on Systems, Man, and Cybernetics: Systems. https://doi.org/10.1109/TSMC.2018.2870881. Chen, X., Cai, G.G., 2011. Joint logistics and financial services by a 3PL firm. Eur. J. Oper. Res. 214 (3), 579–587. Chen, X., Wang, A., 2012. Trade credit contract with limited liability in the supply chain with budget constraints. Ann. Oper. Res. 196 (1), 153–165. Chen, X., 2015. A model of trade credit in a capital-constrained distribution channel. Int. J. Prod. Econ. 159, 347–357. China Green Times. (2019). Sihui provides a green financing–“forestry supply chain financing”. Available at: http://www.forestry.gov.cn/xdly/5201/20190710/ 100817827844799.html, in Chinese. (Accessed date: December 10th, 2019). Dada, M., Hu, Q., 2008. Financing newsvendor inventory. Operations Research Letters 36 (5), 569–573. Daryanto, Y., Wee, H.M., Astanti, R.D., 2019. Three-echelon supply chain model considering carbon emission and item deterioration. Transport. Res. Part E: Logist. Transport. Rev. 122, 368–383. Devalkar, S.K., Krishnan, H., 2019. The impact of working capital financing costs on the efficiency of trade credit. Prod. Oper. Manage. 28 (4), 878–889. Dobos, I., 2005. The effects of emission trading on production and inventories in the Arrow-Karlin model. Int. J. Prod. Econ. 93, 301–308. Du, S., Ma, F., Fu, Z., Zhu, L., Zhang, J., 2015. Game-theoretic analysis for an emission-dependent supply chain in a ‘cap-and-trade’ system. Ann. Oper. Res. 228 (1), 135–149. Du, S., Zhu, L., Liang, L., Ma, F., 2013. Emission-dependent supply chain and environment-policy-making in the ‘cap-and-trade’ system. Energy Policy 57, 61–67. Flysjö, A., 2012. Greenhouse gas emissions in milk and dairy product chains: improving the carbon footprint of dairy products. Department of Agroecology, Aarhus University PhD Thesis. Fujitsu, 2012. The move towards a low carbon society. Available at: https://www.fujitsu.com/ie/Images/low-carbon-society.pdf (accessed date: December 10th, 2019). Gao, G.X., Fan, Z.P., Fang, X., Lim, Y.F., 2018. Optimal Stackelberg strategies for financing a supply chain through online peer-to-peer lending. Eur. J. Oper. Res. 267 (2), 585–597. Glock, C.H., Kim, T., 2015. Coordinating a supply chain with a heterogeneous vehicle fleet under greenhouse gas emissions. Int. J. Logist. Manage. 26 (3), 494–516. Gomez, J., 2019. Carbon tax & carbon pricing – 15-minute guide. Available at: https://ecochain.com/knowledge/carbon-tax-carbon-pricing-fundamentals/ (accessed date: January 20th, 2020). Hua, G.W., Cheng, T.C.E., Wang, S.Y., 2011. Managing carbon footprints in inventory management. Int. J. Prod. Econ. 132 (2), 178–185. Ivashina, V., Iverson, B., 2014. Trade creditors’ behavior in bankruptcy. Working paper. Harvard Business School, Boston. Jaber, M.Y., Glock, C.H., El Saadany, A.M., 2013. Supply chain coordination with emissions reduction incentives. Int. J. Prod. Res. 51 (1), 69–82. Jing, B., Seidmann, A., 2014. Finance sourcing in a supply chain. Decis. Support Syst. 58, 15–20. Jing, B., Chen, X.F., Cai, G.S., 2012. Equilibrium financing in a distribution channel with capital constraint. Prod. Oper. Manage. 21 (6), 1090–1101. Kouvelis, P., Zhao, W., 2011. The newsvendor problem and price-only contract when bankruptcy costs exist. Prod. Oper. Manage. 20 (6), 921–936. Kouvelis, P., Zhao, W.H., 2012. Financing the newsvendor: supplier vs. bank, and the structure of optimal trade credit contracts. Oper. Res. 60 (3), 566–580. Kouvelis, P., Zhao, W., 2017. Who should finance the supply chain? Impact of credit ratings on supply chain decisions. Manuf. Serv. Oper. Manage. 20 (1), 19–35. Lee, K.H., 2009. Why and how to adopt green management into business organizations? The case study of Korean SMEs in manufacturing industry. Manag. Decis. 47 (7), 1101–1121. Lee, H.H., Zhou, J., Wang, J., 2018. Trade credit financing under competition and its impact on firm performance in supply chains. Manuf. Serv. Oper. Manage. 20 (1), 36–52. Li, B., An, S.M., Song, D.P., 2018. Selection of financing strategies with a risk-averse supplier in a capital-constrained supply chain. Transport. Res. Part E: Logist. Transport. Rev. 118, 163–183. Li, S., Gu, M., 2012. The effect of emission permit trading with banking on firm's production-inventory strategies. Int. J. Prod. Econ. 137 (2), 304–308. Li, X.R., Yu, C.W., Xu, Z., Luo, F.J., Dong, Z.Y., Wong, K.P., 2013a. A multimarket decision-making framework for GENCO considering emission trading scheme. IEEE Trans. Power Syst. 28 (4), 4099–4108. Li, X.R., Yu, C.W., Luo, F.J., Ren, S.Y., Dong, Z.Y., Wong, K.P., 2013b. Impacts of emission trading schemes on gencos’ decision making under multimarket environment. Electr. Power Syst. Res. 95, 257–267. Li, X., Li, Y., 2016. Chain-to-chain competition on product sustainability. J. Cleaner Prod. 112, 2058–2065. Li, X., Shi, D., Li, Y., Zhen, X., 2017. Impact of carbon regulations on the supply chain with carbon reduction effort. IEEE Trans. Syst. Man Cybern.: Syst. https://doi. org/10.1109/TSMC.2017.2741670. Meath, C., Linnenluecke, M., Griffiths, A., 2016. Barriers and motivators to the adoption of energy savings measures for small-and medium-sized enterprises (SMEs): the case of the ClimateSmart Business Cluster program. J. Cleaner Prod. 112, 3597–3604. Nace, T., 2017. China shuts down tens of thousands of factories in widespread pollution crackdown. Available at: https://www.forbes.com/sites/trevornace/2017/10/ 24/china-shuts-do wn-tens-of-thousands-of-factories-in-widespread-pollution-crackdown/#17414d4a4666 (accessed date: December 10th, 2019). Ni, J., Chu, L.K., Li, Q., 2017. Capacity decisions with debt financing: The effects of agency problem. Eur. J. Oper. Res. 261 (3), 1158–1169. Sohu Finance, 2013. Industrial and Commercial Bank of China has provided 100 billion Yuan for small and medium-sized enterprises to invest in energy conservation and emission reduction. Available at: http://money.sohu.com/20130726/n382675397.shtml, in Chinese (accessed date: December 10th, 2019). Tang, L., Wu, J., Yu, L., Bao, Q., 2015. Carbon emissions trading scheme exploration in China: a multi-agent-based model. Energy Policy 81, 152–169. Tsao, Y.C., 2017. Managing default risk under trade credit: Who should implement Big-Data analytics in supply chains? Transport. Res. Part E: Logist. Transport. Rev. 106, 276–293. Varian, H.R., 1992. Microeconomic Analysis, third ed. W. W. Norton and Company, New York. Wang, Q., Zhao, D., He, L., 2016. Contracting emission reduction for supply chains considering market low-carbon preference. J. Cleaner Prod. 120, 72–84. Wang, C., Fan, X., Yin, Z., 2019a. Financing online retailers: Bank vs. Electronic business platform, equilibrium, and coordinating strategy. Eur. J. Oper. Res. https:// doi.org/10.1016/j.ejor.2019.01.009. Wang, F., Yang, X., Zhuo, X., Xiong, M., 2019b. Joint logistics and financial services by a 3PL firm: Effects of risk preference and demand volatility. Transport. Res. Part E: Logist. Transport. Rev. 130, 312–328. Wu, D.D., Yang, L., Olson, D.L., 2018. Green supply chain management under capital constraint. Int. J. Prod. Econ. https://doi.org/10.1016/j.ijpe.2018.09.016. Wu, D., Zhang, B., Baron, O., 2019. A trade credit model with asymmetric competing retailers. Prod. Oper. Manage. 28 (1), 206–231. Xia, L., Guo, T., Qin, J., Yue, X., Zhu, N., 2018. Carbon emission reduction and pricing policies of a supply chain considering reciprocal preferences in cap-and-trade system. Ann. Oper. Res. 268 (1–2), 149–175. Xu, J., Chen, Y., Bai, Q., 2016. A two-echelon sustainable supply chain coordination under cap-and-trade regulation. J. Cleaner Prod. 135, 42–56.
28
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
Xu, X., Zhang, W., He, P., Xu, X., 2017a. Production and pricing problems in make-to-order supply chain with cap-and-trade regulation. Omega 66, 248–257. Xu, X., He, P., Xu, H., Zhang, Q., 2017b. Supply chain coordination with green technology under cap-and-trade regulation. Int. J. Prod. Econ. 183, 433–442. Yan, N., He, X., Liu, Y., 2018. Financing the capital-constrained supply chain with loss aversion: supplier finance vs. supplier investment. Omega. https://doi.org/10. 1016/j.omega.2018.08.003. Yan, N., Sun, B., Zhang, H., Liu, C., 2016. A partial credit guarantee contract in a capital-constrained supply chain: financing equilibrium and coordinating strategy. Int. J. Prod. Econ. 173, 122–133. Yang, L., Zhang, Q., Ji, J., 2017. Pricing and carbon emission reduction decisions in supply chains with vertical and horizontal cooperation. Int. J. Prod. Econ. 191, 286–297. Yang, S.A., Birge, J.R., 2018. Trade credit, risk sharing, and inventory financing portfolios. Manage. Sci. 64 (8), 3667–3689. Zhang, B., Wu, D.D., Liang, L., 2018. Trade credit model with customer balking and asymmetric market information. Transport. Res. Part E: Logist. Transport. Rev. 110, 31–46. Zhou, J., Groenevelt, H., 2008. Impacts of financial collaboration in a three-party supply chain. The Simon School, University of Rochester Working Paper. Zhu, W., He, Y., 2017. Green product design in supply chains under competition. Eur. J. Oper. Res. 258 (1), 165–180.
29
Contents lists available at ScienceDirect
Transportation Research Part E journal homepage: www.elsevier.com/locate/tre
Partial credit guarantee and trade credit in an emission-dependent supply chain with capital constraint Song Xu, Lei Fang
T
⁎
Business School, Nankai University, 94 Weijin Road, Nankai District, Tianjin 300071, PR China
ARTICLE INFO
ABSTRACT
Keywords: Emission-dependent supply chain Capital constraint Partial credit guarantee Trade credit Emission reduction investment
This study investigates a supply chain financing (SCF) system with one supplier and one emission-dependent and capital-constrained manufacturer. Unlike the traditional SCF, the manufacturer borrows two loans to execute the ordering decision and make a low-carbon investment, respectively. We derive the equilibrium strategies of the supply chain members under partial credit guarantee (PCG) and a combination of trade credit and PCG and compare with that under a benchmark (well-funded manufacturer). There exists a unique coefficient of credit guarantee for the supplier to decide whether to provide a trade credit. Numerical studies and extension are discussed to obtain more managerial implications.
1. Introduction The greenhouse effect has a significant negative influence on global sustainable development, such as a rise in the sea level and natural disasters. Excessive carbon emissions primarily contribute to the greenhouse effect. Therefore, an increasing number of countries and organizations have taken efforts to curb carbon emissions through carbon emission trading (Du et al., 2013) and environmental tax (Chan et al., 2018), among others. However, the carbon emissions trading mechanism is more effective than compulsory regulations (e.g., environmental tax) in curbing carbon emissions (Hua et al., 2011; Tang et al., 2015). According to the carbon emissions trading mechanism (Du et al., 2015), the manufacturers obtain respective emission caps allocated by the government. The emission permit plays an important role for the manufacturers’ production, because the manufacturers need to submit enough emission permits to regulatory body (i.e., compliance) after production. If the total amount of carbon emissions exceeds the emission cap, the manufacturers are required to buy emission permits from the emissions trading market to emit extra carbon. Alternatively, the manufacturers can sell the surplus emission permits to obtain extra revenue. Generally speaking, larger enterprises have greater advantages to invest in emission reduction improvement. For example, H&M, Marks & Spencer, and Levis, which are fashion apparel manufacturing enterprises, have adopted new emission reduction technologies to minimize their carbon emissions (Li and Li, 2016; Yang et al., 2017). However, some small and medium-sized enterprises (SMEs) also have motivations to invest in emission reduction improvement because of pressures from the environmental regulations and consumer preference. For example, about 40% of Chinese factories has been shut down because of their substandard emission inspected by environmental bureau officials (Nace, 2017). Additionally, according to the case study of Korean manufacturing SMEs (Lee, 2009), one of the most important drivers for the SMEs adopting environmental improvement is to comply with stringent environmental regulations. Another case study based on 202 SMEs (Meath et al. 2016) demonstrates that implementing emission reduction investment can reduce the environmental cost and improve the competition of the enterprises. Furthermore, consumers
⁎
Corresponding author. E-mail addresses: [email protected] (S. Xu), [email protected] (L. Fang).
https://doi.org/10.1016/j.tre.2020.101859 Received 20 February 2019; Received in revised form 22 January 2020; Accepted 25 January 2020 1366-5545/ © 2020 Elsevier Ltd. All rights reserved.
