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Quality improvement in competing supply chains
Int. J. Production Economics 134 (2011) 262–270
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Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe
Quality improvement in competing supply chains Gang Xie a,n, Shouyang Wang a, K.K. Lai b a b
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China Department of Management Sciences, City University of Hong Kong, Hong Kong
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 September 2010 Accepted 28 June 2011 Available online 21 July 2011
In this study, we consider quality improvement in a given segment of the market, shared by two supplier–manufacturer supply chains which offer a given product at the same price but compete on quality. The mechanism on the selection of supply chain structures and quality improvement strategies of the two supply chains is described. In particular, we analyze three possible structure combinations: two integrated supply chains, two decentralized supply chains, and one integrated and one decentralized supply chains. Between the supply chains, Nash’s non-cooperative game is implemented. Numerical experiments illustrate the mechanism and some related issues are discussed. & 2011 Elsevier B.V. All rights reserved.
Keywords: Supply chain Competition Coordination Quality improvement
1. Introduction Supply chain quality is a key component in achieving competitive advantage, and quality management practices are significantly correlated with players’ interactions which influence tangible business results and customer satisfaction levels (Forker, 1997; Baiman et al., 2000; Lin et al., 2005; Bernstein and Federgruen, 2007; Franca et al., 2010; Karipidis, 2011; Rong et al., 2011; Xie et al., 2011). In many industries, competition is shifting from price to quality in specific segments of the market (Gans, 2002; Ren and Zhou, 2008). That is, competitors adopt the same price policy but offer different quality of products in a given market segment. For example, in telecommunications industry, mobile operators China Mobile Limited and China Unicom Limited compete by offering value-added services with different functionalities and quality of service to attract potential customers. In the market for fast food, McDonald’s and KFC compete by providing products with different designs and taste. Also, there are competing pairs such as Coca-Cola and Pepsi-cola in soft drinks market. As the procedure from raw materials to products is not within a single firm but throughout a supply chain, quality of a manufacturer’s products depends on not only its own process quality but also on the quality of its supplier(s) (Reyniers and Tapiero, 1995; Foster Jr, 2008; Robinson and Malhotra, 2005; Hsieh and Liu, 2010). However, there are many quality incidents caused by low quality of raw materials or spare parts. For example, millions of automobiles were recalled by Toyota because of unqualified
n
Corresponding author. Tel.: þ86 10 62545830; fax: þ 86 10 62541823. E-mail address: [email protected] (G. Xie).
0925-5273/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2011.07.007
spare parts from its suppliers in 2009 (TOYOTA, 2010). In China, there were incidents of poisonous powdered milk caused by low quality milk produced by inferior cattle, milk adulterated with melamine and nonstandard production processes used in the milk industry (AQSIQ, 2010). Therefore, quality improvement is an important issue in supply chain quality management. A natural question is whether and what kind of interaction between the manufacturer and its supplier(s) can improve quality of products in a given market segment in a competitive environment. From a supply chain perspective, Singer et al. (2003) derived the conditions under which the supplier and the retailer might devise a mutually beneficial contract that simultaneously increases profit and improves quality. Zhu et al. (2007) considered a buyer who designed a product and owned the brand, but outsourced production to a supplier. Both the buyer and the supplier incurred quality related costs. They explored the roles of different parties in a supply chain in quality improvement, and showed that the buyer’s involvement could have a significant impact on profits of both parties, and of the supply chain as a whole. Chao et al. (2009) proposed a contract with selective root cause analysis which differentiated early failures from late failures to coordinate quality improvement efforts of supply chain members. Different from quality management in a single supply chain, we investigate quality improvement in competing supply chains so as to discover which supply chain structure and quality improvement strategy will be selected by the competing supply chains. With the same price, a higher quality level always brings more consumers in the same market segment. Generally speaking, in the market for a particular product, products with ‘‘high quality, high price’’ are provided for high-end customers, who constitute the most price insensitive segment of the market (Chambers et al., 2006). In a
G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
competitive environment, Nash’s non-cooperative game is usually implemented between competitors (Banker et al., 1998). In a supply chain, coordination between players has an important impact on quality related decisions. Reyniers and Tapiero (1995) modeled the effect of price rebates and after-sales warranty costs on the choice of a supplier from the quality perspective, inspection policy of a manufacturer, and the resultant end product quality. They explored both non-cooperative and cooperative settings and highlighted the importance of strategic and contractual issues in quality management. Forker (1997) linked quality management with process optimization to address both effectiveness and efficiency concerns. The study suggested that system performance was affected by transaction-specific investments in a coordinated relationship. In this study, we consider two supply chain structures—vertical integration and decentralized settings. In a supply chain with vertical integration, the centralized decision-maker can realize coordination within the supply chain (Cachon, 2003; Ferguson et al., 2006; Zhu et al., 2007). In a market segment shared by two competing supply chains, competition