Quality improvement incentive strategies in a supply chain

Transportation Research Part E 114 (2018) 331–342

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Transportation Research Part E journal homepage: www.elsevier.com/locate/tre

Quality improvement incentive strategies in a supply chain a

Seung Ho Yoo , Taesu Cheong a b

b,⁎

T

Division of Interdisciplinary Industrial Studies, Hanyang University, Seoul 04763, South Korea School of Industrial Management Engineering, Korea University, Seoul 02841, South Korea

A R T IC LE I N F O

ABS TRA CT

Keywords: Supply chain Quality management Reward contract Incentive Target quality

This paper investigates several incentive mechanisms for collaborative product quality improvement in a buyer-driven supply chain, and the impacts of those mechanisms on supply chain performance. The buyer, the Stackelberg leader, determines the sales price of a product while the supplier is responsible for production and product quality determination. We develop analytical models incorporating two reward schemes to better understand how the buyer can facilitate the supplier’s quality improvement efforts. We offer managerial insights and practical guidelines for implementing quality management in the supply chain, derived from both an analytical comparison and numerical experiments.

1. Introduction Nowadays, firms commonly focus on their core competencies while outsourcing other functions to the suppliers that possess particular technical and cost advantages. This outsourcing trend has yielded various forms of supply chain. In a typical buyer-supplier relationship such as an OEM (original equipment manufacturer)-CM (contract manufacturer) supply chain or a final assemblersupplier supply chain, the buyer determines the design specification of the product and delegates the production to a supplier. Therefore, the supplier should ensure compliance with the design specification of the product while the design quality of the product is specified by the buyer. However, the more sophisticated the competition among supply chains becomes, the more the buyers need to rely on their suppliers to keep up with the changing needs of consumers by improving time-to-market and operational efficiency. Therefore, the recent outsourcing trend does not allow suppliers to only focus on the quality compliance of their production process but requires them to also engage in product design, which entails investing in their own R&D capabilities (Kaya and Özer, 2009; Xie et al., 2011, 2014). For example, Nike cooperates with its suppliers in product design while almost 100% of shoe production is outsourced (Johnsen and Ford, 2007). Similarly Boeing delegated complete control of the design and production of their parts to approximately fifty suppliers in order to reduce the development time and cost of its 787 Dreamliners (Tang et al., 2009). Apple has also involved many suppliers including Foxconn, LG and Samsung at the product design and development stages (Back et al., 2010). Likewise, many of the store-brands or private-label products of retail and grocery chains are designed and made by agricultural and food manufacturers. Under these circumstances, a buying firm needs to find effective and efficient ways to control the supplier’s quality decisions, which affect customer demand and subsequently the performance of the overall supply chain. In this paper, we investigate such a buyer-supplier supply chain in which a buyer delegates the design of a product as well as its production to a supplier, reflecting the recent outsourcing trend we mentioned above, while the buyer determines its sales price. In this situation, the buyer is well aware that, excluding its sale price decision, the supplier’s quality decision is the main determinant of its own performance, and furthermore that of the overall supply chain. Hence, the buyer needs to find a way to facilitate the supplier’s

⁎

Corresponding author. E-mail addresses: [email protected] (S.H. Yoo), [email protected] (T. Cheong).

https://doi.org/10.1016/j.tre.2018.01.005 Received 1 July 2017; Received in revised form 1 December 2017; Accepted 4 January 2018 Available online 09 May 2018 1366-5545/ © 2018 Elsevier Ltd. All rights reserved.