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
with higher low-carbon awareness possess the willingness to pay more for low-carbon products (Zhu and He, 2017). However, manufacturers, especially small and medium enterprises (SMEs), usually face capital constraints, which worsen when they invest in emission reduction technologies. Therefore, manufacturers need to seek financing sources to execute their operational decisions and emission reduction investments. For example, Industrial and Commercial Bank of China has offered 100 billion yuan to help capitalconstrained SMEs to invest in carbon reduction investments (Sohu Finance, 2013). Additionally, supply chain finance is considered effective in enabling the SMEs to overcome capital constraints and improving the performance of entire supply chains (Yan et al., 2016; Ni et al., 2017; Li et al., 2018). While external bank credit financing (BCF) is popular among capital-constrained manufacturers, the low-level of creditworthiness and collateral of capital -constrained manufacturers limits their direct access to BCF (Gao et al., 2018). Usually, the capital-constrained manufacturers should obtain a partial credit guarantee (PCG) from their suppliers to approach banks for BCF (Yan et al., 2016). This can be attributed to the fact that even if the capital-constrained SMEs fail to repay and approach bankruptcy, the suppliers will bear the responsibility of partially paying the outstanding amount to the bank. Note that the PCG will bring great risk to the supplier. However, if the supplier rejects to provide the guarantee for the manufacturer to obtain loans, the transaction between the supplier and manufacturer might not be able to continue. Furthermore, it is also beneficial for the supplier to improve sales when the manufacturer makes low-carbon investment to attract more consumers with low-carbon awareness. Moreover, even if the supplier undertakes the guarantee risk from the manufacturer, he will make the decision to maximize own expected profit. Trade credit financing (TCF) is another popular financing scheme that supports capital-constrained supply chains (Chen and Wang, 2012; Jing et al., 2012; Kouvelis and Zhao, 2012; Yang and Bridge, 2018). Under TCF, the upstream supplier charges an interest on the delayed payment to the capital-constrained manufacturer. Despite the provision under TCF, an emission-dependent manufacturer seeks another loan through PCG in order to invest in emission reduction technologies. Therefore, we consider two financing schemes for the emission-dependent and capital-constrained manufacturer. Under the PCG scheme, the manufacturer borrows all the funds through PCG to execute the ordering decision and make the emission reduction investment. Under a combination of TCF and PCG (TPCG) scheme, the manufacturer places an order from the supplier through TCF and borrows capital for emission reduction investment from the bank through PCG. According to a report conducted by SWITCH-Asia Network Facility (Agster et al. 2016), some large leading enterprises can provide guarantees to help their up- and downstream SME partners to obtain loans from the banks and improve the environmental performance. Additionally, Taixiang Wood Industry Corporation (China Green Times, 2019), which acts as a core enterprise in a forestry supply chain, provided the guarantee to help his downstream SME manufacturers to obtain green loans from Guangdong Sihui Bank of Agriculture and Commerce. Furthermore, there exist account receivables for the Taixiang after offering trade credit to his downstream SMEs. Finally, six downstream SMEs obtained 5.3 million guarantee green loan and trade credit to execute low-carbon investments and operational decisions. Therefore, we consider PCG and TPCG financing schemes for a capital-constrained manufacturer. These two financing schemes give rise to the following research questions: 1. Which equilibrium strategies are adopted by the supply chain’s members under a benchmark scenario (i.e., well-funded manufacturer), PCG, and TPCG financing schemes, respectively? 2. How does the coefficient of credit guarantee impact the financing equilibrium? Does the supplier always prefer to provide TCF to the manufacturer? 3. How do other important parameters, such as the emission cap, consumer low-carbon awareness, and unit price of emission permit, impact the equilibrium strategies and profits of the supply chain’s members? To address the above questions, we consider a two-echelon supply chain with one supplier and one emission-dependent and capital-constrained manufacturer under the cap-and-trade regulation. The manufacturer borrows loans to execute the ordering decision and make the emission reduction investment through PCG or TPCG. Subsequently, the manufacturer processes the products and sells them to consumers with a low-carbon awareness. We derive the equilibrium strategies of the supply chain’s members under the two financing schemes, and compare with that under a benchmark i.e., well-funded manufacturer. We discuss the impact of the different coefficients of credit guarantee on financing equilibrium and conduct numerical studies to analyze the impact of other important parameters. Additionally, we extend this study to discuss the endogenous interest rates under PCG and TPCG, respectively. The contributions of this study are summarized as follows. We formulate a two-stage Stackelberg game of an emission-dependent supply chain under PCG and TPCG financing schemes and derive the equilibrium strategies of the supply chain’s members. Under the benchmark scenario, the emission cap allocated by the government ceases to influence the decisions of the well-funded manufacturer. Under the two financing schemes, given the interest rate and the wholesale price, an increase in the emission cap negatively influences the optimal ordering quantity determined by the manufacturer. Additionally, when compared to the benchmark scenario, under the two financing schemes, the capital-constrained manufacturer places a larger ordering quantity but invests less in emission reduction. On the supplier’s side, we observe that a trade-off between additional revenue and potential loss occurs when the manufacturer faces bankruptcy, according to different coefficients of credit guarantee. When the coefficient of credit guarantee is within a relatively low range, the supplier expresses reluctance to provide TCF to the capital-constrained manufacturer. This result is contrary to literature (Cao et al., 2019) suggesting that the supplier will always make more profit under TCF than that under BCF. The remaining parts of this paper are organized as following. Section 2 summarizes the relevant literature. Section 3 describes the model and presents the notations used in this study. Section 4 derives the equilibrium strategies of the supply chain’s members under the benchmark scenario, PCG, and TPCG schemes, respectively. Section 5 presents a comparative analysis under the three scenarios. Section 6 carries out numerical studies to analyze the influence of some important parameters. Section 7 extends this study to discuss 2
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the endogenous interest rates under PCG and TPCG, respectively. Finally, Section 8 presents the conclusion and limitations of this study. 2. Literature review This study is related to the following two streams of literature: the emission-dependent supply chains and supply chain finance. We will review the related literature and highlight the differences between this study and existing literature. The emission-dependent supply chain focuses on the production and inventory of a firm under the cap-and-trade regulation. For example, Dobos (2005) analyzed the effect of emission permits on the production and inventory strategies of a firm under the capand-trade system, based on the dynamic Arrow-Karlin model. Extending Dobos’s (2005) model, Li and Gu (2012) further considered the impact of tradable emission permits with banking on a firm’s production and inventory decisions. Li et al. (2013a, 2013b) investigated the impact of the emission trading scheme on the dynamic decision-making of generation companies (GENCOs), under a multimarket environment comprising the electricity, fuel, and carbon markets. However, this study focuses on the operational decision and low-carbon investment of the capital-constrained manufacturer, under a different multimarket environment comprising the emission trading market and the supply chain financing market. In recent years, emphasis has been given to extending the literature on a firm regulated by the cap-and-trade system to an emission-dependent supply chain. For example, Du et al. (2013, 2015) investigated the impact of the emission cap on equilibrium strategies of a supply chain consisting of one emission-dependent manufacturer and one emission permit supplier. Xu et al. (2017a) considered production and pricing decisions in an emission-dependent supply chain in which an upstream manufacturer, under the cap-and-trade regulation, produces two products based on make-to-order production. Yang et al. (2017) explored pricing and carbon emission reduction decisions in two competitive and emission-dependent supply chains with vertical and horizontal cooperation. Some studies (Jaber et al., 2013; Glock and Kim, 2015; Xu et al., 2016; Xu et al., 2017b) investigated different contracts that can be used to achieve two-level supply chain coordination under cap-and-trade regulation. Apart from considering competition or coordination in emission-dependent supply chains, Xia et al. (2018) integrated reciprocal preferences and the consumer with a lowcarbon awareness into an emission-dependent supply chain and analyzed its impact on the decisions and performances of the supply chain’s members. Furthermore, Li et al. (2017) investigated centralized and decentralized supply chain models with a carbon-sensitive demand and compared the optimal decisions of the production quantity and emission reduction effort under absolute-cap and intensity-cap regulations. Daryantoa et al. (2019) explored the impact of emission cost, deterioration, and variable transportation cost on a three-echelon supply chain with a supplier, a third-party logistics service provider, and a buyer. However, the above literature assumes that the supply chain’s members have sufficient capital to execute optimal decisions regarding operation and emission reduction investment. In practice, a manufacturer, especially an SME, is vulnerable to capital constraint. Therefore, to fill this research gap, we consider a capital-constrained and emission-dependent manufacturer who requires two loans to execute the decisions of ordering quantity and emission reduction investment, respectively. Another stream of literature related to this study is supply chain finance. In this domain, the two popular financing schemes BCF and TCF for the capital-constrained supply chain members are highlighted in several studies, such as Dada and Hu (2008), Chen and Wang (2012), Kouvelis and Zhao (2011), and Yang and Birge (2018). For example, Zhang et al. (2018) assumed that a manufacturer offers trade credit to the capital-constrained retailer, by integrating customer balking and asymmetric market information. Unlike the traditional TCF, Tsao (2017) showed that providing trade credit to customers leads to default risk, for an uncertain and credit-period dependent demand; they also discussed who (supplier or retailer) should implement big data analytics to mitigate default risk in the supply chain. Devalkar and Krishnan (2019) focused on the role of TCF in addressing the supplier’s moral hazard problems and how to coordinate the supply chain. Kouvelis and Zhao (2017) investigated the impact of credit ratings on operational and financial decisions of a capital-constrained supply chain. The capital-constrained retailer can obtain short-term financings via both bank loans and trade credits, while the capital-constrained supplier can decide the operational decisions through bank loans and/or an early payment contract. Furthermore, Lee et al., (2017) employed a dyadic panel data set to explore the impact of TCF on different types of competition between supply chain members and firm performance, while Wu et al., (2019) considered quantitative modelling to discuss the role of TCF on inventory competition between two asymmetric retailers. Additionally, some studies have focused on conducting a comparison between BCF and TCF, such as Jing et al. (2012), Jing and Seidmann (2014), Kouvelis and Zhao (2012), and Cai et al. (2014). In this context, it must be noted that capital-constrained enterprise with low trustworthiness face difficulties in directly obtaining loans from the bank. Some studies assumed that the capital-constrained supply chain’s members obtain loans from other financing schemes, such as third-party logistics firms (Chen and Cai, 2011; Wang et al., 2019b), peer-to-peer lending platform (Gao et al., 2018), and electronic business platform (Wang et al., 2019a). Furthermore, some studies assumed that core enterprises with enough capital in the supply chain provide a PCG, enabling capital-constrained SMEs to obtain the loans from banks. For example, Yan et al. (2016) designed a PCG contract for a capital-constrained supply chain and analyzed equilibrium financing strategies and coordination conditions for the PCG contract. Li et al. (2018) extended the study by Yan et al. (2016) and explored two financing strategies—PCG and TCF—for a supply chain comprising one risk-averse supplier and one risk-neutral retailer with capital constraint. They characterized the preference of two financing strategies with different coefficients of credit guarantee and riskaversion degree. However, the above literature ignored the impact of cap-and-trade regulation on the operational, greening, and financing decisions of capital-constrained supply chains. In recent years, some studies have focused on emission-dependent supply chains with capital constraints. For example, Wu et al. (2018) examined a green supply chain financing system comprising one manufacturer and one capital-constrained retailer. However, they considered that the upstream manufacturer had sufficient capital for low-carbon 3
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Table 1 Summary of the literature about supply chain finance. Existing work Dada and Hu (2008) Chen and Wang (2012) Zhang et al., (2018) Devalkar and Krishnan (2019) Wu et al. (2019) Lee et al. (2018) Jing and Seidmann (2014) Jing et al. (2012) Kouvelis and Zhao (2012) Kouvelis and Zhao (2017) Cao and Yu (2018) Yan et al. (2016) Li et al. (2018) Wu et al., (2018) Cao et al. (2019) This study
Cap-and-trade regulation
Yes
Yes Yes
Financing schemes
Uses of loans
BCF TCF TCF TCF TCF TCF BCF/TCF BCF/TCF/BCF + TCF BCF/TCF BCF + TCF/Early payment contract TCF PCG PCG/TCF BCF/TCF BCF/TCF PCG/TPCG
Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Ordering Low-carbon investment + ordering
investment, and hence ignored capital constraints for this investment. Furthermore, they ignored the influence of the cap-and-trade regulation on the decisions of supply chain members. Cao and Yu (2018) investigated that both the manufacturer and retailer are under the cap-and-trade regulation, and the manufacturer provides TCF contract for a capital-constrained retailer. They designed a general contract to achieve supply chain coordination under the cap-and-trade regulation. We summarize the differences between this study and existing literature in Table 1. The most closely related literature to this study is Cao et al. (2019); they compared two financing schemes—BCF and TCF—for a downstream manufacturer who is emission-dependent and capital constraint. They assumed that the manufacturer borrowed only one loan for ordering decision and discussed whether investments in carbon abatement has an impact on the financing equilibrium. However, they ignored the fact that the manufacturer may need another loan for emission reduction investments. The differences between this and Cao et al.’s study (2019) are summarized as follows. On the one hand, we assume that the capital-constrained manufacturer needs two loans for the ordering decision and emission reduction investment, respectively. On the other one hand, we assume that the supplier will provide a PCG contract for the emission-dependent and capital-constrained manufacturer because it is difficult for the manufacturer to directly obtain loan from a bank. We find that when the coefficient of credit guarantee is within a relatively low range, the supplier expresses reluctance to provide TCF to the capital-constrained manufacturer. The result is contrary to that of Cao et al. (2019). 3. Model description We consider a supply chain comprising one supplier and one emission-dependent manufacturer, under the cap-and-trade regulation. The manufacturer purchases raw products from the supplier and, subsequently, sells the products to the consumers with a low-carbon awareness after processing. The manufacturer buys emission permits from the emission trading market if the manufacturer’s total amount of carbon emissions exceeds the emission cap allocated by the government. Alternatively, the manufacturer can sell the surplus emission permits to earn extra revenue. Furthermore, the consumers with a low-carbon awareness exhibit willingness to pay more for low-carbon products (Zhu and He, 2017). This drives the rational manufacturer to invest in the improvement of emission reduction to reduce emission and attract more consumers. Note that carbon emission reduction investment is a long-term investment activity, but the enterprises usually divide the long-term investment into several short-term programs. For example, Fujitsu (2012) completed the fifth short-term program of emission reduction in earlier 2012 and moved to the sixth stage of environmental improvement. In this study, we considered a single-period supply chain problem with a downstream manufacturer who intends to invest in one of short-term programs of emission reduction. However, the manufacturer usually faces capital constraints either when ordering from the supplier or investing in emission reduction. In this study, we consider two financing schemes for the capital-constrained manufacturer—PCG and TPCG. Under the former scheme, with the assistance offered in the form of the supplier’s PCG, the manufacturer borrows all the capital needed from the bank to execute decisions regarding procurement and emission reduction investment. Under the latter scheme, the manufacturer obtains the following two loans: one loan is borrowed through TCF for obtaining raw products before processing, and the other loan is borrowed from the bank through PCG to invest in emission reduction. The framework of the emission-dependent supply chain financing system is shown in Fig. 1. We also set a benchmark wherein the manufacturer has sufficient capital to execute the ordering decision and make the emission reduction investment. The demand will be influenced by the consumers’ willingness to buy low-carbon products and by other uncertain events or factors. Thus, the demand function is characterized as D = e + (Cao et al., 2019), where denotes the consumer low-carbon awareness; e denotes the level of emission reduction, represents the stochastic factor and follows a distribution in the range of [0, + ) . F ( ) and f ( ) represent cumulative distribution function and probability density function, respectively. Let h ( ) = f ( ) F ( ) be the failure rate (Jing et al., 2012), which increases with . 4
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Bank
Government
Int
ere
r (λ
Credit guarantee
λ
Supplier
Low-carbon Investment
)
st r
ate
Emission cap
G
Wholesale price w
Manufacturer
Order quantity Q ion iss em n e f o tio c vel Le redu
Sell
Unit price
p =1
Consumers
Buy
Emission Trading Market
Fig. 1. The framework of an emission-dependent supply chain financing system.