intensity can influence equilibrium distribution structures. McGuire and Staelin (1983) investigated the effect of product competition on Nash equilibrium distribution structures in a duopoly where each manufacturer distributes its goods through a single exclusive retailer. The investigation showed that for low degrees of competition, manufacturers preferred to distribute products through a company store; for more highly competitive goods, manufacturers would be more likely to use a decentralized distribution system. In contrast to Coughlan and Wernerfelt (1989) and Gupta and Loulou (1998) found that decentralization did not always imply a unique equilibrium or more profitable than integration. In the context of a channel duopoly, Iyer (1998) showed that a mixed distribution channel, i.e. a channel in which one manufacturer chose coordination while the other chose non-coordination, could achieve equilibrium in markets with weak brand loyalty. The paper closest to ours is Banker et al. (1998), which developed formal models of oligopolistic competition to investigate whether equilibrium levels of quality increased in competition intensity. They considered asymmetric duopolistic competition where the dominant firm’s potential intrinsic demand decreased. The investigation suggested that the relationship between equilibrium quality and competition intensity depended on what increased competition was perceived as. Similar to Banker et al. (1998), we consider quality-based competition in a market segment. Different from the competition between two firms in Banker et al. (1998), we investigate the quality equilibrium that between two supplier–manufacturer supply chains which provide a certain product to a given market segment. Furthermore, we consider the interaction between suppliers and manufacturers in the two supply chains, and the mechanism on the selection of supply chain structure and quality improvement strategy. Extant literature on supply chain quality management has not considered quality improvement in competing supply chains as yet, to the best of our knowledge. In this study, we analyze quality improvement of players in a single segment of market shared by two supplier–manufacturer supply chains. For simplicity of analysis, we consider the case where quality of products is decided by that of raw materials. Initially, the two suppliers invest in quality and there is no quality improvement in the two supply chains. Then, we describe the mechanism on the selection of supply chain structure and quality improvement strategy of each supply chain. Between the two supply chains, Nash’s non-cooperative game is implemented. In an integrated supply chain, decision-making is centralized. In a decentralized supply chain, the manufacturer may invest in quality improvement for maximization of its own profit.
263
Moreover, quality improvement is analyzed under three possible combinations of structures of the two supply chains: two integrated supply chains, two decentralized supply chains, and one integrated and one decentralized supply chains. In each combination of structures of the two supply chains, we consider two possible scenarios of quality improvement strategies: quality improvement by one chain and quality improvement by both chains. Numerical experiments demonstrate the mechanism and some related issues are discussed. The remainder of the paper is organized as follows. In Section 2, we describe the problem of quality decisions and the mechanism on the selection of supply chain structure and quality improvement strategy of the two supply chains. Then, quality improvement within different structure combinations of the two supply chains, including two integrated supply chains, two decentralized supply chains, and one integrated and one decentralized supply chains, are considered in Section 3, Section 4, and Section 5, respectively. The mechanism is illustrated by way of experiments, and some related issues are discussed, in Section 6. Section 7 draws conclusions and suggests some directions for future investigations.
2. Description of the problem In a given market segment, two supply chains maintain the same price but compete for more consumers with respect to quality of their products. Assumptions on the problem are as follows. Assumption 1. In the same market segment, the two competing supply chains adopt the same price but compete on quality. This assumption is possible; for example, in the same segment of the market, Adidas and Nike sell shoes at almost the same price but offer different designs and product features. Assumption 2. The market is divided into segments with respect to price. That is, the market is divided into segments defined by price of products. This assumption is also reasonable because quality is always tagged by price; for example, high quality means high price. Assumption 3. Consumers in the given market segment can recognize the quality of products provided by any of the supply chains. Nowadays, many competitors try to highlight quality characteristics of their products by advertisements. As a result, consumers can know about the quality of products easily. Following the definition of quality in Banker et al. (1998), we use the term ‘‘quality’’ to refer to both design and conformance quality characteristics that are of interest to the consumer when evaluating the product offered by a supply chain. The following notations are used in the model: s combination of quality improvement strategy and supply chain structures in the two competing supply chains (s¼NN, OII, ODD, OID, TII, TDD and TID); xsi quality of raw materials provided by the ith supply chain within s (i,j¼1, 2, iaj); p price per unit of products in the given market segment; wi wholesale price per unit of raw materials in the ith supply chain; e quality related variable cost of a supplier; CM fixed cost related to quality of a manufacturer; CS fixed cost related to quality of a supplier; vM variable production cost per unit for a manufacturer; vS variable production cost per unit for a supplier; ki share of the intrinsic demand potential for the ith supply chain;
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a demand sensitivity of the ith supply chain’s quality;
(i,j ¼1, 2, iaj) for quality is
b competition intensity denoting the competitive effects of
xNN ¼ i n
quality for the supply chain pair (i,j).