Transportation Research Part E 114 (2018) 331–342

S.H. Yoo, T. Cheong

quality investment. Therefore, we here investigate reward (or incentive) strategies that differ from the subjects of most previous studies addressing supply chain quality management. Previous studies have mainly dealt with a penalty contract based on inspection results or external failures, an approach which imposes a kind of financial punishment for a supplier’s quality failures, in the traditional buyer-supplier relationship. We again remark that in the traditional supply chain a buyer is responsible for product design and maintains a transactional relationship with a supplier while a supplier is responsible for meeting the buyer’s design specification. Thus, in traditional supply chain quality management, the buyer typically uses a penalty scheme to control the conformance to design specifications in production. However, if we consider the recent supply chain trend in which the supplier is responsible for not only production but also collaboration with the buyer on product design, it is difficult for the buyer to maintain a short-term transactional relationship and furthermore difficult to impose a penalty scheme that is based on quality of conformance to the design specifications. In this situation, the more appropriate control mechanism may be a reward scheme that proactively facilitates the supplier’s quality investment and long-term creative efforts in design activities, rather than reactively punishing according to a penalty scheme. Therefore, we introduce two reward strategies to facilitate the supplier’s quality investment and reveal their different characteristics. The two strategies are differentiated by how they incentivize the supplier’s effort based on a target or not. Specifically, one reward contract lacks a target quality level and provides a reward proportional to the supplier’s resulting quality level, and the other provides a reward based on a predetermined target quality level, which is determined according to consumers’ expectations of product quality. Note that the latter strategy can also penalize the supplier, as in previous studies, if the resulting quality level is below the target level. Through a comparison of the two reward strategies along with a no-incentive strategy, we intend to address the following questions. (a) Under what conditions should the buyer consider a reward (or incentive) strategy to facilitate the supplier’s quality effort and investment? (b) Is it a rational and reasonable decision for the buyer to offer a financial reward to the supplier? Is a reward strategy beneficial to not only the supplier but also both the supply chain and the buyer? (c) Which reward strategy guarantees outperformance, specifically, in terms of quality, market, and profit performance of the entire supply chain and of each player? By answering the above questions, we aim to contribute to the literature by bridging the gap between practice and academia. We will clarify the important implications for supply chain practices by offering practical guidelines to supply chain managers, including how to better facilitate the supplier’s quality effort and enhance the overall performance of a supply chain. The remainder of the paper is as follows. Section 2 provides a literature review and discusses our contributions to the existing literature. Section 3 presents the basic model used to address the problem dealt with by this paper and its centralized version is discussed in Section 4. In Section 5, we specifically examine two reward contract schemes along with the conventional wholesale price contract under the decentralized supply chain configuration, and in Section 6 compare them. In Section 7, we perform numerical experiments and discuss their managerial implications. Finally, we summarize our main results and conclude in Section 8. 2. Literature review There have been many previous studies dealing with issues and problems in supply chain quality management, including Reyniers and Tapiero (1995), Baiman et al. (2000, 2001), Lim (2001), Balachandran and Radhakrishnan (2005), Hwang et al. (2006), Chao et al. (2009), Hsieh and Liu (2010), Volodymyr and Christopher (2012), Wan et al. (2014), Dong et al. (2016) and Gao et al. (2016). They investigated a traditional situation in which a buyer delegates only the production process to a supplier, focusing on how the buyer can minimize total cost by controlling the supplier’s quality failures and subsequent defect problems. Most studies adopted a penalty contract as a control mechanism, based on the information from incoming inspections or external failures, since they examined a traditional relationship between players, in which the supplier is only responsible for the product quality conformance to the design specification set by the buyer. Therefore, it is rational and effective to impose a penalty to control the supplier’s failure to confirm with the specification. However, we need to note that imposing a penalty can make the relationship adversarial and thus only proper when the buyer just maintains a short-term, transactional relationship with the supplier. On the other hand, if a buyer needs to build a long-term, mutually-beneficial relationship with a supplier as a strategic partner, not only a penalty but also a reward for the supplier’s high quality performance should be also taken into consideration. This also holds true when considering the recent business environment where the buyer needs to rely more on the complimentary capabilities of its various critical suppliers (with respect to production as well as product design) to cope with consumers’ changing preferences and needs. Thus, our study has more in common with previous studies investigating reward contracts than those investigating penalties only. Starbird (2001) examined the performances of two different quality control schemes, i.e., reward and penalty schemes. This study, like ours, considered the financial incentives for the supplier’s quality performance given a target quality level. However, unlike ours, Starbird (2001) did not consider the effect of quality on consumers’ buying behavior, and the reward for quality performance was not a decision variable. Schmitz (2005) examined a principal-agent model in which the agent determines quality and the principal is the user of an innovation. It considered an incentive contract that differentiated payments depending on cases of failure and success. Differently from Schmitz (2005), our paper considers a more specific supply chain situation and investigates the effect of a target performance level on overall supply chain performance. Kaya and Özer (2009) also considered a recent outsourcing trend in which a supplier is principally responsible for overall product quality, and a per-unit payment incentivizes the supplier to attain a high level of quality. On the other hand, in this 332

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paper, we investigate the choice of a one-time financial reward, especially one based on a target quality level, and examine the different characteristics of reward (or incentive) schemes with and without that target quality level. Hung (2011) studied how to adopt economic incentive schemes to manage the quality of a global supply chain by combining activity-based costing to assess the quality efforts and costs in its model with an illustrative numerical example. Although it considered the incentives based on a target quality scheme similar to ours, it did not take the relationship between the players and their different roles in a supply chain into consideration. Baake and von Schlippenbach (2011) considered the demand model affected by the quality decision of an upstream firm and investigated the buyer’s decision on an incentive contract offering a reward differently with respect to two resulting quality levels, high and low. On the other hand, we investigate a contract that can be either a reward or a penalty scheme depending on whether the resulting quality achieves the target or not, and in which the amount of the reward or penalty is proportional to the achieved quality level. Chen et al. (2015) also investigated how to motivate a supplier by devising quality management contracts. Similar to our model, their product quality is controlled by offering financial support, subsidizing the supplier’s quality investment, and, moreover, they also incorporated a target quality level. He et al. (2016) developed a dynamic model incorporating the effects of the quality and price on the consumer behavior similar to ours. Yang and Xiao (2017) investigated how to coordinate a supply chain with loss-averse consumers in service quality. Differently from ours focusing on quality-dependent reward, those studies utilized contract mechanisms to control quality and cost sharing in He et al. (2016) and a quantity discount contract with service subsidy rate in Yang and Xiao (2017). In addition, Xie et al. (2011, 2014) considered consumer behaviors similar to ours which are affected by not only the buying firm (manufacturer)’s pricing decision but also the supplier’s quality decision. However, they did not consider the incentive strategy but focused on the comparison of supply chain strategies: vertical integration, manufacturer’s Stackelberg and supplier’s Stackelberg. Overall, there have been only a few studies investigating reward contracts in the literature of quality improvement. It is also difficult to find the studies investigating the effect of imposing target quality on the resulting quality and overall performance, even though such practices in incentive contracts are quite common in industry, such as in performance-based contracting. Therefore, by extending the previous studies investigating issues in supply chain quality management, especially based on a reward contract, we aim to contribute to the literature by examining a recent outsourcing trend characterized by the buyer relying heavily on the supplier’s capabilities and the supplier’s decision on product quality having a great impact on consumer behavior and overall supply chain performance. When considering the critical supplier’s motivation to invest in quality, it is assumed that the buyer considers two types of rewards, those with and without a target quality level, which still remain unexplored in the literature of quality management. Moreover, by optimally solving and comparing the two incentive schemes, we intend to provide important implications for supply chain practices, revealing how to facilitate the supplier’s quality effort and enhance the overall supply chain performance. 3. Model formulation We consider a supply chain structure that is composed of two parties – a supplier (S) and a buyer (B) – and assume that the buyer has more bargaining power than the supplier. In this supply chain, the buyer determines the sales price of the product, and the supplier both produces the product and determines its quality. We first present our demand model as follows. Given that a consumer product, such as a vehicle, an electronic device or an item of clothing, is distributed through a supply chain, we assume that the sales price and the quality of the product strongly influences consumer’s purchasing behavior. Therefore, the demand function we assume is defined as follows:

D = α−βp−γ (x 0−x )

(1)

where α is the demand potential, p is the sales price, x is the consumers’ perceived quality of the product (i.e., conformance to consumers’ expectations of product quality), x 0 is the minimum reservation level of the product quality in the target market, and β and γ are coefficients associated with p and (x 0−x ) respectively. It is assumed in this paper that the product quality consumers perceive, x, is a single composite measure which aggregates multiple quality attributes including features, reliability, durability, aesthetics and conformance. In other words, x is expressed by a convex combination of each quality attribute x i along with its corresponding importance or weight wi (i.e., x = ∑i wi x i where ∑i wi = 1 and wi ≥ 0 for all i). On the other hand, x 0 represents the minimum reservation level of the product quality which needs to be satisfied in order to guarantee the positive utility of consumers. Therefore, the difference between the expectation and the perception of the product quality, or quality gap (x 0−x ) , influences consumers’ satisfaction and subsequently buying behavior. We remark that this approach to assess quality by the difference between the expectation and perception has been widely accepted in literature (Parasuraman et al., 1985; Garvin, 1987; Karmarkar and Pitbladdo, 1997; Yoo et al., 2015). In this supply chain, the supplier is responsible for product production and invests in improving product quality. Thus, given the demand function above, the profit functions of the buyer and the supplier, ΠB and ΠS respectively, can be simply expressed as follows:

ΠB = pD−T ΠS = T −cD−λx 2

(2)

λx 2

where T is the transfer payment from the buyer to the supplier, c is the unit production cost, and represents the supplier’s capital investment to achieve x level of product quality. We here assume that the supplier’s capital investment is increasing and convex in x as in Karmarkar and Pitbladdo (1997) and Banker et al. (1998). As product quality significantly affects the consumers’ purchasing behavior and subsequently overall supply chain profit, the rational buyer may intend to control the product quality the supplier is responsible for improving by devising an incentive 333

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mechanism to facilitate the supplier’s investment in product quality improvement. When it comes to the transfer payment T in Eq. (2), it could include not only the payment for the products purchased from the supplier but also an incentive to induce the supplier’s quality improvement effort. In Section 5, we will examine various reward schemes between two players with respect to T. 4. Centralized supply chain We first characterize the optimal decision to the centralized supply chain (Case Full Integration or FI) as a benchmark, in which the product quality and sales price are chosen by a central decision maker to maximize the following total supply chain profit ΠFI :

ΠFI = ΠB + ΠS = (p−c ) D−λx 2

(3)

where D, ΠB and ΠS are defined in Eqs. (1) and (2) respectively. We note that in this ideal case there are no interactions between two players and hence no opportunistic behavior. In order to guarantee the existence of optimal product quality and sales price with their positiveness, we assume the following condition. Condition 1. The following condition guarantees the existence of an optimal positive product quality and sales price in Case FI: 4βλ−γ 2 > 0 . Condition 1 implies that if the effect of product quality on consumers’ buying behavior γ is not significantly large compared to the effect of sales price on demand β and to the magnitude of the supplier’s capital investment λ , there exists an optimal solution to ΠFI . The following theorem is about the optimal solution to ΠFI . ∗

Proposition 1. Assuming that Condition 1 is satisfied, the centralized supply chain has a unique optimal solution (x FI , p FI ∗

x FI =

∗

) where

γ (α−βc−γx 0) 2λ (α−βc−γx 0) ∗ +c and p FI = 4βλ−γ 2 4βλ−γ 2 ∗

∗

where x FI and p FI are the optimal product quality and sales price respectively. ∗

∗

Proof. Given Condition 1, the optimal product quality x FI and sales price p FI can be obtained by solving the system of linear equations,

∂ΠFI (x ,p) ∂x

= 0 and

∂ΠFI (x ,p) ∂p

= 0. □

5. Decentralized supply chain under contracts Thus far, we have examined the case for the centralized supply chain as a benchmark. We now turn our attention to the decentralized supply chain configuration, and develop models for evaluating contract efficiencies using the various reward schemes below. Note that we have a Stackelberg game in which the buyer is the first mover, determining the sales price and the contract, and the supplier is the follower, responsible for product quality. 5.1. Decentralized supply chain under wholesale price contract We first consider the scenario that the buyer only makes payment for the products it purchases from the supplier without any consideration of providing incentives for product quality improvements to the supplier (denoted by Case DW). Thus, the transfer payment in this case is expressed by (4)