Without the loss of generality, we present the following assumptions: (1) The manufacturer has no initial capital. This assumption can simplify the complex derivation and make the results more obvious in this study. It is also widely used in the literature of capital-constrained supply chain (Jing and Seidmann, 2014; Chen, 2015; Jing et al., 2012; Cao et al., 2019). (2) The retail price is fixed and normalized to 1 (Cai et al., 2014; Chen and Wang, 2012). For simplification, the processing cost of the manufacturer is normalized to zero (Yang et al., 2017). (3) All parameters are common knowledge for the bank, supplier, and manufacturer (Kouvelis and Zhao, 2012). Furthermore, similar to Li et al., (2018), we assume that the two interest rates under PCG and TPCG are fixed at the same value. This might occur that the interest rates are purely determined by the industrial benchmark (Kouvelis and Zhao, 2012). We will discuss the impact of difference between the two interest rates on the selection of financing schemes in Sub-section 6.1. In addition, we will relax the assumption of fixed interest rates to discuss the endogenous interest rates in Section 7. For easier representation, the notations throughout this study are summarized in Table 2. The subscript ‘‘i = b ’’ represents the parameters under benchmark, ‘‘i = 1’’ refers to the parameters under PCG, and the subscript ‘‘i = 2 ’’ denotes the parameters under TPCG. 4. Financing equilibrium under two financing schemes 4.1. Benchmark scenario In this section, we consider a benchmark wherein an emission-dependent manufacturer has sufficient capital to execute the Table 2 Notations. Parameters
Definitions
Di ri
Demand of the products Interest rate Consumer low-carbon awareness Stochastic factor of demand Cost coefficient of the emission reduction investment Unit price of the emission permit Initial emission of the per unit of the product Emission cap allocated by the government Coefficient of credit guarantee Cost of the supplier Bankruptcy threshold Probability density function Cumulative distribution function
v pe G cs Ai f (·) F (·) h (·) s i m i
Decision variables wi Qi ei
Failure rate, h (·) = f (·) F (·) Profit of the supplier Profit of the manufacturer
Wholesale price Ordering quantity Level of emission reduction
5
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S. Xu and L. Fang
optimal ordering decision and make a low-carbon investment. The transaction between the manufacturer and supplier is based on the wholesale price contract. We employ the backward induction approach to derive the equilibrium strategies of the two supply chain participants. The emission-dependent manufacturer places an order Qb with the supplier, according to the wholesale price wb , and sells to the low-carbon awareness consumers after processing. Under the cap-and-trade regulation, the manufacturer may obtain extra revenue from selling surplus carbon permits. This motivates the manufacturer to make an emission reduction investment. This investment is a one-off short-term program to reduce the total amount of carbon emissions (Cao et al., 2019); thus, the total cost of the investment is 2 characterized as veb (Zhu and He, 2017; Yang et al., 2017). At the end of period, the manufacturer will obtain the revenue 2 min[Db , Qb] pe ( Qb G eb). Therefore, the manufacturer, who acts as a Stackelberg follower, decides the ordering quantity Qb and the level eb of emission reduction, and the expected profit of the manufacturer can be written as: m b
= E min[Db , Qb]
pe ( Qb
G
eb )
wb Qb
veb2 2
(1)
The supplier who acts as a Stackelberg leader determines the wholesale price according to the best response of the manufacturer. cs Qb . We can obtain the following lemma. The expected profits of the supplier can be written as bs = wb Qb Lemma 1. When the emission-dependent manufacturer has sufficient capital, the optimal ordering quantity and the level of emission reduction p + (1 pe wb ) eb)[1 QbN h (QbN eb)] = pe + cs and eb = e are F (QbN , respectively. The optimal wholesale price under the v benchmark is wb = F (QbN eb) pe . It is obvious that the optimal ordering quantity Qb and the level eb of emission reduction are closely related to the unit price of the emission permit pe , the initial emission , and the consumer low-carbon awareness . Additionally, Qb and eb decrease with the wholesale price; however, it will not be influenced by the emission cap G. The benchmark is similar with that of a capital-constrained downstream member who borrows the loan from a competitive bank (Wu et al., 2018). However, the findings of this scenario are different from the results of the benchmark considered in this study. On the one hand, they considered that the upstream member made the emission reduction investment and simultaneously determined the wholesale price and level of the emission reduction. On the other hand, they ignored the impact of the cap-and-trade regulation on the optimal decisions of the supply chain’s members. 4.2. Financing equilibrium under PCG Under PCG, the manufacturer borrows all the capital needed from the bank through the PCG from the supplier. Given the interest rate r1 and credit guarantee , the supplier first charges a wholesale price w1 for the manufacturer. Subsequently, the manufacturer, who acts as a Stackelberg follower, simultaneously, determines the ordering quantity Q1 and the level e1 of emission reduction. We employ the backward induction approach to derive the equilibrium strategies of the supplier and manufacturer. 4.2.1. Manufacturer’s problem under PCG We assume that the manufacturer has no initial capital to execute the ordering decision and make the emission reduction investment (Cao et al., 2019). This assumption can simplify the complex derivation and make the results more obvious in this study. Additionally, it is widely employed in other literature about capital-constrained supply chains (Jing and Seidmann, 2014; Chen, 2015; Jing et al., 2012). Furthermore, we present a numerical experiment with considering initial capital of the manufacturer (as shown in Fig. A.11 in the Appendix A) to justify that the main result continues to hold. The manufacturer borrows the loan
(
L1 = w1 Q1 +
ve12 2
) from a bank, with a coefficient
of credit guarantee from the supplier. When the demand is realized, the
emission-dependent manufacturer buys or sells the emission permits on the emission trading market according to the total carbon emissions ( Q1 e1) and emission cap G allocated by government. At the end of the selling season, the manufacturer obtains the revenue min[D1, Q1] pe ( Q1 e1 G ) and repays the loan and interest L1 (1 + r1) to the bank. However, the manufacturer faces bankruptcy and pays the revenue earned to the bank in the case of a failure to repay the loan and interest. Therefore, the expected profit of the manufacturer under PCG is characterized as follows: m 1
= E min[D1, Q1]
pe ( Q1
e1
G)
w1 Q1 +
ve12 (1 + r1) 2
+
The retail price should exceed the margin cost, that is, [w1 (1 + r1) + pe ] ruptcy threshold of the manufacturer.
(2)
1. Lemma 2 is presented to demonstrate the bank-
Lemma 2. Under PCG, the manufacturer will be able to repay the loan and the interest to the bank, and hence not face bankruptcy, if the realized demand D1 = e1 + variable should satisfy
A1
is no less than A1 = pe ( Q1
e1
(
G ) + w1 Q1 +
e1 .
ve12 2
) (1 + r ) , namely, the minimum realized random 1
The bankruptcy threshold A1 plays an important role in characterizing the profit functions of the supply chain’s members under PCG and in simplifying the analysis procedure (Wang et al., 2019a). Additionally, it also significantly impacts the endogenous interest rate, which we will discuss in sub-section 7.1. 6
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According to Lemma 2, we present the following proposition to show the manufacturer’s optimal decisions of ordering quantity and the level of emission reduction. Proposition 1. Under PCG, given the wholesale price w1, (1) the optimal ordering quantity and the level of emission reduction determined by [w1 (1 + r 1) + pe ] + pe e1 ) = [w1 (1 + r1) + pe ] F (A1 e1 ) and e1 = the manufacturer should satisfy F (Q1 , respectively; (2) the v (1 + r 1 ) optimal ordering quantity Q1 and the level e1 of emission reduction decrease with the wholesale price w1, and (3) the optimal ordering quantity Q1 decreases with the emission cap G. However, the level e1 of emission reduction is not influenced by the emission cap G. The proofs are presented in the Appendix A. Proposition 1 demonstrates that the manufacturer should consider the wholesale price, the unit price of the emission permit, and the initial emission of per unit of the product when determining the optimal ordering quantity. When determining the optimal level of emission reduction, the manufacturer should consider the wholesale price, the coefficient of the emission reduction investment, and the interest rate but without considering the ordering quantity. Proposition 1 also demonstrates a straightforward managerial insight that the manufacturer will make conservative decisions on the optimal ordering quantity and the level of emission reduction, when the supplier charges a higher wholesale price. However, it is interesting to note that the manufacturer will make a radical decision regarding the ordering quantity when the government allocates a lower emission cap. According to Lemma 2, if the government provides a lower emission cap, the bankruptcy probability of the manufacturer will increase. Given the interest rate and wholesale price, the additional bankruptcy risk will be borne by the bank or by the supplier, not by the manufacturer. Therefore, the manufacturer should exploit this factor and place a larger order to maximize own expected profit. 4.2.2. Supplier’s problem under PCG
(
The manufacturer borrows the loan L1 = w1 Q1 +
ve12 2
) from the bank with a PCG from the supplier and, subsequently, pays w Q 1
1
to the supplier to procure an optimal quantity of raw products before processing. Therefore, the supplier can obtain the profit (w1 cs ) Q1 if the revenue of the manufacturer can cover the loan and interest. However, when the manufacturer faces bankruptcy at the end of the selling season, the supplier bears the responsibility of partially repaying the loan [L1 (1 + r1) + pe ( Q1 e1 G ) min(D1, Q1)] to the bank. Therefore, the profit of the supplier is shown as follows: s 1
w1 Q1 w1 Q1
=
cs Q1 cs Q1
E {[L1 (1 + r1) + pe ( Q1
e1
if + min (D1, Q1)]}
G)
A1
e1 if A1
e1 >
0
(3)
The feasible region of the wholesale price determined by the supplier should satisfy the following constraints. First, in the e1 ) of the entire supply chain must exceed the marginal cost (cs + pe ) . As decentralized supply chain, the marginal revenue F (Q1 e1 ) is increasing with w1. The minimum wholesale price should satisfy (Q1 e1 ) is decreasing with w1, we can obtain that F (Q1 e1 ) = (cs + pe ) or Q1 = F 1 (cs + pe ) + e1 . According to Proposition 1, the optimal ordering quantity the equation F (Q1 [w1 (1 + r1) + pe ] F (Q1 e1 ) = [w1 (1 + r1) + pe ] F (A1 e1 ) ; should satisfy thus, we have
Q1 = F F
1
1
cs + pe
cs + pe w1 (1 + r 1) + pe
ve1 2 (1 + r 1 ) 2
+ pe (e1 + G )
w1 (1 + r 1) + pe
+ pe (e1 + G )
ve1 2 (1 + r 1 ) 2
+ e1 . w1 is the smaller root of [w1 (1 + r1) + pe ][F
1 (c s
+ pe ) + e1 ]=
+ e1 . Furthermore, the unit retail price set by the manufacturer should be larger than
the unit cost of procurement and carbon emission 1
[w1 (1 + r1) + pe ], and the wholesale price must obtain
1
pe
(1 + r 1 )
w1 .
= w1
Lemma 3. Under PCG, the feasible region of the wholesale price should be in the range of [w1, w1 ]. The supplier decides the optimal wholesale price to pursuit the maximum profit, we derive the first order of Eq. (3), and have
1 d 1s = dw1 h (Q1 where (w1) = Proposition w1
w1 =
w1 w^1
[w1 (1 + r1) + pe ] Q1 h (A1 e1 )
1 (w1)
+
e1 )
[w1 (1 + r1) + pe ] h (A1
2 (w1)
+
2. Under PCG, if (w1) 1
3 (w1) .
e1 )
The equations of
given
the
best
× [1
(w1)]
1 (w1) ,
2 (w1) ,
response
of
(4)
and
the
3 (w1)
are shown in Proof of Proposition 2.
manufacturer’s
decisions,
. The unique wholesale price w1 is implied by (w1) =
if
(w1 )
if
(w1) < 1 and (w1 ) > 1
1
the
1 (w1)
+
wholesale 2 (w1)
+
price
3 (w1)
is
= 1,.
Proposition 2 demonstrates that, under PCG, the wholesale price determined by the supplier heavily depends on sensitivity coefficient (w1) ; this reflects the sensitivity coefficient of the ordering quantity with respect to the wholesale price w1. If the send s
0 (because (w1) is increasing with w1, see Proof of Proposition 2). The sitivity coefficient (w1) 1, we have (w1) 1 and dw1 1 managemental implication is that the ordering quantity decided by the manufacturer would be very sensitive to the wholesale price. In other words, if the supplier intends to set a slight high wholesale price, the manufacturer would significantly reduce his ordering quantity. The profit of the supplier will also decrease with reduced product sales. Therefore, the supplier should set the lowest wholesale price in order to prevent the manufacturer’s ordering quantity from decreasing significantly. However, when (w1 ) 1, we have
(w1)
1 and
d 1s
dw1
0 . It indicates that the ordering quantity determined by the manufacturer will be little sensitive to the 7
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S. Xu and L. Fang
wholesale price. Thus, the supplier can set the highest wholesale price without worrying about reduced product sales. When (w1) < 1 and (w1 ) > 1, the supplier should set a unique wholesale price to achieve the maximum profit. 4.3. Financing equilibrium under TPCG Under TPCG, the manufacturer obtains the following two loans: one loan is borrowed through TCF for obtaining raw products before processing, and the other loan is borrowed from the bank through PCG to invest in emission reduction. Given the coefficient of credit guarantee and interest rate r2 , the supplier provides a TCF to the manufacture and charges a wholesale price w2 . Subsequently, the manufacturer, who acts as a Stackelberg follower, simultaneously, decides the ordering quantity Q2 and the level e2 of emission reduction. We also employ the backward induction approach to derive the equilibrium strategies of the supplier and manufacturer. 4.3.1. Manufacturer’s problem under TPCG The supplier who acts as a Stackelberg leader decides postponed wholesale price w2 under TPCG. Note that the postponed wholesale price w2 is the only contract variable under trade credit, because it can be consisted of a wholesale cash price w and an associated interest rate rT , i.e. w2 w (1 + rT ) . This assumption is in line with other literature of trade credit in supply chains (e.g. Cao et al. 2019; Jing et al. 2012). Subsequently, the manufacturer determines the ordering quantity Q2 of the raw products and the level of 2 emission reduction e2 . The total cost of emission reduction investment is characterized as ve2 . To execute the emission reduction 2
2
investment, the manufacturer can borrow the loan ve2 from a bank through a PCG from supplier. When the demand is realized, the 2 emission-dependent manufacturer will buy or sell the emission permits on the emission trading market according to the total carbon emissions ( Q2 e2) and emission cap G. At the end of the selling season, if the manufacturer fails to repay to the bank and supplier, the manufacturer will face bankruptcy. Therefore, the expected profit of the manufacturer can be written as: m 2
= E min(D2 , Q2)
pe ( Q2
e2
G)
w2 Q2
ve22 (1 + r2) 2
+
(5)
Lemma 4. Under TPCG, the manufacturer will not face bankruptcy, when the realized demand D2 = e2 +
A2 = w2 Q2 +
ve 22 (1 2
+ r2 )
pe (G + e2
Q2) , namely, the minimum realized random variable should satisfy
is no less than
A2
e2 .