2½eða þ bÞ þ CS ½ðwi vS Þða þ bÞeki aþ eb½ðwj vS Þða þ bÞekj a 4½eða þ bÞ þ CS 2 e2 b
2
:
ð2:3Þ In this study, xsi and xsj are decision variables and other variables are exogenous variables, known to both supply chains. In addition, we assume that p 4wi þvM and wi 4vS þ exsi (i,j¼1, 2, iaj). These inequalities ensure that each player in a decentralized supply chain makes a positive profit. Extending the quality definition in Banker et al. (1998), we assume that the primary demand function for products provided by the ith supply chain is decided by quality xsi and xsj , as follows: Dsi
xsi bðxsj xsi Þ
¼ ki a þ a
ð2:1Þ
where ki þkj ¼1, i, j¼1, 2, iaj. Here, kia is the potential intrinsic demand for the ith supply chain, which is irrespective of quality. In a specific combination s of quality improvement strategy and supply chain structures, demand function Dsi implies three key empirical regularities: (i) Dsi has a positive correlation with the ith supply chain’s quality; (ii) Dsi has a negative correlation with preponderance of xsj over xsi , i.e. xsj xsi ; and (iii) if both supply chains increase their quality by one unit, then sales of both should increase. In a market segment consisting of two competing supply chains (Fig. 1), both suppliers and manufacturers know the distribution of demand, and they organize the required production for meeting the demand. Initially, there is no quality improvement in the two decentralized supply chains, s¼NN, and the competition between them takes place in the following sequential steps: (i) The two suppliers simultaneously select their quality levels; (ii) The two supply chains observe each other’s quality choices; (iii) Demand is realized based on quality levels set by the two supply chains. Profit PNN Si ðxÞ of the ith supplier is NN NN NN NN 2 PNN Si ðxÞ ¼ ðwi vS exi Þ½ki a þða þ bÞxi bxj f CS ðxi Þ :
Proof. See the Appendix.
Corollary 2.2. In case of two decentralized supply chains, quality of products provided by a supply chain increases in wholesale price wi (i,j ¼1, 2, iaj) but decreases in its share ki of potential instinct demand. Proof. Straightforward and, therefore, omitted.
Proposition 2.1. When there are two decentralized supply chains n and quality is decided by the two suppliers, equilibrium solution xNN i
Results stated in Corollary 2.2 indicate that a higher wholesale price wi makes the ith supplier enhance its equilibrium quality to achieve higher demand and profit. However, with increase of share ki of potential intrinsic demand, the ith supplier will decrease its equilibrium quality because reduction of quality cost is more than the decrease of revenue caused by demand reduction. As a result, quality enhancement of products by both supply chains can be realized by raising wholesale price wi and wj of raw materials. For enhancement of equilibrium quality of products provided by a certain supply chain, an efficient way is to reduce the share of its potential intrinsic demand in the given market segment. With the equilibrium solution, we can derive profit PNN Mi ðxÞ of the ith manufacturer NN PNN bxNN : Mi ðxÞ ¼ ðpwi vM Þ½ki a þ ða þ bÞxi j n
price
quality
ð2:4Þ
PNN Mi ðxÞ
and are Generally speaking, only when profits positive, will the players manufacture the products. Then, we continue to analyze decisions of the two competing supply chains on selection of quality improvement strategy and channel structure. Let s1 and s2 be combinations of quality improvement strategies and structures of the two competing supply chains after decisions of the first mover and the second mover, respectively. Decision sequences of the two supply chains are described as follows: (i) The two supply chains observe each other’s quality levels; (ii) As the first mover, the ith supply chain selects its supply chain structure and quality improvement strategy to maximize its profit, i.e. s1 is formed; (iii) After observing actions of the ith supply chain, the second mover, i.e. the jth supply chain, selects its supply chain structure and quality improvement strategy to maximize its profit, i.e. s2 is formed; (iv) Demand is realized based on quality levels set by the two supply chains.
Products
Products
orders Raw materials
n
PNN Si ðxÞ
orders Raw materials
&
ð2:2Þ
This model is similar to other studies which have modeled the selection of quality (Moorthy, 1988; Tagaras and Lee, 1996; 2 Banker et al., 1998). Fixed costs f þ CS ðxNN i Þ are increasing and NN convex in quality level xi . Therefore, Proposition 2.1 and Corollary 2.2 summarize our findings on quality of products before quality improvement.
quality
&
price
Fig. 1. Business flow of two competing supply chains.
G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
For the first mover i (i,j ¼1, 2, iaj), selection of supply chain structure and quality improvement strategy s and formation of s1 can be described as follows: s1 ¼ s ¼
arg s A fNN,OII,ODD,OIDg
max Psi ðxÞ:
ð2:5Þ
After observing actions of the first mover i, the second mover j selects its supply chain structure and quality improvement strategy, and s2 can be described as s2 ¼ s ¼
arg s A fNN,OII,ODD,OID,TII,TDD,TIDg
max Psj ðxÞ:
ð2:6Þ
According to Banker et al. (1998), the industry quality provided by the two competing supply chains is x~ s ¼ ððDsi xsi þ Dsj xsj Þ=ðDsi þDsj ÞÞ, and the industry profit is Ps ¼ Psi þ Psj . In the following sections, we analyze quality improvement decisions under different combinations of structures of the two competing supply chains: two integrated supply chains (II), two decentralized supply chains (DD), and one integrated and one decentralized supply chains (ID), where centralized decision-making is realized in an integrated supply chain but the manufacturer invests in quality improvement only for maximization of its own profit. In all the three combinations of structures, Nash’s noncooperative game is implemented between two supply chains.