T DW = wD

where w is the unit wholesale price the buyer determines. To identify an equilibrium of the sequential game, we solve it backwards. Given that no conditions exist that guarantee the semidefiniteness of the Hessian matrix of ΠB with respect to p and w when the transfer payment is defined as Eq. (4), the following property can be claimed. Observation 1. There exists no optimal solution to guarantee the concavity of the buyer’s profit function under a wholesale price contract. Observation 1 implies that the wholesale price-only contract could be inadequate for controlling the supply chain because the product quality the supplier is responsible for determining indeed influences the customers’ buying behavior and the contract does not allow the buyer influence the supplier’s decisions on quality improvement efforts. Therefore, in the following subsections we will consider other types of contracts which take quality-dependent incentives into account. Based on the discussion above, in this paper we assume that the wholesale price is treated as being exogenous. Then, given the wholesale price w, the best responses of the buyer and supplier can be obtained by solving the sequential games, and the following ∗ ∗ best responses p and x of the buyer and supplier respectively (i.e., p DW and x DW ) are as follows:

p DW * =

2λ (α−βw−γx 0) + γ 2 (w−c ) γ (w−c ) + w, and x DW * = 2λ 4βλ 334

(5)

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5.2. Decentralized supply chain under reward contract without target quality level In this section, we examine the scenario in which the buyer offers quality-dependent rewards to the supplier in order to encourage the supplier to invest in quality (denoted by Case DR). To do so, we assume that the transfer payment in this case is defined as (6)

T DR = wD + rx where r is the marginal reward when the resulting product quality level is x. Backward induction induces the supplier’s best-response as follows: ∗

x DR (r ) =

γ (w−c ) + r . 2λ

The buyer’s optimal decisions on p and r are

p DR* =

4λ (α−γx 0−βw ) + γ 2 (w−c ) γ (2λ (α−γx 0−βw )−(4βλ−γ 2)(w−c )) + w and r DR* = 2 8βλ−γ 2 8βλ−γ ∗

The conditions required to ensure that r DR > 0 so that there can be a feasible reward contract are as follows. ∗

Condition 2. Either of the following conditions should be satisfied to guarantee r DR > 0 : (4βλ − γ 2)(w − c ) + βw + 2λ α − βw (4βλ − γ 2)(w − c ) x0 < γ − 2λ 2λ (α − βw − γx 0)

(a) α > (b)

(c) (w−c ) <

γx 0

4βλ − γ 2

The individual conditions in Condition 2 imply that (a) the market size α should be large enough to warrant profitability by offering quality-dependent incentives to the supplier, (b) as the level of x 0 is insufficient, incentives could help the supplier to easily facilitate its investment in quality, or (c) when w−c , the marginal profit of a product for the supplier, is insufficient, the buyer could provide financial support to the supplier for implementing quality improvements. 5.3. Decentralized supply chain under reward contract with target quality level We turn our attention to the scenario in which, unlike the previous ones, the buyer requires the supplier to meet a certain level of quality to get rewarded. The buyer assesses the quality level the supplier achieves with respect to the target quality x 0 and then decides the incentives or penalties to the supplier according to the contract (denoted by Case DT). We remark that in industry such practices in incentive contracts are quite common. For example, performance-based contracting (PBC) is common in many industries such as the defense sector or the commercial airline industry (Jin and Wang, 2012). In a PBC agreement, the contract is made based on quantifiable performance metrics, and a customer specifies the reliability goals or performance criteria (Jin and Wang, 2012). If we let xT be the target quality level, the transfer payment in Case DT , T DT , can be defined as T DT = wD−r (xT −x ) . The retailer assesses the supplier’s quality x based on the target xT , and the supplier would get rewarded or penalized. If xT > x (i.e., the resulting quality is below the level of target quality xT ), then the amount r (xT −x ) will be the penalty to the supplier; on the other hand, if x > xT , then the amount r (xT −x ) becomes the reward to the supplier. Note that T DT can be considered as the general form of other transfer payments in Cases W and DR. With xT = 0, T DT becomes T DT = T DR = wD + rx in Eq. (6), while T DT = T DW = wD in Eq. (4) with r = 0 . Since we assume that every player in this supply chain understands customers’ expectations of product quality and, accordingly, their purchasing behaviors, it is reasonable to set the minimum level of product quality that customers expect x 0 as the target quality xT in this scenario (i.e. xT = x 0 ). Thus, the transfer payment T in this scenario, T DT , can be defined as below:

T DT = wD−r (x 0−x ).

(7)

To identify an equilibrium of the sequential game in this scenario, we solve the last stage of the game for the supplier after ∗ plugging Eq. (7) in Eq. (2), and the supplier’s best response x DT , which is a function of r, can be obtained as follows: ∗

x DT (r ) =

γ (w−c ) + r . 2λ ∗ x DT (r )

(8)

∗ x DR (r )

= . We here note that ∗ Next, by plugging the supplier’s best response, Eq. (8), in the retailer’s profit function, we have the buyer’s best responses, p DT ∗ DT and r as ∗

p DT = r

DT ∗

=

4λ (α − βw − γx 0) + γ 2 (w − c ) 8βλ − γ 2

+w+

γ (2λ (α − βw − γx 0) − (4βλ − γ 2)(w − c )) 8βλ − γ 2

2γλx 0 8βλ − γ 2

+

8βλ2x 0 8βλ − γ 2

2γλx 0

∗

= p DR + =r

DR∗

8βλ − γ 2

+

, and

8βλ2x 0 8βλ − γ 2

335

(9)