Similar to Lemma 2, the bankruptcy threshold A2 also plays an important role in characterizing the profit functions of the supply chain’s members under TPCG and in simplifying the analysis procedure (Wang et al., 2019a). Additionally, in sub-section 7.2, we will discuss the relationship between the bankruptcy threshold A2 and the endogenous interest rate under TPCG. We have written the following proposition to show the manufacturer’s optimal ordering quantity and the level of emission reduction. Lemma 5. Under TPCG, given the postponed wholesale price w2 , the optimal ordering quantity and the level of emission reduction should [w 2 + pe ] + pe e2 ) = [w2 + pe ] F (A2 e2 ) and e2 = satisfy F (Q2 , respectively. v (1 + r ) 2
Lemma 5 shows that the optimal ordering quantity and the level of emission reduction under TPCG are similar with that under PCG. The optimal ordering quantity determined by the manufacture will be influenced by the wholesale price, the unit price of the emission permit, and the initial emission of per unit of the product. The optimal level of emission reduction decreases with the wholesale price, the coefficient of emission reduction investment, and the interest rate; however, it is independent of the ordering quantity. 4.3.2. Supplier’s problem under TPCG Under TPCG, the manufacturer obtains two loans from the supplier and bank, respectively. At the end of the selling season, if the manufacturer earns sufficient revenue to repay loans to the supplier and bank, then the supplier will also obtain a revenue w2 Q2 . However, if the manufacturer faces bankruptcy, then there will be two situations because of the sequence of the repayment to the supplier and bank. We assume that the bankrupt manufacturer repays to the bank, before repaying the remaining revenue to the e2 G )] of supplier (Yang and Birge, 2018; Ivashina and Iverson, 2014). In the first situation, the revenue [min(D2 , Q2 ) pe ( Q2 the
manufacturer
is
large
enough
to
cover
the
bank’s
ve 2
loan
and
interest
ve2 2 (1 2
+ r2)
(i.e.,
min(D2 , Q2 ) b2 = 22 (1 + r2) + pe ( Q2 e2 G ) ); however, it fails to meet the repayment obligation to the supplier. As a result, the supplier only obtains min(D2 , Q2 ) b2 . In the second situation, the revenue of the manufacturer fails to cover the loan and interest from the bank; hence, the manufacturer uses the entire revenue to repay the bank loan, and the supplier fails to obtain any revenue from the manufacturer. Additionally, the supplier has the responsibility to repay a part of the loan and interest [b2 min(D2 , Q2 )] to the bank. Therefore, the profit of the supplier under TPCG can be written as: s 2
=
w2 Q2 cs Q2 E min(D2 , Q2 ) cs Q2 [b2
b2 cs Q2 Emin (D2 , Q2 )]
if + if A2 if b2
A2 e2 > e2 >
e2 b2 0
e2 (6)
The constraints of the feasible region of the postponed wholesale price under TPCG are similar to that under PCG. First, the 8
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e2 ) of the entire supply chain must exceed the marginal cost (cs + pe ) in the decentralized supply chain. marginal revenue F (Q2 e2 ) increases with w2 . The minimum wholesale price should satisfy the e2 ) decreases with w2 , we can find that F (Q2 As (Q2 e2 ) = (cs + pe ) or Q2 = F 1 (cs + pe ) + e2 . According to Proposition 3, the optimal ordering quantity should equation F (Q2 satisfy F (Q2
e2 ) = [w2 + pe ] F (A2
the smaller root of [w2 + pe ][F
1 (c s
e2 ) ; thus, we have [w2 + pe ] Q2 = F 1
+ pe ) + e2 ] = F
cs + pe
cs + pe
ve2 2 (1 + r 2 ) 2
+ pe (e2 + G )
w 2 + pe
ve2 2 (1 + r 2 ) 2
+ pe (e2 + G )
w 2 + pe
1
+ e2 . w2 is
+ e2 . Furthermore, the unit retail price
set by the manufacturer must exceed the unit cost of procurement and carbon emission 1 wholesale price can be written as w2 = 1 pe .
(w2 + pe ) , and thus the maximum
Lemma 6. Under TPCG, the feasible region of the postponed wholesale price should be in the range of [w2, w2 ]. As the supplier decides the optimal wholesale price to obtain the maximum profit, we derive the first order of Eq. (6) and have
1 d 2s = dw2 h (Q2 where
(w 2 ) =
Proposition w2
w2 =
w2 w^ 2
[w2 + pe ] Q2 h (A2 e2 )
+
3 (w 2 ) .
Under TPCG, (w 2 ) 1
given
1 (w 2 )
3. if
+
e2 )
[w2 + pe ] h (A2
2 (w 2 )
if
(w 2 )
if
(w2) < 1 and
e2 )
× (1
The equations of the
best
(w2 )) 1 (w 2 ) ,
response
of
(7) 2 (w 2 ) ,
and
the
. The unique w2 is implied by
1
3 (w 2 )
are shown in Proof of Proposition 3.
manufacturer’s
(w 2 ) =
1 (w 2 )
decisions,
+
2 (w 2 )
+
the
wholesale
3 (w 2 )
price
is
= 1.
(w 2 ) > 1
Proposition 3 shows that, under TPCG, the wholesale price is heavily dependent on sensitivity coefficient (w1) ; this reflects the sensitivity coefficient of the ordering quantity with respect to the wholesale price w2 . The sensitivity coefficient of the ordering d s
0 . The result quantity under TPCG is similar with that of Proposition 2 under PCG. When (w2 ) 1, we have (w2 ) 1 and dw2 2 indicates that the ordering quantity determined by the manufacturer is little sensitive to the wholesale price. Therefore, to earn more profit, the supplier can set the highest wholesale price without worrying about reduced product sales. However, when (w2 ) 1, we d s
0 . The result reveals that the ordering quantity is very sensitive to the wholesale price. If the supplier have (w2 ) 1 and dw2 2 intends to set a slight high wholesale price, the profit of the supplier will also significantly decrease because of reduced product sales. Therefore, the supplier should set the lowest wholesale price to prevent the manufacturer’s ordering quantity from decreasing significantly. When (w2 ) < 1 and (w2 ) > 1, the supplier will set a unique optimal wholesale price. 5. Comparative analysis To get more managerial insights, we assume that the stochastic factor of demand follows an exponential distribution with mean y, which is similar to Yan et al. (2019). We compare the optimal ordering decision and emission reduction investment under the three situations (i.e., benchmark and two financing schemes), and derive the following Proposition 4. Proposition 4. Assume that the stochastic factor of the demand follows an exponential distribution with mean y. We get that (1) e1 e2 eb and Qb eb and Qb Q1 Q2 if w2 w1 (1 + r1) ; (2) e2 < e1 Q2 < Q1 if w2 > w1 (1 + r1) . Proposition 4 shows that when the supplier charges a lower wholesale price under TPCG (w2 w1 (1 + r1) ), the manufacturer will exhibit willingness to improve the optimal ordering quantity and the level of emission reduction under TPCG than that under PCG. Otherwise, the manufacturer will make the opposite decisions. The reason is that if the supplier expresses willingness to provide a trade credit and sets a lower wholesale price under TPCG, then the manufacturer will face relatively less risk of bankruptcy and make more radical decisions regarding the optimal ordering quantity and the level of emission reduction. It is interesting to note that the capital-constrained manufacturer will invest less in the emission reduction and place a large order under the two financing schemes, when compared to that under the benchmark scenario. The capital-constrained manufacturer has a limited responsibility to repay the loans and interest in the case of bankruptcy. Hence, the manufacturer will make a radical decision regarding the ordering quantity, even if the bankruptcy probability increases. However, the optimal level of emission reduction is heavily dependent on the wholesale price and interest rates. As the supplier charges higher wholesale prices under the two financing schemes than that under the benchmark scenario, the manufacturer will take a more conservative decision regarding the optimal level of emission reduction. Proposition 5. Assume that the stochastic factor of demand follows an exponential distribution with mean y. In this case, there exists a unique coefficient of credit guarantee 0 < < 1 such that the supplier prefers to provide PCG for the manufacturer when 0 < < but < 1. prefers to provide TPCG when Proposition 5 shows that the supplier will set different wholesale prices to induce the manufacturer to choose a PCG or a TPCG financing scheme according to the different coefficients of credit guarantee. There exists a trade-off between the additional revenue and the potential loss if the manufacturer faces bankruptcy. We can obtain the managerial insight that if the coefficient of credit guarantee is within a lower range (0 < < ), the supplier would not provide trade credit and set a wholesale price to induce the manufacturer to borrow all the capital from the bank. The reason is that the supplier will have lesser responsibility to cover the 9
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potential loss from outstanding amount under the PCG financing scheme. Otherwise ( < < 1), the supplier should exhibit willingness to provide trade credit. Note that the supplier undertakes greater risk from the manufacturer under TPCG than that under PCG. However, the risks for the supplier under PCG would become close to that under TPCG, when coefficient of credit guarantee is within a higher range. Then, although the supplier undertakes a bit higher risk under TPCG, he will obtain a risk premium because of providing trade credit for the manufacturer. Therefore, when coefficient of credit guarantee is within a higher range, the supplier should choose to provide trade credit guarantee to maximize own expected profit. In Section 6, we will conduct two numerical experiments to analyze the impact of some important factors under the benchmark, PCG, and TPCG financing schemes. Furthermore, we will discuss the impact of the endogenous interest rates in Section 7. 6. Numerical study To show the robustness of the results in the numerical studies, we assume that the stochastic factor of demand follows two different distributions, that is, an exponential distribution (Yan et al., 2016) and a uniform distribution (Li et al., 2018), and both their means are set as 10. We obtain similar results with the two different distributions. To save space, the results of the impact of coefficient of credit guarantee with uniform distribution are presented in the Appendix A (see Figs. A.1–A.6). The main parameters are set based on real-word industrial data and prior literature. Specifically, the Fiji SME credit guarantee scheme (Asian Development Bank, 2016) was implemented by Reserve Bank of Fiji to promote the local business industry in 2012, and the maximum interest rate was set as 10% per year. Therefore, the interest rates in this study are set as r1 = r2 = 0.1. Additionally, in dairy industry, around 1.5 kg CO2e will be emitted to produce one kg milk (Flysjö, 2012). Thus, the initial carbon emission of per unit product is set as = 1.5 kg. Furthermore, more than 40 countries have been implementing carbon pricing policies, and the range of carbon pricing varies from one to 130 $ per ton (Gomez, 2019). Therefore, the unit price of the emission permit is set as pe = 0.13 $ per kg. Moreover, referring to prior literature of emission-dependent supply chain (Wang et al., 2016), we set the same ratio of cost coefficient of lowcarbon investment to unit production cost (i.e., v cs = 300 ): cs = 0.15 and v = 45. 6.1. The impact of coefficient of credit guarantee and emission cap In this sub-section, we will discuss the impact of the coefficient of credit guarantee and emission cap G on the equilibrium strategies of the supply chain’s members. The consumer low-carbon awareness is set as = 15. We can obtain wb (G = 3) = 0.45, Qb (G = 3) = 6.17, and eb (G = 3) = 0.12 . Apparently, the wholesale price wb (G = 3) = 0.45 under the benchmark scenario is less than that under the two financing schemes (see Fig. 2). Furthermore, Fig. 2 demonstrates that the optimal wholesale price increases with the coefficient of credit guarantee but decreases with the emission cap allocated by the government. The reason is that the supplier bears a higher bankruptcy risk from the manufacturer with a higher coefficient of credit guarantee. Hence, the supplier will raise the wholesale price to balance the bankruptcy risk from the manufacturer. When the government allocates a higher emission cap for the manufacturer, the manufacturer places a relatively small order (see Fig. 3). Therefore, the supplier will decrease the wholesale price to induce the manufacturer to place a larger order. When the coefficient of credit guarantee is within a higher range, the wholesale price w2 set by the supplier under TPCG is lower than w1 (1 + r1) under PCG. It means that when the supplier is required to provide a very high credit guarantee, he will undertake more risk under PCG than that under TPCG. Therefore, the supplier prefers to provide trade credit and sets a lower wholesale price under TPCG. Figs. 3 and 4 respectively show that the optimal ordering quantity and the level of emission reduction decrease with the coefficient of credit guarantee. The reason is that the supplier raises the wholesale price to balance the bankruptcy risk from the manufacturer with a higher coefficient of credit guarantee. In addition, the results demonstrate that the optimal decisions of the
Fig. 2. Optimal wholesale price under different coefficients of credit guarantee and emission caps (Exponential distribution). 10
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Fig. 3. Optimal ordering quantity under different coefficients of credit guarantee and emission caps (Exponential distribution).
Fig. 4. Optimal level of emission reduction under different coefficients of credit guarantee and emission caps (Exponential distribution).
manufacturer heavily depend on the wholesale price determined by the supplier. The optimal ordering quantity and the level of emission reduction under TPCG are higher than that under PCG when w2 w1 (1 + r1) , and the result is consistent with Proposition 4. Furthermore, the optimal ordering quantity Qb (G = 3) = 6.17 under the benchmark scenario is less than that under PCG and TPCG. The reason is that the manufacturer has limited responsibility to repay loans and interest. Hence, the capital-constrained manufacturer will make a radical decision regarding the ordering quantity, when compare to that under the benchmark scenario.
Fig. 5. The profit of supplier under different coefficients of credit guarantee and emission caps (Exponential distribution). 11
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Fig. 6. The profit of the manufacturer under different coefficients of credit guarantee and emission caps (Exponential distribution).