3.2. Quality improvement by two chains When both two supply chains invest in quality improvement, s¼TII, competition between the two supply chains takes place in the following sequential steps: (i) The two supply chains observe each other’s quality levels; (ii) The two supply chains implement quality improvement; (iii) Demand is realized based on quality levels set by the two supply chains. Profit PTII i ðxÞ of the ith supply chain is TII TII TII TII 2 NN 2 PTII Þ CS ðxNN Þ2 : i ðxÞ ¼ ðpvexi Þ½ki a þ ða þ bÞxi bxj f c½ðxi Þ ðxi i n
Then, Proposition 3.1 and Corollary 3.2 summarize our findings. Proposition 3.1. When coordination is realized in both supply chains, the ith supply chain implements quality improvement but the jth supply chain does not, and equilibrium solutions for quality are n
3. Integrated supply chains
3.1. Quality improvement by one chain
(i) The two supply chains observe each other’s quality levels; (ii) The ith supply chain implements quality improvement while the jth supply chain does not; (iii) Demand is realized based on quality levels set by the two supply chains. When the ith supply chain finds that its profit will be enhanced n n by improving quality level from xNN to xOII , it will attempt to invest i i in quality improvement. As the jth manufacturer does not invest in quality improvement, equilibrium quality of the jth supply chain n n will change from xNN to xOII . With channel coordination, profit j j POII ðxÞ of the ith supply chain after quality improvement is i OII OII OII OII 2 NN 2 POII Þ CS ðxNN Þ2 i ðxÞ ¼ ðpvexi Þ½ki a þ ða þ bÞxi bxj f c½ðxi Þ ðxi i n
n
ð3:1Þ where c ¼ minfCM ,CS g and v¼vM þvS. In the jth supply chain, the jth supplier will select a quality level that maximizes profit POII j ðxÞ of the jth supply chain as follows:
a
4½eða þ bÞ þ c½eða þ bÞ þCS e2 b
2
,
and ¼ xOII j n
OII OII 2 þ bÞxOII j bxi f CS ðxj Þ :
ð3:2Þ
In the following subsection, we continue to analyze the case where both supply chains implement quality improvement.
2½eða þ bÞ þc½ðpvÞða þ bÞekj a þ eb½ðpvÞða þ bÞeki a 4½eða þ bÞ þ c½eða þ bÞ þCS e2 b
2
: ð3:5Þ
When coordination is realized and quality improvement is n implemented by both supply chains, equilibrium solution xTII i (i,j ¼1, 2, i aj) for quality is xTII ¼ i n
When only one supply chain invests in quality improvement, s¼OII, competition between the two supply chains takes place in the following sequential steps:
e
2½eða þ bÞ þCS ½ðpvÞða þ bÞeki a þ eb½ðpvÞða þ bÞekj a
ð3:4Þ
In a given market segment with two integrated supply chains, decision-making for quality improvement is centralized in each supply chain. The objective of quality improvement for the central decision-maker is to maximize profit of the supply chain. We consider two cases of quality improvement strategies: quality improvement by one chain in Section 3.1 and quality improvement by two chains in Section 3.2, as follows.
xOII j Þ½kj a þð
n
ð3:3Þ
xOII ¼ i
POII j ðxÞ ¼ ðpv
265
2½eða þ bÞ þc½ðpvÞða þ bÞeki a þ eb½ðpvÞða þ bÞekj a 4½eða þ bÞ þ c2 e2 b
2
: ð3:6Þ
Proof. See the Appendix.
&
Corollary 3.2. In structure combination II, equilibrium quality of products provided by a supply chain increases in price p but decreases in its share ki (i,j ¼1, 2, iaj) of potential intrinsic demand. Proof. Straightforward and, therefore, omitted.
&
From Corollary 3.2, we can find that in structure combination II of two integrated supply chains, enhancement of equilibrium quality of products provided by both supply chains can be realized by raising price of products. For enhancement of equilibrium quality of products provided by a supply chain, an efficient way is to reduce the share of its potential intrinsic demand in the given market segment.
4. Decentralized supply chains Different from integrated supply chains, in the case of two decentralized supply chains (DD), manufacturers invest in quality improvement for maximizing their own profits.