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Table 1 Solution summary: contract. Case

Reward r ∗

DR

γ (2λD0 − ΨFI πs ) Ψ ∗ 8βλ2x 0 r DR + Ψ

DT

respectively. ∗ We remark that Conditions 1 and 2 guarantee r DT > 0 and hence the buyer’s reward contract offered to the supplier becomes ∗ ∗ ∗ ∗ ∗ ∗ ∗ feasible. Furthermore, x DT (r DT ) > x DR (r DR ) because x DT (r ) = x DR (r ) for a given r, as observed above, and x DT is isotone in r. 6. Supply chain model comparison In this section, we first summarize all the results obtained in Sections 4 and 5 and then compare the supply chain models with various reward schemes for evaluating contract efficiencies as discussed in the earlier sections. 6.1. Model summary We first summarize the optimal contract, the best responses and optimal profits of every scenario discussed earlier, in Tables 1–3 respectively. In the tables, D0FI and D0 represent the amount of demand that is independent of each player’s decisions in centralized and decentralized supply chains respectively, ΨFI and Ψ represent the conditions for guaranteeing the existence of optimal solutions, and πs represents the marginal profit of the supplier. 6.2. Comparison of variables In Tables 1–3, we summarize all the results including the optimal decisions and optimal profits of the supply chain models given Table 2 Solution summary: price, quality and demand. Case

Price p∗

Quality x ∗

Consumer response D∗

FI

2λD0FI ΨFI

2βλD0FI ΨFI

DW

2λD0 + γ 2πs 4βλ

γD0FI ΨFI γπs 2λ

DR

4λD0 + γ 2πs +w Ψ ∗ 2γλx 0 DR p + Ψ

DT

+c

+w

2λD0 + γ 2πs 4λ β (4λD0 + γ 2πs ) Ψ ∗ 2βγλx 0 D DR + Ψ

γ (D0 + 2βπs ) Ψ

∗

x DR +

4βλx 0 Ψ

D0FI = α−βc−γx 0 , D0 = α−βw−γx 0 , ΨFI = 4βλ−γ 2 > 0, Ψ = 8βλ−γ 2 > 0, πs = w−c > 0 .

Table 3 Solution summary: profits. Case

Buyer Π∗B

Supplier Π∗S

Supply Chain Π∗

FI

λ (D0FI )2 ΨFI

N/A

λ (D0FI )2 ΨFI

DW

(2λD0 + γ 2πs )2 16βλ2

πs D0 2

(2λD0 + γ 2πs )2 16βλ2

DR

(4λD0 + γ 2πs )2 8λ Ψ

DT

∗

Π DR + B

+

γ 2πs2 8λ

2λx 0 (γD0 + 2βλx 0) γx 0 (4βλ − γ 2) πs − Ψ Ψ

πs D0 2 ∗

+

Π sDR +

+

πs D0 2

γ 2 (4λD0 + γ 2πs )2 γ 2πs2 − 16λ 16λ Ψ2

(16βλ − γ 2)(4λD0 + γ 2πs )2 16λ Ψ2

4βγλx 0 πs x 0 (2γλ ΨFI D0 + (6βλ − γ 2)(8x 0 βλ2 + γ 3πs )) − Ψ Ψ2

Π DR +

D0FI = α−βc−γx 0 , D0 = α−βw−γx 0 , ΨFI = 4βλ−γ 2 > 0, Ψ = 8βλ−γ 2 > 0, πs = w−c > 0 .

336

∗

γ 2πs2 16λ 2 2 2 2βλx 0 (4γλD0 + γ 3πs ) 4βλ x 0 (4βλ − γ ) − Ψ2 Ψ2

+

πs D0 2

+

Transportation Research Part E 114 (2018) 331–342

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Fig. 1. Illustration of dominance among models ( A: x 0 =

γ ΠS γ (α − βw ) − , 2λ 4βλ − γ 2

B: x 0 =

α − βw (4βλ − γ 2)ΠS − , γ 2γλ

C: α =

(4βλ − γ 2)ΠS 2λ

+ βw ).

in Sections 4 and 5. The following proposition characterizes the relationship among the optimal decisions in the decentralized supply chain models. Proposition 2. Given Conditions 1 and 2, (a) (b) (c) (d)

∗

∗

r DT > r DR , ∗ ∗ ∗ x DT > x DR > x DW , ∗ ∗ ∗ and p DT > p DR > p DW ∗ ∗ ∗ DT DR DW hold. D >D >D