Fig. 5 demonstrates that the profit of the supplier decreases with the coefficient of credit guarantee under the two financing schemes. For the supplier, there exists a trade-off between the additional revenue from TCF and the potential loss when the manufacturer faces bankruptcy. Specifically, if the coefficient of credit guarantee is less than the threshold, the supplier will express reluctance to provide trade credit to the manufacturer. The result is consistent with Proposition 5. Furthermore, it is worth noting that when the government provides a higher emission cap G, the supplier would be easier in a better position to change the decision with regards to providing a trade credit to the manufacturer. The reason is that, with an increase in the emission cap, the capitalconstrained manufacturer would make a more conservative decision regarding the ordering quantity. Consequently, the supplier would face a lower risk from the manufacturer under TPCG; additionally, the supplier would be in a better position to earn additional profit by providing trade credit. Fig. 6 shows that the profit of the manufacturer decreases with the coefficient of credit guarantee under the PCG and TPCG financing schemes. The result indicates that the manufacturer has a lower bargaining power when the coefficient of credit guarantee increases. The manufacturer might be squeezed by the supplier, because the supplier can set a higher wholesale price and earn more risk premiums. Furthermore, it is worth noting that the profit of the manufacturer bm(G = 3) = 1.43 under the benchmark scenario is larger than that under the two financing schemes. The reason is that the capital-constrained manufacturer seeks credit guarantee from the supplier in order to obtain loans from the bank. Therefore, the supplier will determine a higher wholesale price (see Fig. 2) to squeeze the manufacturer. Fig. 7 demonstrates that the tendency of the profit generated by the entire supply chain is similar to that generated by the supplier (see Fig. 5), who acts as a Stackelberg leader and has a greater bargaining power in the supply chain financing (SCF) system. Therefore, the supplier has a significant influence on the profit of the entire supply chain. The profit of the entire supply chain increases with the emission cap G provided by the government under TPCG. The reason is that, given the higher emission cap, the supplier has lower responsibility for bankruptcy risk from the manufacturer. Additionally, the supplier would be in a better position to earn additional profits by providing trade credit. However, when the credit guarantee is within a relatively low range, the profit of the entire supply chain would decrease with the emission cap under PCG. The supplier bears a lower risk from the manufacture under
Fig. 7. The profit of entire supply chain under different coefficients of credit guarantee and emission caps (Exponential distribution). 12
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Fig. 8. Impact of difference between r1 and r2 on unique coefficient r2 = 0.1
of credit guarantee. Note: r12 = r1
r2 , r1 = 0.06, 0.08, 0.1, 0.12, 0.14 , and
PCG than that under TPCG with a lower credit guarantee. Furthermore, the manufacturer determines a higher ordering quantity, and thus the supplier earns a larger profit with lower emission cap under PCG. As we assume that the interest rates are fixed at the same value under PCG and TPCG, we further discuss the impact of the difference between r1 and r2 on the unique coefficient of credit guarantee. As shown in Fig. 8, the unique coefficient of credit guarantee is decreasing when the difference between the interest rates increases. The result indicates that with the increasing of the differences between r1 and r2 , the supplier would be easier in a better position to change the decision with regards to providing a trade credit to the manufacturer. The reason might be that compared with fixed interest rate under TPCG, the supplier undertakes more risk with the increasing of interest rate under PCG. 6.2. Impact of the consumer low-carbon awareness and the unit price of the emission permit In this sub-section, we will discuss the impact of the consumer low-carbon awareness and the unit price of the emission permit on the equilibrium strategies of the supply chain’s members. This section will also discuss their expected profits. The emission cap and the coefficient of credit guarantee are set as G = 3 and = 0.8, respectively. The results of the benchmark are shown in Appendix A (see Table A1). It is interesting to note that the wholesale price increases with the consumer low-carbon awareness under the benchmark scenario but decreases under PCG and TPCG financing schemes (see Fig. 9). As the consumer low-carbon awareness increases, the manufacturer exhibits willingness to procure a large order from the supplier. In this case, the supplier faces a lower bankruptcy risk from the manufacturer and sets a lower wholesale price. Additionally, the wholesale price decreases with the unit price of emission permit under the two financing schemes. The reason might be that the government usually allocates a lower emission cap, and the manufacturer makes a conservative decision on ordering quantity with increasing of unit price of emission permit (see Fig. 10). Therefore,
Fig. 9. Optimal wholesale price under the scenario comprising different consumer low-carbon awareness and unit prices of the emission permit.
13
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Fig. 10. Optimal ordering quantity under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit.
the supplier charges a lower wholesale price when unit price of emission permit increases. According to Figs. 10 and 11, we find that both the ordering quantity and the level of emission reduction increase with the consumer low-carbon awareness under the benchmark scenario (see Table A1), PCG, and TPCG. This is because the demand increases with the consumer low-carbon awareness, and the manufacturer improves the level of emission reduction and places a larger order. However, the level of emission reduction under the benchmark scenario is larger than that under PCG and TPCG. These results are consistent with Proposition 4. It is worth noting that when the consumer low-carbon awareness is within a relatively low range, an increase in the unit price of emission permit leads to raise the level of emission reduction. Alternatively, the increasing unit price of emission permit will reduce the level of emission reduction. The reason might be that when the consumer low-carbon awareness is within a relatively low range and the unit price is higher, the manufacturer will place a lower order and raise the level of emission reduction to reduce the cost of emission. According to Fig. 12, we find that the profit of the supplier increases with the consumer low-carbon awareness under the benchmark scenario (see Table A1) and two financing schemes. The reason is that the market demand increases with the consumer low-carbon awareness and the manufacturer orders more raw products from the supplier. Furthermore, the profit of the supplier under the TPCG financing scheme is always higher than that under the PCG financing scheme, this is because we assume that the coefficient of PCG is within a higher range (i.e., = 0.8). The result is consistent with Proposition 5 and Fig. 7. Moreover, Fig. 12 demonstrates that the lower the unit prices of emission permit, the higher profit of the supplier. The reason might be that the manufacturer has greater motivation to place a larger order when the unit prices of emission permit decreases. As a result, the supplier can set a higher wholesale price to earn more profit from the manufacturer. Fig. 13 shows that the profit of the manufacture increases with consumer low-carbon awareness under the two financing schemes and the benchmark scenario (see Table A1). The profit of the manufacturer under the benchmark scenario is higher than that under the two financing schemes. The result is consistent within Sub-section 6.1. Furthermore, an increase in the consumer low-carbon awareness motivates the manufacturer to select TPCG. The reason might be that with the increasing of the consumer low-carbon awareness, the bankruptcy risk of the manufacturer decreases. The supplier can obtain more profits from the TCF risk premiums. As a result, the supplier would set the wholesale price to induce the manufacturer to select TPCG, when the consumer low-carbon
Fig. 11. Optimal level of emission reduction under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit. 14
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Fig. 12. The profit of the supplier under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit.
Fig. 13. The profit of the manufacturer under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit.
awareness is within a larger range. Fig. 14 demonstrates that the tendency of the profit generated by the entire supply chain is similar with that generated by the supplier (see Fig. 13) because the supplier acts as a Stackelberg leader in the SCF system. Therefore, the decision of the supplier has a significant influence on the profit of the entire supply chain.
Fig. 14. The profit of entire supply chain under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit. 15
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7. Extension: Endogenous interest rate Apart from the scenario of the fixed interest rate determined by the industrial benchmark, there might exist another scenario that interest rate is decided by the bank. Therefore, we further discuss that the bank acts as a Stackelberg leader and charges two interest rates for the manufacturer under the PCG and TPCG schemes, respectively. We assume that the capital market is perfect, and the bank occupies a competitively priced (Zhou and Groenevelt, 2008; Yan et al., 2016; Bi et al., 2018). Then, we demonstrate the impact of endogenous interest rates on the profits of supplier. 7.1. Bank’s problem under PCG To reduce the potential loss, the bank requires the supplier to provide a credit guarantee for the manufacturer. According to the best responses of the supplier and manufacturer, the bank charges an interest rate r1 for the manufacturer under PCG. At the end of the selling period, if the manufacturer earns enough revenue to repay loan obligation, then the bank will obtain the loan and interest L1 (1 + r1) . However, if the revenue of the manufacturer cannot cover L1 (1 + r1) , then the manufacturer will be e1 G )] to the bank. Additionally, the supplier has the responsibility required to repay the entire revenue [min(D1, Q1 ) pe ( Q1 to repay [A1 min(D1, Q1 )] to the bank because of providing a credit guarantee . As we assume that the bank is in a competitive capital market, the loan L1 is equal to the expected revenue of the bank, as shown below:
L1 = E min{L1 (1 + r1), [min(D1, Q1 )
pe ( Q1
e1
G )] + [A1
(8)
(D1, Q1 )]}
We derive the Proposition 6 to show the optimal decision of the bank. Proposition 6. Under PCG, given the coefficient of credit guarantee and the best response of supplier and manufacturer, the optimal interest rate charged by the bank is characterized as r1 =
A e1 ) 0 1 F (x ) dx . L1
(1
Proposition 6 demonstrates that the optimal interest rate charged by the bank is heavily dependent on the loan size L1 , the coefficient of credit guarantee, and the bankruptcy threshold A1 of the manufacturer. When the supplier provides no credit guarantee, that is, = 0 , the optimal decisions of the capital-constrained manufacturer become identical to that of the manufacturer with sufficient capital. The result is similar to that in the prior literature (Kouvelis and Zhao, 2012; Jing et al., 2012; Chen, 2015). However, when the supplier provides full credit guarantees, that is, = 1, the bank will not face any bankruptcy risk from the manufacturer and charge no interest rate because of a perfectly competitive banking market. 7.2. Bank’s problem under TPCG 2
Under TPCG, the bank provides a loan ve2 to the manufacturer and charges an interest rate r2 based on the best responses of the 2 manufacturer and the supplier. It must be noted that, under TPCG, the bank prioritizes collection of the outstanding amount (Yang and Birge, 2018; Ivashina and ve 2 e2 G ) of the manufacturer cannot cover 22 (1 + r2) , then the Iverson, 2014). Therefore, if the revenue min(D2 , Q2 ) pe ( Q2 manufacturer will use the entire revenue to repay the loan amount and interest. However, the supplier cannot collect any liquidation [b2 min(D2 , Q2 )] to the bank, where from the manufacturer, and has the responsibility to repay
b2 =
ve 2 2 (1 2
+ r2) + pe ( Q2
e2
G).
2
As we assume that the bank is in a competitive capital market, the loan ve2 is equal to the expected revenue of the bank, shown as 2 below:
ve2 2
2
= E min
ve2 2 (1 + r2), min(D2 , Q2 ) 2
pe ( Q2
e2
G ) + [b2
min(D2 , Q2 )]
(9)
We have the following proposition to show the optimal decision of the bank. Proposition 7. Under TPCG, given the coefficient interest rate charged by the bank is r2 =
(1
b ) 02
of credit guarantee and the best response of the supplier and manufacturer, the optimal
e2
ve 2 2 2
F (x ) dx
. 2
Proposition 7 demonstrates that the optimal interest rate under TPCG is heavily dependent on the loan size ve2 and coefficient 2 of credit guarantee. However, different from that under PCG, the optimal interest rate is not directly influenced by the bankrupt threshold A2 of the manufacturer. The reason is that the bank prioritizes the collection of the outstanding amount. As a result, the ve 2 bank only focuses on the expected revenue of the manufacturer for procuring the loan amount and interest 22 (1 + r2) .
16
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Fig. 15. The optimal interest rates under different coefficients of credit guarantee.
7.3. Comparison analysis under endogenous interest rates In this section, we discuss the influence of endogenous interest rates on the profits of supplier under PCG and TPCG. Due to the limited space, we put other results (e.g. the optimal decisions of the supplier and manufacturer) in the Appendix A (see Figs. A.7–A.10). The parameters are set the same as the numerical study in Section 6.1 and G = 3. Fig. 15 demonstrates that the optimal interest rate decreases with coefficient of credit guarantee under PCG, because bank would transfer more risk to the supplier. However, under TPCG, an increase in the credit guarantee leads to raise the interest rate and, 0.5), the supplier has a weaker subsequently, to decrease. When credit guarantee range increases in a relatively low (0 < dominant and would set a higher wholesale price to hedge the risk from the manufacturer (see Fig. A.7). Thus, the manufacturer has to make a more conservative decision on the ordering quantity and level of emission reduction under TPCG (see Figs. A.8 and A.9) The demand might be significantly decreasing with credit guarantee, when the consumers have higher low-carbon awareness and the level of emission reduction is decreasing. Therefore, the bank would set a higher interest rate. Alternatively (0.5 < < 1), the bank would transfer more risk to the supplier. However, the supplier has a greater dominant and would set a lower wholesale price to induce the manufacturer to place a larger order and invest more on emission reduction. Thus, the bank would bear less risk and set a lower interest rate. Especially, when = 1, the bank would transfer the entire risk to the supplier, thus setting no interest rate under PCG and TPCG. According to Fig. 16, it is obvious that the profit of the supplier is heavily dependent on the interest rate decided by the bank. The tendency of the profit generated by the supplier is completely opposite to that of the optimal interest rate under PCG and TPCG. The profit of the supplier increases with the credit guarantee under PCG. The reason is that, with an increase in the credit guarantee, the bank transfers the risk to the supplier and charges a lower interest rate for the manufacturer under PCG. As a result, the supplier may have greater bargaining power on wholesale price to extract the amount from the manufacturer and earn more profit. However, under TPCG, an increase in the credit guarantee leads to a decrease in the profit of the supplier and, subsequently, to an 0.5), the bank charges a higher interest rate, increase. When the credit guarantee is increasing within a relatively low range (0 <
Fig. 16. The profit of the supplier with endogenous interest rates. 17
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and the supplier has a lower bargaining power and bears a higher bankruptcy risk from the manufacturer. As a result, the supplier might set a higher wholesale price (see Fig. A.7) to keep the manufacturer from making a radical decision regarding operations (see Figs. A.8 and A.9). Alternatively (0.5 < < 1), the bank would charge a lower interest rate, and the supplier would have a greater bargaining power and earn more profit from the manufacturer. When = 1, the profit of the supplier under TPCG would be identical to that under PCG because the supplier would face the entire bankruptcy risk from the manufacturer under PCG and TPCG. Fig. 16 also shows that the profit of the supplier under PCG is higher than that under TPCG, when the credit guarantee is within a middle range. However, the supplier exhibits willingness to provide TCF to the manufacturer, when the credit guarantee is within a relatively higher range. Therefore, the main insights of fixed interest rates in Proposition 5 continue to hold. 8. Conclusion This study investigates an SCF system with one supplier and one capital-constrained and emission-dependent manufacturer under the cap-and-trade regulation. We consider PCG and TPCG financing schemes for the manufacturer to execute the decisions regarding the emission reduction investment and the order quantity. We derive the equilibrium strategies of the supply chain’s members under the two financing schemes, and compare with that under a benchmark i.e., the manufacturer has enough capital. Additionally, we relax the assumption of fixed interest rates under the two financing schemes and find that the main insights of fixed interest rates continue to hold. According to the results of the analysis, we find that the optimal ordering quantity and the level of emission reduction will not be influenced by the emission cap under the benchmark scenario. However, under PCG and TPCG, given the wholesale price, the optimal ordering quantity decreases with the emission cap. Furthermore, we find that the wholesale price determined by the supplier is heavily dependent on the sensitivity of the ordering quantity under the two financing schemes. Additionally, the capital-constrained manufacturer will place a large order, but invest less in the emission reduction, under the two financing schemes when compared to that under the benchmark. According to a different credit guarantee, there exists a trade-off for the supplier between the additional revenue and the potential loss when the manufacturer faces bankruptcy. Specifically, if the credit guarantee is within a relatively low range, the supplier will not exhibit willingness to provide TCF to the manufacturer. According to the results of the numerical study, we find that the supplier can obtain more profit under the two financing schemes than that under the benchmark scenario. However, the capital-constrained manufacturer would earn less profit. The reason is that the supplier will squeeze the manufacturer by determining a higher wholesale price. This is because the bank would require the capitalconstrained manufacturer to obtain credit guarantee from the supplier. Additionally, the adoption of PCG or TPCG will bear the same outcome for the manufacturer when the consumer low-carbon awareness is within a relatively low range. However, there are a few limitations in this study that need attention. For example, finance leasing is another popular financing scheme that is considered by the emission-dependent and capital-constrained enterprise. It is possible to derive some managerial insights when the capital-constrained enterprise selects finance leasing or other financing schemes. Furthermore, in practice, the manufacturer expresses reluctance to share information to the upstream supplier. We can consider the information asymmetry between the supply chain’s members to extend this study. CRediT authorship contribution statement Song Xu: Conceptualization, Methodology, Writing - original draft, Investigation. Lei Fang: Supervision, Writing - review & editing, Funding acquisition. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgement This work was supported by the National Natural Science Foundation of China [grant No.71671095]. Appendix A Proof of Lemma 1. Under benchmark, the expected profit of the manufacturer can be written as: m b
= E min(Db , Qb) + pe (G + eb =Qb
Qb 0
eb
Qb )
F (x ) dx + pe (G + eb
Qb )
We first take the first and second derivatives of d2 bm dQb2
=
f (Qb
we can obtain:
veb2 2
wb Qb
wb Qb m b
veb2 2
(A.1)
with respect to the ordering quantity Qb :
eb) , respectively. Then, taking the first and second derivative of d bm deb
= F (Qb
eb) + pe
veb and
d2 bm deb2
=
2f
(Qb 18
eb )
m b
d bm dQb
= F (Qb
eb)
(pe + wb) and
with respect to the level eb of emission reduction,
v , respectively. Furthermore, differentiating
m b
Qb
with
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang 2 m b
respect to the level eb of emission reduction, we can obtain:
eb) > 0 . As
det H (Qb, eb) = vf (Qb definite, and
m b
m b
Qb
eb). Then, we can obtain the determinant
= f (Qb
Qb deb
< 0 and det H (Qb, eb) > 0 , we verify that the Hessian matrix H (Qb, eb) is a negative
is a joint concave in Qb and eb . Then, the optimal ordering quantity and the level of emission reduction should satisfy: p + (1
p
w )
b e F (Qb eb) = pe + wb and eb = e . v eb) pe written and have cs Qb . We plug wb = F (QbN The expected profit of the supplier can be written as: bs = wb Qb s eb) pe cs ) QbN . Then, we take the first derivatives of bs with respect to QbN , shown as b (QbN ) = (F (QbN
d bs
dQbN
= (F (QbN
F (QbN
eb)
eb)[1
pe
cs )
eb) . Therefore, the optimal ordering quantity is Qb = QbN , where should satisfy
QbN f (QbN
eb)] = pe + cs , and the optimal wholesale price is wb = F (QbN
QbN h (QbN
eb )
pe . □
Proof of Proposition 1. Under PCG, the expected profit of the manufacturer can be written as:
{
= E min(~ + e1, Q1)
m 1
=Q1
pe ( Q1
e1
(w Q + ) (1 + r ) + p (G + e 1
ve12 2
1
1
(w Q + ) (1 + r ) }
G)
e
1
=1
Q1 2 m 1 Q12
=
w1 (1 + r1)
f ( Q1
pe
e1 )[h (Q1
e1)
m 1
=
ve1 (1 + r1) + pe + F (Q1
=
v (1 + r1)
e1 2 m 1 e12
= v (1 + r1)
2f
( Q1
Furthermore, differentiating 2 m 1
Q1 e1
= f (Q1
m 1
Q1
(A.3)
e1)
(A.4)
e1)]
with respect to the level e1 of emission reduction, we can obtain:
e1) + [ve1 (1 + r1)
e1 )[ h (Q1 m 1
e1)
e1)
e1) + [ve1 (1 + r1)
F (Q1
(A.2)
with respect to the ordering quantity Q1:
[w1 (1 + r1) + pe ] h (A1
Then, taking the first and second derivatives of
+
1
e1) + [w1 (1 + r1) + pe ] F (A1
[w1 (1 + r1) + pe ]2 f (A1
e1)
= F ( Q1
F (Q1
m 1
ve12 2
Q1 e1 F (x ) dx A1 e1
Q1)
1
(1) We first take the first and second derivatives of m 1
1
pe
pe
] F (A1
]2 f (A1
[ve1 (1 + r1)
e1)
(A.5)
e1) pe
] h (A1
(A.6)
e1)]
with respect to the level e1 of emission reduction, we can obtain:
e1) + [ve1 (1 + r1)
pe
][w1 (1 + r1) + pe ] f (A1
e1)
(A.7)
Then, we can obtain the determinant det H (Q1, e1) :
det H (Q1, e1) = v (1 + r1 ) F (Q1
e1)[h (Q1
e1)
[w1 (1 + r1) + pe ] h (A1
(A.8)
e1)] > 0
2 m 1 Q12
< 0 and det H (Q1, e1) > 0 , we verify that the Hessian matrix H (Q1, e1) is a negative definite, and As and e1. Then, the optimal ordering quantity and the level of emission reduction should satisfy: F (Q1
e1) = [w1 (1 + r1) + pe ] F (A1
F (Q1
e1) = [
ve1 (1 + r1) + pe ] F (A1
m 1
is joint concave in Q1 (A.9)
e1)
(A.10)
e1)
The optimal level e1 of emission reduction can be rewritten as e1 = (2) Taking the derivative of e1 with respect to w1, we have creases with the wholesale price.