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G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
4.1. Quality improvement by one chain
and
When only one supply chain invests in quality improvement, s¼ODD, competition between the two supply chains takes place in the following sequential steps:
xODD ¼ j
(i) The two supply chains observe each other’s quality levels; (ii) The ith manufacturer implements quality improvement while the jth manufacturer does not; (iii) Demand is realized based on quality levels set by the two supply chains. In the ith supply chain, the manufacturer invests in quality improvement to maximize its own profit. Profit of the ith manufacturer is ODD PODD bxODD CM ½ðxODD Þ2 ðxNN Þ2 , Mi ðxÞ ¼ ðpwi vM Þ½ki a þ ða þ bÞxi i j i n
ð4:1Þ For the jth supply chain, profit of the jth supplier is
PODD ðxÞ ¼ ðwj vS Sj
e
xODD Þ½kj a þ ð j
a
ð4:2Þ After quality improvement is implemented by the ith manufacturer, profit of the ith supplier is
PODD ðxÞ ¼ ðwi vS exODD Þ½ki a þ ða þ bÞxODD bxODD f CS ðxNN Þ2 , Si i i j i n
n
n
ð4:3Þ and profit of the jth manufacturer is ODD PODD bxODD : Mj ðxÞ ¼ ðpwj vM Þ½kj a þða þ bÞxj i n
NN PODD Mi ðxÞ Z PMi ðxÞ
n
n
ð4:8Þ
Or else, if quality improvement is implemented by both chains, n then equilibrium solution xTDD (i, j ¼1, 2, iaj) of quality is i xTDD ¼ i n
ðpwi vM Þða þ bÞ : 2CM
ð4:9Þ
Proof. See the Appendix.
&
Corollary 4.2. In structure combination DD, in a supply chain with quality improvement, quality of products increases in price p and competition intensity b but decreases in wholesale price wi. However, in a supply chain without quality improvement, quality of products increases in wholesale price wj but decreases in its share kj of potential intrinsic demand. &
From Corollary 4.2, we can obtain managerial insights as follows: in structure combination of two decentralized supply chains, enhancement of equilibrium quality of products provided by both supply chains can be realized by raising price of products and lowering wholesale price of the first mover. For enhancement of equilibrium quality of products provided by a supply chain without quality improvement, an efficient way is to raise wholesale price wj and to reduce its share kj in potential intrinsic demand in the market segment.
ð4:4Þ
PODD ðxÞ Z PNN Si Si ðxÞ
and are Only if conditions met, will manufacturer Mi invest in quality and supplier Si will agree to quality improvement. 4.2. Quality improvement by two chains When both supply chains invest in quality improvement, s¼TDD, competition between the two supply chains takes place in the following sequential steps: (i) The two supply chains observe each other’s quality levels; (ii) The two manufacturers implement quality improvement; (iii) Demand is realized based on quality levels set by the two supply chains. Profit of the ith manufacturer is
PTDD Mi ðxÞ ¼ ðpwi vM Þ½ki a þð
ðwj vS Þða þ bÞekj a þ ebxODD i 2½eða þ bÞ þ CS
Proof. Straightforward and, therefore, omitted.
þ bÞxODD bxODD f CS ðxODD Þ2 : j i j
n
n
a þ bÞxTDD bxTDD CM ½ðxTDD Þ2 ðxNN Þ2 : i i j i n
5. One integrated and one decentralized supply chains In structure combination of one integrated and one decentralized supply chains (ID), the ith supply chain is vertically integrated and the jth supply chain is a decentralized setting. In this case, we consider two cases: quality improvement by one supply chain and quality improvement by two supply chains. 5.1. Quality improvement by one chain When only one supply chain invests in quality improvement, s¼OID, competition between the two supply chains takes place in the following sequential steps: (i) The ith supply chain invests in quality improvement with coordination while the jth supply chain does not; (ii) The two supply chains observe each other’s choice of quality levels; (iii) Demand is realized based on the quality levels.