First, Proposition 2(a) indicates that the buyer offers higher level of rewards to the supplier under Case DT than Case DR. In Case DT, the buyer provides the minimum level of product quality to the supplier and the supplier receives incentives if its product quality surpasses that level. Thus, in this case, it would be necessary for the buyer to offer higher rewards to the supplier, which could induce the supplier to achieve a higher product quality level than its minimum requirement level. We note that this reward mechanism works only if Condition 2 holds. ∗ Second, as presented in Proposition 2(b), the product quality x of Case DT , x DT , dominates that of other decentralized models, and Case DR also dominates Case DW which lacks any incentives for the supplier to expend effort on quality improvement. We can observe similar relations in p and D as well (see Proposition 2(c) and (d)). The results indicate the intuitive conclusion that it is possible to improve the product quality and moreover supply chain performance by offering incentives to the supplier (Case DR or DT) rather than not doing so (Case DW). Fig. 1 illustrates the comparison of x from each scenario (i.e., DW , DR and DT), presented in Table 2, and the shaded area in the figure corresponds to the regions of α and x 0 that guarantee the feasibility of Cases DR and DT. We here note that Cases DT and DR always show the higher demand in Proposition 2(d) even though the incentive strategies yield higher prices. This is interesting since the demand is affected by not only quality but also price as in Eq. (1). This shows the effectiveness of quality incentive strategies on the market performance. In the following section, for a better understanding of the incentive mechanisms discussed in this paper and their impacts from the perspective of supply chain coordination, we perform numerical experiments with a sensitivity analysis and discuss the managerial insights we observe. 7. Numerical experiments and managerial insights In this section, we use a numerical example to gain further insights by comparing supply chain performance with respect to examined reward contracts. In the numerical studies, we assume x 0 = 40, w = 60, c = 30 , α = 1400 , β = 6, γ = 5 and λ = 2 , which satisfy Conditions 1 and 2 so that Cases DR and DT exist. The computational results are presented in Table 4. To evaluate supply chain performance, we evaluate two performance measures introduced in Cachon (2003): the contract efficiency, which represents how closely the supply chain profit from each contract in a decentralized supply chain approaches that of the centralized supply chain, and the profit shares of each player over the profit of the entire supply chain. In addition, we include the impact of the incentive offering, which represents how much the incentive can improve supply chain profit over the situation without any incentives as presented in Table 4. For example, we can observe that the contract in Case DT is better than contracts in other decentralized supply chain cases in terms of contract efficiency and incentive impact on Π . The results presented in Table 4 also show that the contract of Case DT, in which the target quality level is given to the supplier, induces higher profits for both the buyer and the 337

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Table 4 Numerical results when x 0 = 40, w = 60, c = 30, α = 1400, β = 6, γ = 5, λ = 2 (†: decision variable).

Buyer’s decision

Sales price p† Reward r † Total reward rx Transfer payment T

Supplier’s response

Product quality x† Investment λx 2

Benchmark

Basic

Incentive

Case FI

Case DW

207.39

145.63

165.21

176.48

N/A

0

188.03

296.20

N/A N/A

0 30825.00

15889.70 53765.76

21192.70 63125.09

Case DR

Case DT

221.74

37.50

84.51

111.55

98336.48

2812.50

14282.88

24886.49

1064.35

513.75

631.27

698.87

Consumer response

Demand D

Profit

Buyer’s profit ΠB Supplier’s profit ΠS SC profit Π

90469.57 N/A 90469.57

43989.84 12600.00 56589.84

50526.76 20544.85 71071.61

60211.27 17272.41 77483.67

Performance

Contract efficiency Π/ΠFI Buyer’s profit share ΠB /Π Supplier’s profit share ΠS /Π

100.00%

62.55%

78.56%

85.65%

100.00% 0.00% N/A

77.73% 22.27% 0.00%

71.09% 28.91% 25.59%

77.71% 22.29% 36.92%

Incentive impact on Π, (Π−ΠDW )/ΠDW

supply chain than other cases and that the supplier obtains the superior results in Case DR (i.e., ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ Π DT > Π DR > Π DW , Π DT > Π DR > Π DW and ΠSDR > ΠSDT > ΠSDW ). Although higher rewards for quality improvement are proB B B vided to the supplier in Case DT, the incentives induce the supplier to make even higher investments in product quality which deteriorate the supplier’s profit. Thus, while the effort to enhance quality makes the buyer and the overall supply chain better off, it ultimately makes the supplier worse off. But, we note that the supplier can still earn better profits in Cases DR or DT than in Case DW in which there is no incentive to the supplier. We perform the sensitivity analysis to examine the equilibrium behaviors of the decentralized supply chain models and the results are summarized in Table 5. Specifically, we vary the value of one parameter α, β , γ , λ, x 0 or c, within its respective range (see the first row in Table 5) and see how its variation influences the decision variables and profits of each player in the supply chain and the overall supply chain performance for each scenario. For example, the cell value ‘[96,196(↑)]’ at the intersection of row p−DW and column α means that the sales price p DW in the wholesale price contract (Case DW) increases (↑) from 96 to 196 when the demand potential α is increased from 800 to 2000. The results presented in Table 5 show that in a decentralized system the domain potential α and the minimum product quality level x 0 may have no influence on the supplier’s decision on product quality x. However, the incentive offers to the supplier make it respond to the market changes during its decision on product quality. Specifically, as α increases (i.e., market size increases), quality improvement efforts due to the offers to the supplier result in an increase in product quality, which subsequently helps the players in the supply chain to gain a larger market share. Also, under a scenario in which the consumers’ expectation of product quality level increases (i.e., x 0 increases), the optimal product quality level set by the supplier depends on how the incentives are offered to the supplier. For example, the contract in Case DT can lead the supplier to keep up with a trend of increasing consumer expectation; however, under the incentive scheme in Case DR in which the supplier’s incentives are simply proportional to the quality level the supplier achieves rather than linked to a target quality level, the supplier would not keep up with increases in consumer product quality expectation because the supplier also considers its investment in quality improvement and such an increase in quality would deteriorate the profitability of the supplier. Thus, it is important to decide the target quality level reflecting changes in market conditions in order to keep up with the contemporary business environment and maintain competitiveness in the market. According to Tables 4 and 5, Case DT outperforms the other cases in the decentralized system in terms of contract efficiency (Π/ΠFI ) and the impacts of incentives on supply chain profit ((Π−ΠDW )/ΠDW ). Fig. 2 presents the changes in those performance measures caused by varying the values of α and x 0 . However, we can observe that while Case DR yields a larger profit share to the supplier, Case DT yields a fairly low one. The observation implies that the supply chain performance improvement in Case DT becomes possible thanks to the supplier’s sacrifice for product quality enhancement, while the supplier has to accept the contract offer of the buyer with bargaining power in many general practices. If the supply chain wants to enhance its overall capabilities by supporting a supplier in a long-term relationship, Case DR is more desirable than Case DT. In Table 4, both Cases DW and DT yield a higher buyer’s profit share than Case DR. At high α or low x 0 , the buyer’s profit share from Case DW without incentive is higher than both Cases DR and DT as presented in Fig. 2(c) and (d). Therefore, if the buyer, as the focal company in the supply chain, only considers its relative share among the supply chain’s overall profit, the buyer will have less motivation to offer incentives to the supplier since Case DW without any incentives can guarantee the highest buyer’s profit share, especially at high α or low x 0 . Based on the observations from Table 5, we summarize in Table 6 the set of conditions under which the incentive impact on Π (or Π − ΠDW ) increases. If the supply chain is under the conditions summarized in Table 6, it can have a chance to enhance its overall profit DW Π