de1 dw1
=
v
[w1 (1 + r 1) + pe ] + pe v (1 + r 1 )
.
< 0 . Therefore, the optimal level of emission reduction de-
According to Eq. (A.9), taking the first-order derivation of Q1 with respect to w1, we have:
dQ1 = dw1 If
1 h (Q1
2
v
1 (1 + r1 ) [w1 (1 + r1) + pe ] h (Q1
[w1 (1 + r 1) + pe ] Q1 h (A1 e1 )
e1 )
[w1 (1 + r 1) + pe ] h (A1
e1 )
[w1 (1 + r1) + pe ] Q1 h (A1 e1 )
e1 )
[w1 (1 + r1) + pe ] h (A1
is larger than zero, then we can obtain
Kouvelis and Zhao (2012), Chen and Cai 1 [w1 (1 + r1) + pe ] Q1 h (A1 e1 ) > 1 Q1 h (Q1 e1 ) > 1
(A.11)
e1 ) dQ1 dw1
< 0 . As 1
Q1 h (Q1 ) > 0 has been proofed in
(2011), and Gao et al., (2018), dQ Q1 h (Q1 ) > 0 . Therefore, we can obtain dw1 < 0 . 1
19
we
have
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
(3) Taking the first-order derivation of Q1 with respect to G, we have:
pe h (A1
dQ1 = dG h (Q1
e1 )
e1 )
[w1 (1 + r1) + pe ] h (A1
e1 )
<0
(A.11)
It is obvious that given the wholesale price, e1 will not be influenced by the carbon quota G allocated by the government. In addition, we can also obtain other intuitive result. Under PCG, given the wholesale price the optimal ordering quantity Q1 and the level e1 of emission reduction decrease with the wholesale price w1. de Taking the derivative of e1 with respect to w1, we have dw1 = v < 0 . Therefore, the optimal level of emission reduction decreases 1 with the wholesale price. According to Eq. (A.9), taking the first-order derivation of Q1 with respect to w1, we have:
If
1
1 (1 + r1 ) [w1 (1 + r1) + pe ] h (Q1
2
dQ1 = dw1
v
[w1 (1 + r 1) + pe ] Q1 h (A1 e1 ) e1 ) [w1 (1 + r 1) + pe ] h (A1 e1 )
h (Q1
[w1 (1 + r1) + pe ] Q1 h (A1 e1 )
e1 )
[w1 (1 + r1) + pe ] h (A1
is larger than zero, then we can obtain
Kouvelis and Zhao (2012), Chen and Cai 1 [w1 (1 + r1) + pe ] Q1 h (A1 e1 ) > 1 Q1 h (Q1 e1 ) > 1
(A.12)
e1 ) dQ1 dw1
< 0 . As 1
Q1 h (Q1 ) > 0 has been proofed in
(2011), and Gao et al., (2018), we dQ Q1 h (Q1 ) > 0 . Therefore, we can obtain dw1 < 0 . □
have
1
Proof of Proposition 2. Under PCG, the expected profit of the supplier can be rewritten as: s 1
= (w1 Q1 A1
+
cs Q1 )[1 e1
c1 Q1
cs Q1 )
A1
d 1s
s 1 dQ1
=
dw1
Q1 dw1
=[w1
+
cs
s 1 de1
= where 3 (w1)
(w1) = =
v
We d (A1 e1 ) dw1
e1
+
1
1 (w1)
cs ) [h (Q1 1
have
+
+
e1 )]
e1 )
Additionally, we take the derivative
dQ1 dw1
de
e1 ) dw1 + Q1
[Q1 (1 + r1) + pe ] F (A1
1
3 (w1) ,
× [1 in
which e1 )]
(A.14) 1 (w1)
e1 ) Q 1
0.
Furthermore, e1 )
[w1 (1 + r 1) + pe ] h (A1 e1 ) [1 Q1 h (Q1 e1 )] of 1 [w1 (1 + r 1) + pe ] Q1 h (A1
Q1 h (Q1
[ (1 + r1 ) Q1 h (A1
h (Q1
e1 ) =
<0 , and (A1
dh (Q1 d (Q1
e1 ) =
e1 ) , e1 )
e1 )
h (A1
d (A1 e1 ) dw1
e1 )[Q1
dh (A1 d (A1
= (1 + r1 ) Q1
2 (w1)
as
e1 )
=
Therefore, we can obtain
e1 )
(1 + r1 ) F (A1
[w1 (1 + r1) + pe ] Q1 h (A1 e1 ) Q1 + Q1 h (A2 ) =
with
and
w1
(i.e.,
e1 )] is increasing with w1.
e1 )]
e2 )[Q2 d (Q1 e1 ) dw1
e1 )
[w1 (1 + r 1) + pe ] h (A1
e1 ) + [w1 (1 + r1) + pe ] Q1 h (A1 2
(1 + r 1 ) F (A1 e1 )][1 Q1 h (Q1 e1 )] , 1 [w1 (1 + r 1) + pe ] Q1 h (A1 e1 )
decreases
e1)
e1 )
e2 ] ]] × [1
e1 )][Q1
< 0.
(w1 ) > 0 . Furthermore, we have
20
e1 ] > 0
Q1 h (Q1
1 (1 + r1 ) [w1 (1 + r 1) + pe ] h (Q1
=
e1 ) > (Q1 e1 ) > Q1 and obtain the following inequality We have (A1 numerator> [1 Q1 h (Q1 e1 )] × [ h (Q1 e1 ) + [w1 (1 + r1) + pe ] h (A1 e1 )] Q1 + [ Q1 h (Q1
[1
with respect to w2 . The denominator of the derivative is obviously
e1 ) dQ e1 , Q1 = dw1 , (Q1 e1 ) 1 1 [w1 (1 + r 1) + pe ] Q1 h (A1
h (Q1
(A1
< 0 ), we have that [1
e1 ] ] × [1
[w1 (1 + r1) + pe ][h (A1
e1 ) =
=
(w1 cs )(1 + r 1 ) , [w1 (1 + r 1) + pe ]
.
larger than zero, and the numerator can be written as: numerator=[ h (Q1
e1 )
(w1)]
[w1 (1 + r 1) + pe ] Q1 h (A1
h (Q1
min(D1, Q1 ) dF (x )
w1
[w1 (1 + r 1) + pe ] Q1 h (A1 e1 ) pe (1 + r 1 ) 1 (w1) = [w1 (1 + r 1) + p ]2 > e
= (1 + r1 ) Q1
Q1)
with respect to w1, we have
[w1 (1 + r 1) + pe ] h (A1
1
pe (G + e1
1
s 1
] F (A1
2 (w1)
e1 )
) (1 + r )
(A.13)
[w1 (1 + r1) + pe ] F (A1 pe
ve1 2 2
F (x ) dx
[w1 (1 + r 1) + pe ] Q1 h (A1 e1 ) e1 ) [w1 (1 + r 1) + pe ] h (A1 e1 )
h (Q1
2 (w 1
s 1
+
e1 dw1
[ve1 (1 + r1) 1
1
0
Taking the first derivative of
e1 )]
(w Q
w1 Q1
0
= (w1 Q1
F (A1
.
e1 )]
, where
[w1 (1 + r1) + pe ] Q1 h (A1 e1 ) e1 ) [w1 (1 + r 1) + pe ] h (A1 e1 )
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
3
2Q 1
(w ) =
× >
2Q 1
{
2 (w e1 ) [w1 (1 + r 1) + pe ] Q1 h (A1 e1 )] 1 cs ) Q1 [h (Q1 e1 ) 1 [w1 (1 + r 1) + pe ] Q1 h (A1 vQ1 2
1 cs ) vQ1
{[w1 (1 + r 1) + pe ]Q1 h (A1
e1 )[Q1 e1 ] ] [h (Q1 e1 )] [w1 (1 + r1) + pe ] Q1 h (A1
[1
2 (w
+
1
e1 )} e1 )
[w1 (1 + r 1) + pe ] Q1 h (A1
[h (Q1
1
1
e1 ) [w1 (1 + r 1) + pe ] Q1 h (A1 e1 )] e1 ) [w1 (1 + r 1) + pe ] Q1 h (A1
}
.
2 (w
2 (w e1 ) [w1 (1 + r 1) + pe ] Q1 h (A1 e1 )] c ) e )[Q e ]] [h (Q 1 cs ) Q1 [h (Q1 + vQ1 s [1 [w (1 +1 r ) +1p ] Q1 h (A1 e )] e1 ) 1 [w1 (1 + r 1) + pe ] Q1 h (A1 vQ1 2 1 1 1 1 1 1 e 2 (w h (Q1 e1 ) (1 + r 1 ) 1 cs ) > 1 > 0 e1 )] [1 [w1 (1 + r 1) + pe ] Q1 h (A1 vQ1 2 [w1 (1 + r 1) + pe ]
Therefore, we can obtain that (w1) =
1 (w1)
+
2 (w1)
+
3 (w1)
increases with w1.