ð4:5Þ After quality improvement is implemented, profit of the ith supplier is
PTDD Si ðxÞ ¼ ðwi vS
e
n xTDD Þ½ki a þ ð i
a
n n n þ bÞxTDD bxTDD f CS ðxNN Þ2 : i j i
ð4:6Þ Then, Proposition 4.1 and Corollary 4.2 summarize our findings. Proposition 4.1. When both supply chains are decentralized, if quality improvement is implemented by one chain, then equilibrium solutions of quality are xODD ¼ i n
ðpwi vM Þða þ bÞ , 2CM
ð4:7Þ
Then, profit function of the ith supply chain is
POID ðxÞ ¼ ðpvexOID Þ½ki a þða þ bÞxOID bxOID i i i j Þ2 ðxNN Þ2 CS ðxNN Þ2 f c½ðxOID i i i n
n
ð5:1Þ
while profit function of the jth supplier is OID POID Þ½kj a þða þ bÞxOID bxOID f CS ðxOID Þ2 : Sj ðxÞ ¼ ðwj vS exj j i j
ð5:2Þ As quality of products in the jth supply chain changes from n n xNN to xOID , profit of the jth manufacturer is j j OID POID bxOID : Mj ðxÞ ¼ ðpwj vM Þ½kj a þ ða þ bÞxj i n
n
ð5:3Þ
G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
5.2. Quality improvement by two chains When both supply chains invest in quality improvement, s¼TID, competition between the two supply chains takes place in the following sequential steps: (i) The two supply chains observe each other’s quality levels; (ii) The two supply chains implement quality improvement; (iii) Demand is realized based on quality levels set by the two supply chains. Then, profit function of the ith supply chain is TID TID TID PTID i ðxÞ ¼ ðpvexi Þ½ki a þ ða þ bÞxi bxj 2 NN 2 f c½ðxTID Þ CS ðxNN Þ2 : i i Þ ðxi n
n
ð5:4Þ
Profit function of the jth manufacturer is
PTID Mj ðxÞ ¼
TID TID 2 NN 2 ðpwj vM Þ½kj a þ ða þ bÞxTID Þ j bxi CM ½ðxj Þ ðxj n
ð5:5Þ where profit
TIDn NN n PTID Þ Z PNN Þ Mj ðxj Mj ðxj
PTID Sj ðxÞ
PTID Sj ðxÞ ¼
and
TIDn NN n PTID Þ Z PNN Þ, Sj ðxj Sj ðxj
and
of the jth supplier is
ðwj vS exTID Þ½kj a þða þ bÞxTID bxTID f CS ðxNN Þ2 : j j i j n
n
n
n
267
Corollary 5.4. In structure combination ID, when there is quality improvement by both chains, quality of products increases in price p but decreases in share ki of potential intrinsic demand and wholesale price wj. In particular, quality of products provided by the jth supply chain increases in b. Proof. Straightforward and, therefore, omitted.
&
From Corollary 5.3, we can obtain managerial insights as follows. In structure combination of one integrated and one decentralized supply chains, when the integrated supply chain implements quality improvement while the decentralized supply chain does not, enhancement of equilibrium quality of products provided by both supply chains can be realized by raising price of products and wholesale price of the decentralized chain and reducing their shares in potential intrinsic demand. From Corollary 5.4, we can obtain managerial insights as follows. In structure combination of one integrated and one decentralized supply chains, when both supply chains implement quality improvement, enhancement of equilibrium quality of products provided by both supply chains can be realized by raising price of products and lowering wholesale price of the decentralized chain. In particular, enhancement of equilibrium quality of products provided by the first mover can be realized by reducing its share in potential intrinsic demand in the market segment.
ð5:6Þ Therefore, we have Proposition 5.1, as follows. Proposition 5.1. In structure combination ID, if quality improvement is implemented by only the ith supply chain, s ¼OID, then equilibrium solutions of quality are ¼ xOID i n
2½eða þ bÞ þ CS ½ðpvÞða þ bÞeki a þ eb½ðwj vS Þða þ bÞekj a 4½eða þ bÞ þc½eða þ bÞ þ CS e2 b
2
,
ð5:7Þ and ¼ xOID j n
2½eða þ bÞ þ c½ðwj vS Þða þ bÞekj a þ eb½ðpvÞða þ bÞeki a 4½eða þ bÞ þc½eða þ bÞ þ CS e2 b
2
:
6. Analysis with experiments In this section, we illustrate the mechanism with numerical experiments. In a competitive environment, in order to reflect the impact of competition intensity b on the results, we suppose that b is variable and other parameters are fixed. Let ki ¼0.4, wi ¼wj ¼6, a¼ 1000, a ¼200, p¼ 20, vS ¼1, vM ¼2, e ¼2, f¼ 1000, CS ¼3000, CM ¼2000 and bA[100, 300]. The migration of equilibrium supply chain structures and quality improvement strategy are shown in Fig. 2, where curves s and s1
ð5:8Þ
12000
Or else, if quality improvement is implemented by both supply chains, s¼TID, then equilibrium solutions of quality are
10000
¼ xTID i n
ðpvÞða þ bÞeki a þ ebxTID j 2½eða þ bÞ þ c
,
ð5:9Þ
and xTID j
n
s1=OID
8000
n
6000
s=NN
4000
ðpwj vM Þða þ bÞ ¼ : 2CM
Proof. See the Appendix.
ð5:10Þ
0
&
Let A¼(p wj vM)/(2CM), B ¼(p v)(a þ b) ekia, M¼ a þ(c/e) and N ¼p v Ac. We have Theorem 5.2, as follows: Theorem 5.2.
n When B rMN, xTID pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i
2000
increases in b. Or else, when
10000 9000 8000
decreases in b; if B 4MN, if b o ðBMNÞ=ðeAÞM, then xTID i pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n b 4 ðBMNÞ=ðeAÞM, then xTID increases in b . i
7000
Proof. See the Appendix.
4000
n
&
Then, Corollary 5.3 and 5.4 can be derived as follows. Corollary 5.3. In structure combination ID, when there is quality improvement by one chain, quality of products increases in price p and wholesale price wj, but decreases in share ki of potential intrinsic demand. Proof. Straightforward and, therefore, omitted.