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Table 5 Sensitivity analysis. Parameters Parameter ranges

α

β [4.5,7.5]

c

[3.8,6.2]

λ [1.4,2.6]

x0

[800,2000]

[10,70]

[15,45]

Buyer’s decision p DW DR DT r DR DT

[96,196(↑)] [98,233(↑)] [109,244(↑)] [19,357(↑)] [127,465(↑)]

[123,184(↓)] [131,234(↓)] [139,251(↓)] [103,361(↓)] [204,483(↓)]

[143,150(↑)] [152,190(↑)] [160,207(↑)] [119,310(↑)] [213,444(↑)]

[142,152(↓)] [155,189(↓)] [165,203(↓)] [163,248(↓)] [292,337(↓↑)]

[133,158(↓)] [148,182(↓)] [168,185(↓)] [146,230(↓)] [257,335(↑)]

[115,176(↑)] [160,170(↓)] [171,182(↓)] [164,212(↑)] [272,320(↑)]

Supplier’s response x DW DR DT

[38,38(−)] [42,127(↑)] [69,154(↑)]

[38,38(−)] [63,128(↓)] [88,158(↓)]

[29,47(↑)] [58,124(↑)] [82,157(↑)]

[29,54(↓)] [60,142(↓)] [85,174(↓)]

[38,38(−)] [74,95(↓)] [102,121(↑)]

[0,75(↑)] [72,97(↓)] [99,124(↓)]

Consumer’s response D DW DR DT

[214,814(↑)] [226,1037(↑)] [293,1105(↑)]

[469,559(↓)] [533,784(↓)] [596,861(↓)]

[498,540(↑)] [554,781(↑)] [599,884(↑)]

[492,554(↓)] [570,775(↓)] [633,855(↓)]

[439,589(↓)] [530,733(↓)] [648,750(↓)]

[510,518(↑)] [600,663(↓)] [667,731(↓)]

DW DR DT DW DR DT DW DR DT DW

[7600,110365(↑)] [7682,133935(↑)] [10606,150380(↑)] [3600,21600(↑)] [4002,44229(↑)] [2919,38767(↑)] [11215,131965(↑)] [11683,178165(↑)] [13525,189147(↑)] [58%,73%(↓)]

[29297,69378(↓)] [31382,90603(↓)] [37508,107480(↓)] [11250,13950(↓)] [14491,36969(↓)] [12108,32866(↓)] [40547,83328(↓)] [45873,127573(↓)] [49616,140346(↓)] [40%,75%(↑)]

[41359,48627(↑)] [44346,63064(↑)] [50972,78146(↑)] [11880,13320(↓)] [16768,31135(↑)] [13499,29063(↑)] [54679,60507(↑)] [61113,94199(↑)] [64472,107210(↑)] [31%,80%(↓)]

[40363,51139(↓)] [44430,64945(↓)] [53536,76653(↓)] [12600,12600(−)] [17489,30238(↓)] [13351,28457(↓)] [52963,63739(↓)] [61919,95183(↓)] [66887,105110(↓)] [38%,73%(↑)]

[32084,57771(↓)] [36013,67576(↓)] [52842,70014(↓)] [10350,14850(↓)] [15740,25796(↓)] [7212,25379(↓)] [42434,72621(↓)] [51752,93373(↓)] [60054,95393(↓)] [61%,64%(↑)]

[36329,52383(↓)] [44664,57340(↓)] [55320,66053(↓)] [6300,18900(↓)] [13926,26856(↓)] [9324,24912(↓)] [42629,71283(↓)] [58590,84196(↓)] [64645,90965(↓)] [57%,67%(↓)]

DR DT DW DR DT DR DT

[76%,79%(↑↓)] [83%,88%(↑↓)] [68%,84%(↑)] [66%,75%(↑)] [77%,80%(↓↑)] [4%,35%(↑)] [21%,43%(↑)]