When (w1) > 1, we find that (w1 ) > (w1) > (w1) > 1 . In this situation, we can obtain that
d 1s dw1
< 0 , the optimal wholesale d s
price is w1 = w1. In addition, when (w1 ) < 1, we have that (w1) < (w1) < (w1 ) < 1 . In this situation, we can obtain that dw1 > 0 ; the optimal wholesale price is w1 = w1 . When (w1) < 1 and (w1 ) > 1, we have strates that there exists a unique wholesale price w1 when (w1) = 1. □
d 1s
dw1 w = w 1 1
< 0 and
1
d 1s
dw1 w = w 1 1
> 0 , which demon-
Proof of Lemma 5. Under TPCG, the expected profit of the manufacturer can be written as: m 2
{
= E min(D2 , Q2 ) =Q2
pe ( Q2
ve22 (1 2
w 2 Q2
G
+ r2)
e2)
pe ( Q2
G
d =1 dQ2
d 2 2m dQ2 2
=
w2
pe
F (Q 2
ve2 (1 + r2) + pe + F (Q2
d 2 2m = de2 2
2f
v (1 + r2)
(Q 2
Furthermore, differentiating 2
m 2
Q2 e2
= f (Q 2
F (x ) dx
(A.15)
e2)
(A.16) (A.17)
m 2
with respect to the level e2 of emission reduction, we can obtain:
e2) + [ve2 (1 + r2)
e2) + [ve2 (1 + r2)
m 2
+
e2)
Then, taking the first and second derivatives of
d 2m = de2
}
with respect to the ordering quantity Q2 :
m 2
e2) + [w2 + pe ] F (A2
e2) + [w2 + pe ]2 f (A2
f (Q 2
+ r2)
Q 2 e2 A2 e 2
e2)
We first take the first and second derivatives of m 2
ve 22 (1 2
w2 Q2
pe
] F (A2
]2 f (A2
pe
e2)
(A.18)
e2)
(A.19)
with respect to the level e2 of emission reduction, we can obtain:
Q2
e2 ) + [w2 + pe ][ve2 (1 + r2)
pe
] f (A2
e2)
(A.20)
Then, we can obtain the determinant det H (Q2, e2) :
det H (Q2, e2) = v (1 + r2 ) F (Q2
e2)[h (Q2
e2 )
[w2 + pe ] h (A2
e2 )] > 0
d 2m
As dQ < 0 and det H (Q2, e2) > 0 , we verify that the Hessian matrix H (Q2 , e2) is a negative definite, and 2 and e2 . Then, the optimal ordering quantity and the level of emission reduction should satisfy:
F (Q 2
e2 ) = [w2 + pe ] F (A2
m 2
is joint concave in Q2 (A.21)
e2 )
[w2 + pe ] + pe
e2 =
(A.22)
v (1 + r2 )
Proof of Proposition 3. The expected profit of the supplier under TPCG can be rewritten as: s 2
= (w2 Q2
A2
cs Q2 )
b2
Taking the first derivative of d 2s dw 2
=
s 2 dQ2 Q2 dw 2
=[w2
+
cs
s 2 de 2 e2 dw 2
As
dQ2 dw 2
=
v (1 + r 2 )
s 2,
F (x ) dx
pe
b2
e2
0
F (x ) dx
(A.23)
we have
s 2
w2
(w2 + pe ) F (A2
+[ [ve2 (1 + r2 ) 2
+
e2 e2
e2 ) + (1
] F (A2
1 1 [w 2 + pe ] h (Q2
e2 ) + (1
[w 2 + pe ] Q2 h (A2 e2 )
) pe F (b2
e2 )]
)[ve2 (1 + r2) e2 )
[w 2 + pe ] h (A2
e2 )
and
de2 dw 2
21
=
dQ2 dw 2
pe v (1 + r 2 )
] F ( b2 ,
d 2s dw 2
de
e2 )] dw2 + Q2 F (A2 2
can be rewritten as
e2 )
(A.24)
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
1 d 2s = dw2 h (Q2 where 3 (w 2 )
(w 2 ) = =
2 (w
2
[w2 + pe ] Q2 h (A2 e2 )
1 (w 2 )
cs )
Similar to (w2) = 1 (w2 ) +
+
2 (w 2 )
w 2 2 (1 ) F (b 2 v (1 + r 2 )
2
e2 )
[w2 + pe ] h (A2
+
× (1
in which
3 (w 2 )
e2 ) [h (Q2 [1
e2 )
e2 )
1 (w 2 )
[w 2 + pe ] h (A2
[w 2 + pe ] Q2 h (A2
(w1) = proofing (w2 ) + 3 (w2 ) > 0 .
1
(w2 ))
(w1) +
=
e2 )]
e2 )]
2
(w 2
(w1) +
(A.25) cs ) + (1
) pe F (b2
e2 )
[w 2 + pe ]
.
in
(w1) > 0
3
,
2 (w 2 )
=
[1 Q2 h (Q2 e2 )] F (A2 e2 ) [1 [w 2 + pe ] Q2 h (A2 e 2 )]
Proposition
2,
we
also
and have
d s
When (w2 ) > 1, we have that (w2 ) > (w2) > (w2 ) > 1 . In this situation, we can obtain that dw2 < 0 , and the optimal 2 wholesale price is w2 = w2 . Additionally, when (w2 ) < 1, we have that (w2 ) < (w2 ) < (w2 ) < 1 . In this situation, we can obtain that d 2s dw 2
w2= w 2
d 2s
> 0 ; the optimal wholesale price is w2 = w2 . When
dw 2
(w2 ) < 1 and
> 0 , that demonstrates that there exists an unique wholesale price w2 when
(w2 ) > 1, we have
d 2s
dw 2 w = w 2 2
< 0 and
(w1) = 1. □
Proof of Proposition 4. We employ the proof by contradiction to indicate wb < w1 (1 + r1) . The minimum wholesale price under PCG e1 ) w1= w1 (QbN eb) . We should satisfy F (Q1 e1 ) w1= w1 = (cs + pe ) (wb + pe ) = F (QbN eb) . Therefore, we have (Q1 e1 ) w1= w1 = Q1 (cs + pe ). assume wb w1 (1 + r1) . We can rewrite the equation of minimum wholesale price under PCG as Q1 F (Q1 Taking the first order of the equation with respect to Q1, we have d (Q1 F (Q1 e1)) dQ1 = F (Q1 e1 )[1 Q1 h (Q1 e1 )] w1= w1 = cs + pe . The optimal ordering quantity under benchmark can be written as F (QbN eb)[1 QbN h (QbN eb)] = pe + cs . eb)[1 QbN h (QbN eb)]. As we assume wb w1 (1 + r1) , we e1 )[1 Q1 h (Q1 e1 )] w1= w1 = F (QbN Therefore, we have F (Q1 can further obtain However, the result contradicts with that F (Q1 e1 ) w1= w1 > F (QbN eb ) . F (Q1 e1 ) w1= w1 = (cs + pe ) (wb + pe ) = F (QbN eb ) . Therefore, we can obtain wb < w1 (1 + r1) . The proof of wb < w2 is similar with that of wb < w1 (1 + r1) , and we omit here. Finally, we can obtain eb > e1 and eb > e2 . Q1 . Similar to Jing et al., (2012), we can rewrite the equation of the optimal ordering quantity Then, we intend to proof Qb e1 ) is a unimodal function in Q1 F (Q1 e1 ) = Q1 [w1 (1 + r1) + pe ] F (A1 e1 ) . As the assumption of failure rate, Q1 F (Q1 [D1, D1]. Thus, there exist a unique Q1, and Q1 F (Q1 e1 ) is increasing in [D1, Q1], but decreasing in [Q1, D1]. As d [Q1 F (Q1 e1)] dQ1 = F (Q1 e1 )[1 Q1 h (Q1 e1)], we have [1 Q1 h (Q1 e1)] = 0 Furthermore, when w1 (1 + r1) + pe = 1, 1 pe G = 0 based on assumption of the optimal ordering quantity with exponential distribution we have 2 ve1 2 (1 + r1) pe e1
Q1 [1
(Q1
1
y ln[w1 (1 + r1) + pe ] + 2 ve1 2 (1 + r1)
[w1 (1 + r1) + pe ]] =
e1 ) = Q1 [w1 (1 + r1) + pe ] F [Q1 [w1 (1 + r1) + pe ]
dQ1 dw1 < 0 ,
we
have
[1
QbN h (QbN
eb)] =
e1 ] pe + cs
F (QbN
pe e1
pe G ,
and
then
obtain
e1)] = 0
we,
Q1 F
. Therefore, we have Q1 = Q1 = Q1 when w1 (1 + r1) + pe = 1. As
eb)
=0 and [1
Q1 (w1 ) h (Q1 (w1)
and
thus
Q2 is similar with that of Qb Q1 , and we omit here. Q1 = Q1 (w1) QbN . The proof of Qb [w1 (1 + r 1) + pe ] + pe [w 2 + pe ] + pe e = According to e1 = and , we consider two scenarios w2 w1 (1 + r1) and w2 > w1 (1 + r1) 2 v (1 + r 1 ) v (1 + r 2 ) to discuss the comparison of the optimal decisions of the manufacturer under different financing schemes. If w2 w1 (1 + r1) , we have e1 e2 because we assume r1 = r2 . Then, we intend to verify Q2 > Q1 . We assume that the stochastic factor of demand follows an exponential distribution with mean y. The optimal ordering quantities under PCG and TPCG can be rewritten as 1 1 Q1 [1 [w1 (1 + r1) + pe ]] = y ln[w1 (1 + r1) + pe ] + 2 ve1 2 (1 + r1) pe e1 pe G and Q2 [1 (w2 + pe )] = y ln[w2 + pe ] + 2 ve2 2 (1 + r2) 1 ve 2 (1 2 2
+ r2)
pe e2
pe e2 .
pe G , respectively. When w2 = w1 (1 + r1) = w2 , we transfer to compare The
derivative
of
1 ve 2 (1 2 2
+ r1)
pe e2
with
pe e1
pe G
respect
to
e2
is
larger
1 ve 2 (1 2 1
+ r1)
than
zero,
pe e1
that
and
is,
1 v (1 + r2 ) e2 pe = [w2 + pe ] = v (1 + r1 ) e1 pe > 0 . We find that 2 vx 2 (1 + r1) pe x is increasing with x . As e1 < e2 , we can Q 2 ( w 2 ) > Q1 . obtain Q2 pe = [w2 + pe ] = v (1 + r1 ) e1 pe . The derivative of When w2 = w1 (1 + r1) = w2 , we have v (1 + r2 ) e2 1 ve 2 (1 + r2) pe e2 pe G e2 with respect to e2 is less than zero, that is, ve2 (1 + r2) pe = [w2 + pe ] < 0 . Therefore, we 2 2
pe G e2 < 2 ve1 2 (1 + r1) can obtain 2 ve2 2 (1 + r2) pe e2 that of w2 w1 (1 + r1) , and we omit here. □ 1
1
e1 . The proof of scenario w2 > w1 (1 + r1) is similar to
d 2s (w 2 , )
b2
= 0 d we intend to proof Case 1. s 2
e2
F (x ) dx < 0 . Therefore, both s s = 0 and 1 ( ) > 2 ( ) when
s 1 (w1 , s 2( ) >
d 1s (w1 , )
e1
F (x ) dx < 0 and
) and 2s (w1 , ) are monotonically decreasing with s = 1. □ 1 ( ) when
[0, 1]. Then,
Proof of Proposition 5. By the Envelope Theorem (Varian, 1992, p. 490), we have
d
= 0 . The profit of the supplier under PCG and TPCG can be rewritten as
= (w2 Q2 cs Q2 ) mean y, we have
A2
b2
e2 e2
A1
=
0
s 1
= (w1 Q1
cs Q1 ) and
F (x ) dx , respectively. As the stochastic factor of demand follows an exponential distribution with
22
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang s 12
s 1
=
s 2
=(w1
cs ) Q1
=cs (Q2
A2 e2 b2 e2
As x > ln x , we have
) when
s 2(
) >
Case 2.
A2 e2 b2 e2
cs ) Q2 + A2
Q1 ) + w1 Q1
> w 1 Q1
s 1 (
(w 2
e2
w1 Q1 y
F (x ) dx = y
w1 Q1 y
e
b2
y
F (x ) dx
e2
b2
e2
F (x ) dx
A2
e
A2
+e
y
e2
y
e2
e
> ln
= 0.
(
b2
y
e2
(A.26)
w1 Q1 y
)+
b2
e2
ln 1
y
e
= 1. The profits of the supplier under PCG and TPCG can be rewritten as A2
w 2 Q2 y
s 1
> 0 . Therefore, we can obtain
= (w1 Q1
A1
cs Q1 )
0
e2
e1
F (x ) dx
= (w2 Q2 cs Q2 ) F (x ) dx , respectively. We first employ the proof by contradiction to indicate w1 (1 + r1) w2 and 0 s s = 1, and then proof = 1. We have when We assume w1 (1 + r1) w2 when 2 ( = 1) > 1 ( = 1) . s Q2 1 s s s Q1 Q2 <0 = F (Q1 e1 ) cs pe and because and 2 (Q 2 w 2 ) 2 (Q 2 w 2 ) 1 (Q1 w1 ) , w Q s 2
2
s
s 2 (Q2
s 1 (Q1
w2 )
w1 ) = (w 2
s 2(
= 1) > 1
2
s
= (w2 + pe ) F (A2
Q2
and
s 2 (Q 2
(1 + r2 ) A1 0
e1
pe x
w2 )
s 2 (Q1
e2
F (x ) dx
0
s 2 (Q 2
pe G .
pe e2
e2 )
cs
Given
pe = F (Q2
w2 ) = [w1 (1 + r1)
the
e2 )
cs ] Q1
0
F (x ) dx . Therefore, we can obtain
s 2 (Q 2
w2 )
s 2
F (x ) dx = w1 Q2 r1 > 0
= (w2 Q2
wholesale
w2)
w2 when A2
cs Q2 )
e2
0
price
(w1 (1 + r 1) + pe ) Q1 + 12 ve2 2 (1 + r 2) pe e2
s 2 (Q 2
e1
0
w2 ,
(A.27)
= 1. Then, we
F (x ) dx , where we
can
pe > 0 . When w2 = w1 (1 + r1) = w2 , we have Q2 (w2 )
cs
x is decreasing with x, we can obtain that
pe G
A1
cs ) Q1
w1 ) . Therefore, we have w1 (1 + r1)
s 1 (Q1
w2 )
(w 1
= 1) . Similar to Cao et al. (2019), we first discuss
s 1 (
A2 = (w2 + pe ) Q2 + 2 ve2 2 (1 + r2 )
obtain
A2
cs ) Q2
The result the result contradicts with that
intend to proof
1
pe > 0 hold. However, when w1 (1 + r1) = w 2 , we have Q1 = Q2 (w 2 ), e1 = e2 (w 2 ), and
> 0 and Q2 = F (Q2 e2 ) cs 2 A1 = A2 (w 2 ) , thus obtaining
pe G
e2
F (x ) dx .
(w1 (1 + r 1) + pe ) Q1 + 12 ve 2 2 (1 + r 2) pe e 2
0 s 1 (Q1
w1 ) and
s 2(
) >
s 1 (
pe G
) when
e2
As
Q1 1 vx 2 2
F (x ) dx is less than
= 1.
Proof of Proposition 6. Under PCG, the equation of the bank’s problem is shown as follows:
L1 = E min{L1 (1 + r1), [min(~ + e1 , Q1 ) =
+ A1
L1 (1 + r1 ) dF (x ) +
e1
= L1 (1 + r1)
(1
A1
)
e1
0
A1
e1
0
pe ( Q1
(1
e1
G )] + [A1
) D1 + A1
pe ( Q1
e1
min(~ + e1 , Q1 )]} G ) dF (x )
F (x ) dx
(A.28)
Therefore, the optimal interest rate charged by the bank under PCG can be written as r1 =
A ) 0 1
(1
L1
e1 F (x ) dx
□
Proof of Proposition 7. Under TPCG, the equation of the bank’s problem is shown as follows: ve2 2 2
= Emin =
=
b2 0 ve2 2
2
{
e2
ve2 2 (1 2
(1
(1 + r2)
+ r2 ), min (~ + e2 , Q2 ) ) D2 (1
pe ( Q2 )
b2 0
e2 e2
pe ( Q2
e2
G ) + b2 dF (x ) +
G ) + [b2 + b2 e2
ve2 2 (1 2
min (~ + e2 , Q2 )]
}
+ r2 ) dF (x )
F (x ) dx
(A.29)
Therefore, under TPCG, the optimal interest rate charged by the bank can be written as r2 =
(1
b e2 ) 02 F (x ) dx . ve 2 2 2
□
Figs. A.1-A.6 show the impact of coefficient of credit guarantee on the optimal decisions and profits of the supply chain members with uniform distribution. The results are similar with those of exponential distribution, as shown in main text. Figs. A.7–A.9 demonstrate the optimal decisions of the supplier and manufacturer with endogenous interest rates. Fig. A.10 shows the profits of the manufacturer with endogenous interest rates under PCG and TPCG. Compared with Proposition 5 and Fig. 5, Fig. A.11 demonstrates that the main result continues to hold, thus justifying the assumption of no initial capital of the manufacturer (see Table A1).