&
6000
100 120 140 160 180 200 220 240 260 280 300 s2=TID
s2=OII
s1=OID
5000 3000 2000 1000 0
100 120 140 160 180 200 220 240 260 280 300
Fig. 2. Maximum profits of supply chain i and j as functions of competition intensity and migration of equilibrium supply chain structures.
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G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
16000
1.6
s2=TID
15500
s=NN
1.4
0.8
14000
s2=OII
0.6
13500
0.4
13000
0.2 0
100 120 140 160 180 200 220 240 260 280 300
Fig. 3. Industry profits as functions of competition intensity.
reflect the impacts of competition intensity b on maximum profits of the ith supply chain before and after the migration; curves s1 and s2 reflect the impacts of competition intensity b on maximum profits of the jth supply chain before and after the migration. When s¼NN, there is no quality improvement and both supply chains are decentralized. For the first mover i, according to Eq. (2.5), there is s1 ¼ OID ¼ arg max Psi ðxÞ, bA[100,300].
1.2
After s1 ¼OID is determined by the ith supply chain, the second mover j has to select its own supply chain structure and quality improvement strategy from {OII, TII, OID, TID}. According to Eq. (2.6), s2 ¼ arg max Psj ðxÞ, bA[100,300], and there is
0
s A fNN,ODD,OIDg
TIDj
0.6 0.4 0.2 100 120 140 160 180 200 220 240 260 280 300
1.6 1.4 1.2
As the migration of equilibrium supply chain structures and quality improvement strategies takes place, industry profit becomes the function of competition intensity b in NN, OII and TID (Fig. 3). Comparing industry profits in OII, TID with that in NN, we find 8 TID NN > < P ðxÞ 4 P ðxÞ, b ¼ 100 OII NN P ðxÞ 4 P ðxÞ, b A ½120,160 : > : OII P ðxÞ o PNN ðxÞ, b A ½180,300
OIIj
0.8
s A fOII,TII,OID,TIDg
OII,
NNj
1
(
b ¼ 100 : b A ½120,300
100 120 140 160 180 200 220 240 260 280 300
1.6 1.4
TID,
TIDi
1
14500
s2 ¼
OIIi
1.2
15000
12500
NNi
NN
OII
TID
1 0.8 0.6 0.4 0.2 0
100 120 140 160 180 200 220 240 260 280 300
Fig. 4. The impact of competition intensity on quality of supply chain i, j and industry quality.
Therefore, the following observations can be made:
Competition intensity has a significant impact on profit and
the selection of supply chain structure and quality improvement strategy. Vertical integration (VI) is a dominant strategy for each supply chain in quality improvement. There is a prisoners’ dilemma (for example, when bA[180,300]): though strategy VI brings more profit for the supply chain which adopts it when s1 ¼OID, two supply chains with VI, i.e. s2 ¼ OII, may cause lower profits for both chains than when s¼NN.
When s¼NN, OII and TID, quality levels in different supply chain structures and quality improvement strategies are shown in Fig. 4, where curves si, sj and s reflect the impacts of competition intensity b on quality levels in supply chain i, j and industry quality. From Fig. 4, the following observations can be made:
Generally, quality improvement by both chains can achieve
higher industry quality than quality improvement by one chain. n n As xTID 4 xOII , quality improvement by the manufacturer j j contributes more to quality enhancement than vertical integration.
From these observations, we can also find that competition intensity b may be used to adjust supply chain structure and quality improvement strategy, and thus to improve the quality of products.
7. Conclusions and future work In this paper, we have described the mechanism on the selection of supply chain structure and quality improvement strategy of two competing supply chains which share a given segment of the market for a given product. Prices of products provided by the two supply chains are the same, and competition between them is based on quality of products. In each supply chain, the supplier provides raw materials, which are processed by the manufacturer into products for the given market segment. Quality of products is decided by that of raw materials. We analyze three possible structure combinations of the two supply chains in the given market segment: two integrated supply chains, two decentralized supply chains, and one integrated and one decentralized supply chains. The study provides valuable insights into the mechanism that leads to quality enhancement
G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
and the selection of supply chain structure and quality improvement strategy by competing supply chains. In future work, quality determined by both raw materials and production process and quality determined by competition among supply chains with uncertain demand are expected to be worth further studying.
combination II as xTII ¼ i n
2½eða þ bÞ þc½ðpvÞða þ bÞeki a þ eb½ðpvÞða þ bÞekj a
We sincerely thank the referees for their valuable suggestions and comments. This work was supported by the National Natural Science Foundation of China (Nos. 70871107, 70731003) and China Postdoctoral Science Foundation (Grant no. 20060400103), and Main Direction Program of Knowledge Innovation of Chinese Academy of Sciences (No. KACX1-YW-0906).