[62%,84%(↑)] [68%,91%(↑)] [72%,83%(↓)] [68%,72%(↑↓)] [76%,78%(↑↓)] [13%,53%(↓)] [22%,68%(↓)]

[48%,90%(↓)] [54%,95%(↓)] [76%,80%(↑)] [67%,73%(↓)] [73%,79%(↓)] [12%,56%(↑)] [18%,77%(↑)]

[56%,86%(↑)] [62%,92%(↑)] [76%,80%(↓)] [68%,72%(↑)] [73%,80%(↑)] [17%,49%(↓)] [26%,65%(↓)]

[78%,79%(↑)] [80%,91%(↑)] [76%,80%(↓)] [70%,72%(↓)] [73%,88%(↑)] [22%,29%(↓)] [31%,42%(↑)]

[78%,79%(↑↓)] [85%,86%(↑)] [73%,85%(↑)] [68%,76%(↑)] [73%,86%(↑)] [18%,37%(↑)] [28%,52%(↑)]

Profit ΠB

ΠS

Π

Π/ΠFI

ΠB /Π

Π − ΠDW ΠDW

γ

to a higher level by facilitating a quality incentive strategy and better controlling the supplier. We remark that the impact of each incentive strategy is different with respect to changes in consumers’ expectations about product quality x 0 , as apparent from Table 5. If we carefully understand those dynamics above, the adoption of incentives will guarantee a higher level of profit enhancement. Overall, it is important to keep an integrated perspective on the supply chain decision structure since changes in an environmental factors can influence the interactions among supply chain players and hence the overall performance. 8. Conclusion In this paper, we evaluate reward strategies for better facilitating the supplier’s quality improvement efforts and furthermore improving overall supply chain performance in a buyer-driven supply chain comprising a single supplier and a single buyer where the supplier produces products and determines their quality. We introduce two reward strategies, differentiated by whether there is a target quality level to incentivize the supplier’s effort or not. Then, we compare those strategies analytically and conduct intensive numerical experiments to reveal their different characteristics and gain better insights into reward contract efficiency, as described below.

• First, we reveal the conditions under which supply chain firms can adopt a reward strategy. When the market size is sufficiently • • •

large, the consumers’ expectation on product quality is not sufficiently high or the supplier’s marginal profit is not sufficiently high, the buyer can be motivated to provide the financial support to the supplier for quality improvement. Second, any incentive offerings enhance the overall performances of a supply chain. Regardless of whether the strategy includes a target quality level or not, any reward strategies will yield better quality, market and profit performances than a basic wholesale price contract lacking incentives for quality. Third, when the buyer sets a target quality level to incentivize the supplier’s effort, the incentive offer makes the supplier respond to the market changes when making its decision on product quality. Therefore, the buyer offers higher rewards to the supplier than without a quality target. These different reward offerings have differing effects on the overall performances in a supply chain. Fourth, due to a higher reward offering, the reward scheme incorporating a target induces a better quality performance than the 339

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Fig. 2. Equilibrium behaviors of profit performances (%) in α and x 0 (× :DW , ∘: DR, •:DT ).

• •

strategy without a target. Using the reward strategy incorporating a target allows a higher sales price and guarantees a better market performance. Fifth, the reward strategy with a target enhances the overall profit performances of not only the supply chain but also the buyer better than the strategy without a target. However, this is possible thanks to the supplier’s sacrifices for product quality investment, while the supplier has to accept the contract offer of the buyer with power in many practices. Considering this, the no-target strategy helps better enhance and maintain the overall capabilities of suppliers in the context of long-term relationships. Sixth, the incentive strategy needs to be more facilitated, especially when a market expands, consumers are more sensitive to product quality, the quality investment becomes more efficient or the production process becomes less efficient. Under these conditions, a supply chain can expect incentive offerings to have a higher impact on profit performance. The target reward 340

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Table 6 Environmental changes that enhance the effect of reward offerings. Incentive impact on Π increases when Case DR

Case DT

expands (increasing α ) • Market Demand is less sensitive to sales price (decreasing β ) • Demand is more sensitive to quality (increasing γ ) • Quality investment incurs less money (decreasing λ ) • Production cost increases (increasing c) • • Consumer expectation decreases (decreasing x ) • Consumer expectation increases (increasing x ) 0

0

strategy is also more appropriate when consumers prefer a high-class product. Overall, we reveal that incentive strategies can help enhance overall supply chain performances. Moveover, we provide the important implications of the results of our investigation into the unique characteristics of incentive strategies and offer necessary guidelines for the adoption of incentive strategies into supply chain practices. We believe that this paper contributes to bridging the gap between theory and practice in supply chain quality management. Despite its contribution, this study is not free from several limitations which may serve as a guideline for a further study. First, we obtain the optimal solutions as closed forms and show the comparison results of important variables in Proposition 2 in their analytical forms. However, we do not show the analytical results of profit comparison due to the mathematical complexity, while only showing numerical analysis results. If there is a future study clearly comparing profits, it may better generalize the results of this study. Second, we focus on comparing two incentive schemes with and without target quality, but there may exist other types of incentives which can better facilitate the supplier’s quality and overall performance. Therefore, a future study may investigate the effects of other incentive types and compare the results with the present study. Third, in this study, we adopt a linear demand function and a quadratic quality investment cost. However, there are other functional forms for demand and quality cost. Therefore, we can generalize the results of this study if there is a future study testing whether those results still hold. We believe that the present study can be a foundation for such future research directions. Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2015R1C1A1A02036682). 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