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S. Xu and L. Fang
Fig. A1. Optimal wholesale price under different coefficients of credit guarantee and emission caps (Uniform distribution).
Fig. A2. Optimal ordering quantity under different coefficients of credit guarantee and emission caps (Uniform distribution).
Fig. A3. Optimal level of emission reduction under different coefficients of credit guarantee and emission caps (Uniform distribution).
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Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
Fig. A4. The profit of supplier under different coefficients of credit guarantee and emission caps (Uniform distribution).
Fig. A5. The profit of the manufacturer under different coefficients of credit guarantee and emission caps (Uniform distribution).
Fig. A6. The profit of entire supply chain under different coefficients of credit guarantee and emission caps (Uniform distribution).
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Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
Fig. A7. The optimal wholesale price with endogenous interest rates.
Fig. A8. The optimal ordering quantity with endogenous interest rates.
Fig. A9. The optimal level of emission reduction with endogenous interest rates.
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S. Xu and L. Fang
Fig. A10. The profit of manufacturer with endogenous interest rates.
Fig. A11. The profit of supplier with considering the manufacturer’s insufficient initial capital (set as 1). Table A1 The results of the benchmark under the scenario comprising different consumer low-carbon awareness and unit prices of emission permit. Consumer low-carbon awareness
Wholesale price
Ordering quantity
Level of emission reduction
Profit of the supplier
Profit of the manufacturer
Profit of the entire supply chain
10 ( pe = 0.13 ) 12 14 16 18 20
0.4643 0.4654 0.4664 0.4674 0.4683 0.4692
5.9882 6.3063 6.6831 7.1184 7.6125 8.1640
0.0786 0.0934 0.1082 0.1229 0.1376 0.1521
1.1548 1.2081 1.2710 1.3435 1.4256 1.5169
1.8826 1.9891 2.1147 2.2594 2.4232 2.6060
3.0374 3.1972 3.3857 3.6029 3.8488 4.1229
10 ( pe = 0.12 ) 12 14 16 18 20
0.4681 0.4694 0.4706 0.4718 0.4730 0.4741
6.1164 6.4411 6.8250 7.2686 7.7724 8.3355
0.0809 0.0962 0.1114 0.1265 0.1415 0.1564
1.1854 1.2412 1.3068 1.3824 1.4681 1.5635
1.9459 2.0571 2.1882 2.3393 2.5104 2.7014
3.1313 3.2983 3.4950 3.7217 3.9784 4.2649
10 ( pe = 0.11) 12 14 16 18 20
0.4719 0.4733 0.4748 0.4762 0.4776 0.4789
6.2467 6.5775 6.9685 7.4211 7.9339 8.5092
0.0831 0.0989 0.1145 0.1300 0.1454 0.1607
1.2182 1.2763 1.3447 1.4237 1.5128 1.6127
2.0106 2.1264 2.2632 2.4208 2.5993 2.7987
3.2287 3.4028 3.6079 3.8445 4.1121 4.4114
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References Agster, R., Eisinge, F., Cochu, A., 2016. Enabling SME access to finance for sustainable consumption and production in Asia: An overview of finance trends and barriers in China. Available at: http://www.switch-asia.eu/fileadmin/user_upload/Publications/2016/Green_Fina nce_Study_-_2016_-_China.pdf (Accessed date: December 10th, 2019). Asian Development Bank, 2016. Credit guarantees challenging their role in improving access to finance in the Pacific region. Available at: https://www.adb.org/sites/ default/files/publication/ 203871/credit-guarantees.pdf (Accessed date: January 20th, 2020). Bi, G., Fei, Y., Yuan, X., Wang, D., 2018. Joint operational and financial collaboration in a capital-constrained supply chain under manufacturer collateral. Asia-Pac. J. Oper. Res. https://doi.org/10.1142/S0217595918500100. Cai, G., Chen, X., Xiao, Z., 2014. The roles of bank and trade credits: Theoretical analysis and empirical evidence. Prod. Oper. Manage. 23 (4), 583–598. Cao, E., Yu, M., 2018. Trade credit financing and coordination for an emission-dependent supply chain. Comput. Ind. Eng. 119, 50–62. Cao, E., Du, L., Ruan, J., 2019. Financing preferences and performance for an emission-dependent supply chain: Supplier vs. bank. Int. J. Prod. Econ. 208, 383–399. Chan, H.L., Choi, T.M., Cai, Y.J., Shen, B., 2018. Environmental taxes in newsvendor supply chains: A mean-downside-risk analysis. IEEE Transactions on Systems, Man, and Cybernetics: Systems. https://doi.org/10.1109/TSMC.2018.2870881. Chen, X., Cai, G.G., 2011. Joint logistics and financial services by a 3PL firm. Eur. J. Oper. Res. 214 (3), 579–587. Chen, X., Wang, A., 2012. Trade credit contract with limited liability in the supply chain with budget constraints. Ann. Oper. Res. 196 (1), 153–165. Chen, X., 2015. A model of trade credit in a capital-constrained distribution channel. Int. J. Prod. Econ. 159, 347–357. China Green Times. (2019). Sihui provides a green financing–“forestry supply chain financing”. Available at: http://www.forestry.gov.cn/xdly/5201/20190710/ 100817827844799.html, in Chinese. (Accessed date: December 10th, 2019). Dada, M., Hu, Q., 2008. Financing newsvendor inventory. Operations Research Letters 36 (5), 569–573. Daryanto, Y., Wee, H.M., Astanti, R.D., 2019. Three-echelon supply chain model considering carbon emission and item deterioration. Transport. Res. Part E: Logist. Transport. Rev. 122, 368–383. Devalkar, S.K., Krishnan, H., 2019. The impact of working capital financing costs on the efficiency of trade credit. Prod. Oper. Manage. 28 (4), 878–889. Dobos, I., 2005. The effects of emission trading on production and inventories in the Arrow-Karlin model. Int. J. Prod. Econ. 93, 301–308. Du, S., Ma, F., Fu, Z., Zhu, L., Zhang, J., 2015. Game-theoretic analysis for an emission-dependent supply chain in a ‘cap-and-trade’ system. Ann. Oper. Res. 228 (1), 135–149. Du, S., Zhu, L., Liang, L., Ma, F., 2013. Emission-dependent supply chain and environment-policy-making in the ‘cap-and-trade’ system. Energy Policy 57, 61–67. Flysjö, A., 2012. Greenhouse gas emissions in milk and dairy product chains: improving the carbon footprint of dairy products. Department of Agroecology, Aarhus University PhD Thesis. Fujitsu, 2012. The move towards a low carbon society. Available at: https://www.fujitsu.com/ie/Images/low-carbon-society.pdf (accessed date: December 10th, 2019). Gao, G.X., Fan, Z.P., Fang, X., Lim, Y.F., 2018. Optimal Stackelberg strategies for financing a supply chain through online peer-to-peer lending. Eur. J. Oper. Res. 267 (2), 585–597. Glock, C.H., Kim, T., 2015. Coordinating a supply chain with a heterogeneous vehicle fleet under greenhouse gas emissions. Int. J. Logist. Manage. 26 (3), 494–516. Gomez, J., 2019. Carbon tax & carbon pricing – 15-minute guide. Available at: https://ecochain.com/knowledge/carbon-tax-carbon-pricing-fundamentals/ (accessed date: January 20th, 2020). Hua, G.W., Cheng, T.C.E., Wang, S.Y., 2011. Managing carbon footprints in inventory management. Int. J. Prod. Econ. 132 (2), 178–185. Ivashina, V., Iverson, B., 2014. Trade creditors’ behavior in bankruptcy. Working paper. Harvard Business School, Boston. Jaber, M.Y., Glock, C.H., El Saadany, A.M., 2013. Supply chain coordination with emissions reduction incentives. Int. J. Prod. Res. 51 (1), 69–82. Jing, B., Seidmann, A., 2014. Finance sourcing in a supply chain. Decis. Support Syst. 58, 15–20. Jing, B., Chen, X.F., Cai, G.S., 2012. Equilibrium financing in a distribution channel with capital constraint. Prod. Oper. Manage. 21 (6), 1090–1101. Kouvelis, P., Zhao, W., 2011. The newsvendor problem and price-only contract when bankruptcy costs exist. Prod. Oper. Manage. 20 (6), 921–936. Kouvelis, P., Zhao, W.H., 2012. Financing the newsvendor: supplier vs. bank, and the structure of optimal trade credit contracts. Oper. Res. 60 (3), 566–580. Kouvelis, P., Zhao, W., 2017. Who should finance the supply chain? Impact of credit ratings on supply chain decisions. Manuf. Serv. Oper. Manage. 20 (1), 19–35. Lee, K.H., 2009. Why and how to adopt green management into business organizations? The case study of Korean SMEs in manufacturing industry. Manag. Decis. 47 (7), 1101–1121. Lee, H.H., Zhou, J., Wang, J., 2018. Trade credit financing under competition and its impact on firm performance in supply chains. Manuf. Serv. Oper. Manage. 20 (1), 36–52. Li, B., An, S.M., Song, D.P., 2018. Selection of financing strategies with a risk-averse supplier in a capital-constrained supply chain. Transport. Res. Part E: Logist. Transport. Rev. 118, 163–183. Li, S., Gu, M., 2012. The effect of emission permit trading with banking on firm's production-inventory strategies. Int. J. Prod. Econ. 137 (2), 304–308. Li, X.R., Yu, C.W., Xu, Z., Luo, F.J., Dong, Z.Y., Wong, K.P., 2013a. A multimarket decision-making framework for GENCO considering emission trading scheme. IEEE Trans. Power Syst. 28 (4), 4099–4108. Li, X.R., Yu, C.W., Luo, F.J., Ren, S.Y., Dong, Z.Y., Wong, K.P., 2013b. Impacts of emission trading schemes on gencos’ decision making under multimarket environment. Electr. Power Syst. Res. 95, 257–267. Li, X., Li, Y., 2016. Chain-to-chain competition on product sustainability. J. Cleaner Prod. 112, 2058–2065. Li, X., Shi, D., Li, Y., Zhen, X., 2017. Impact of carbon regulations on the supply chain with carbon reduction effort. IEEE Trans. Syst. Man Cybern.: Syst. https://doi. org/10.1109/TSMC.2017.2741670. Meath, C., Linnenluecke, M., Griffiths, A., 2016. Barriers and motivators to the adoption of energy savings measures for small-and medium-sized enterprises (SMEs): the case of the ClimateSmart Business Cluster program. J. Cleaner Prod. 112, 3597–3604. Nace, T., 2017. China shuts down tens of thousands of factories in widespread pollution crackdown. Available at: https://www.forbes.com/sites/trevornace/2017/10/ 24/china-shuts-do wn-tens-of-thousands-of-factories-in-widespread-pollution-crackdown/#17414d4a4666 (accessed date: December 10th, 2019). Ni, J., Chu, L.K., Li, Q., 2017. Capacity decisions with debt financing: The effects of agency problem. Eur. J. Oper. Res. 261 (3), 1158–1169. Sohu Finance, 2013. Industrial and Commercial Bank of China has provided 100 billion Yuan for small and medium-sized enterprises to invest in energy conservation and emission reduction. Available at: http://money.sohu.com/20130726/n382675397.shtml, in Chinese (accessed date: December 10th, 2019). Tang, L., Wu, J., Yu, L., Bao, Q., 2015. Carbon emissions trading scheme exploration in China: a multi-agent-based model. Energy Policy 81, 152–169. Tsao, Y.C., 2017. Managing default risk under trade credit: Who should implement Big-Data analytics in supply chains? Transport. Res. Part E: Logist. Transport. Rev. 106, 276–293. Varian, H.R., 1992. Microeconomic Analysis, third ed. W. W. Norton and Company, New York. Wang, Q., Zhao, D., He, L., 2016. Contracting emission reduction for supply chains considering market low-carbon preference. J. Cleaner Prod. 120, 72–84. Wang, C., Fan, X., Yin, Z., 2019a. Financing online retailers: Bank vs. Electronic business platform, equilibrium, and coordinating strategy. Eur. J. Oper. Res. https:// doi.org/10.1016/j.ejor.2019.01.009. Wang, F., Yang, X., Zhuo, X., Xiong, M., 2019b. Joint logistics and financial services by a 3PL firm: Effects of risk preference and demand volatility. Transport. Res. Part E: Logist. Transport. Rev. 130, 312–328. Wu, D.D., Yang, L., Olson, D.L., 2018. Green supply chain management under capital constraint. Int. J. Prod. Econ. https://doi.org/10.1016/j.ijpe.2018.09.016. Wu, D., Zhang, B., Baron, O., 2019. A trade credit model with asymmetric competing retailers. Prod. Oper. Manage. 28 (1), 206–231. Xia, L., Guo, T., Qin, J., Yue, X., Zhu, N., 2018. Carbon emission reduction and pricing policies of a supply chain considering reciprocal preferences in cap-and-trade system. Ann. Oper. Res. 268 (1–2), 149–175. Xu, J., Chen, Y., Bai, Q., 2016. A two-echelon sustainable supply chain coordination under cap-and-trade regulation. J. Cleaner Prod. 135, 42–56.
28
Transportation Research Part E 135 (2020) 101859
S. Xu and L. Fang
Xu, X., Zhang, W., He, P., Xu, X., 2017a. Production and pricing problems in make-to-order supply chain with cap-and-trade regulation. Omega 66, 248–257. Xu, X., He, P., Xu, H., Zhang, Q., 2017b. Supply chain coordination with green technology under cap-and-trade regulation. Int. J. Prod. Econ. 183, 433–442. Yan, N., He, X., Liu, Y., 2018. Financing the capital-constrained supply chain with loss aversion: supplier finance vs. supplier investment. Omega. https://doi.org/10. 1016/j.omega.2018.08.003. Yan, N., Sun, B., Zhang, H., Liu, C., 2016. A partial credit guarantee contract in a capital-constrained supply chain: financing equilibrium and coordinating strategy. Int. J. Prod. Econ. 173, 122–133. Yang, L., Zhang, Q., Ji, J., 2017. Pricing and carbon emission reduction decisions in supply chains with vertical and horizontal cooperation. Int. J. Prod. Econ. 191, 286–297. Yang, S.A., Birge, J.R., 2018. Trade credit, risk sharing, and inventory financing portfolios. Manage. Sci. 64 (8), 3667–3689. Zhang, B., Wu, D.D., Liang, L., 2018. Trade credit model with customer balking and asymmetric market information. Transport. Res. Part E: Logist. Transport. Rev. 110, 31–46. Zhou, J., Groenevelt, H., 2008. Impacts of financial collaboration in a three-party supply chain. The Simon School, University of Rochester Working Paper. Zhu, W., He, Y., 2017. Green product design in supply chains under competition. Eur. J. Oper. Res. 258 (1), 165–180.
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