2
:
Proof of Proposition 4.1. When quality improvement is implemented by one chain, we differentiate Eqs. (4.1) and (4.2) with ODD and xODD , respectively. Let @PODD ¼ 0 and respect to xODD Mi ðxÞ=@xi i j
ðxÞ=@xODD ¼ 0. There are @PODD Sj j 8 < ðpwi vM Þða þ bÞ2CM xODD ¼0 i ebxODD ¼ ðwj vS Þða þ bÞekj a : 2½eða þ bÞ þCS xODD j i
:
Then, we can derive equilibrium solutions in supply chain structure combination DD as
Appendix
¼ xODD i
ðpwi vM Þða þ bÞ , 2CM
¼ xODD j
ðwj vS Þða þ bÞekj a þ ebxODD i : 2½eða þ bÞ þ CS
n
Proof of Proposition 2.1. We differentiate Eq. (2.2) with respect NN to xNN and let @PNN ¼ 0. The first-order conditions charSi ðxÞ=@xi i acterizing equilibrium quality are NN ¼ ðwi vS Þða þ bÞeki a: 2½eða þ bÞ þ CS xNN i ebxj
Then, we can derive the equilibrium solution for quality as follows: n
4½eða þ bÞ þ c2 e2 b
TII 2 Since @2 PTII i ðxÞ=@ðxi Þ ¼ 2½eða þ bÞ þc o 0, the profit function is strictly concave.
Acknowledgements
xNN ¼ i
269
2½eða þ bÞ þ CS ½ðwi vS Þða þ bÞeki a þ eb½ðwj vS Þða þ bÞekj a 4½eða þ bÞ þ CS 2 e2 b
2
:
n
n
ODD 2 Since @2 PODD Þ ¼ 2CM o 0 and @2 PODD ðxÞ=@ðxODD Þ2 ¼ Mi ðxÞ=@ðxi Sj j 2½eða þ bÞ þCM] o0, profit functions are strictly concave. When quality improvement is implemented by both chains, we and let @PTDD differentiate Eq. (4.5) with respect to xTDD Mi ðxÞ= i TDD @xi ¼ 0, so we have
ðpwi vM Þða þ bÞ2CM xTDD ¼ 0, i
NN 2 Since @2 PNN Si ðxÞ=@ðxi Þ ¼ 2½eða þ bÞ þ CS o 0, the profit function is strictly concave with respect to xNN i .
Proof of Proposition 3.1. Differentiating Eqs. (3.1) and (3.2) with respect to xOII and xOII respectively and equating them to zero, we i j obtain the following functions: 8 OII < 2½eða þ bÞ þcxOII i ebxj ¼ ðpvÞða þ bÞeki a : OII : 2½eða þ bÞ þCS xj ebxOII i ¼ ðpvÞða þ bÞekj a
then equilibrium solutions of quality are xTDD ¼ i n
ðpwi vM Þða þ bÞ : 2CM
TDD 2 Þ ¼ 2CM o 0, the profit functions are Since @2 PTDD Mi ðxÞ=@ðxi strictly concave.
Proof of Proposition 5.1. When quality improvement is implemented by one chain, we differentiate Eqs. (5.1) and (5.2) with and xOID , respectively. Let @POID ðxÞ=@xOID ¼ 0 and respect to xOID i i j i
Then, we can derive equilibrium solutions for quality in case of quality improvement by one chain in supply chain structure combination II as ¼ xOII i n
¼ xOII j n
2½eða þ bÞ þ CS ½ðpvÞða þ bÞeki a þ eb½ðpvÞða þ bÞekj a 2
4½eða þ bÞ þ c½eða þ bÞ þ CS e2 b
2½eða þ bÞ þ c½ðpvÞða þ bÞekj a þ eb½ðpvÞða þ bÞeki a 2
4½eða þ bÞ þ c½eða þ bÞ þ CS e2 b
OID ¼ 0. There are @POID Sj ðxÞ=@xj 8 < 2½eða þ bÞ þcxOID ebxOID ¼ ðpvÞða þ bÞeki a i j
: 2½eða þ bÞ þCS xOID ebxOID ¼ ðwj vS Þða þ bÞekj a j i
:
, Then, we derive equilibrium solutions in supply chain structure combination ID as follows:
:
OII 2 and @2 POII Since @2 POII i ðxÞ=@ðxi Þ ¼ 2½eða þ bÞ þc o 0 j ðxÞ= OII 2 @ðxj Þ ¼ 2½eða þ bÞ þ CS o0, the profit function is strictly concave. In the same way, we differentiate Eq. (3.3) with respect to xTII i TII and let @PTII i ðxÞ=@xi ¼ 0. The first-order conditions characterizing equilibrium quality are TII 2½eða þ bÞ þ cxTII i ebxj ¼ ðpvÞða þ bÞeki a:
Then, we can derive equilibrium solutions for quality in case of quality improvement by two chains in supply chain structure
xOID ¼ i n
2½eða þ bÞ þ CS ½ðpvÞða þ bÞeki a þ eb½ðwj vS Þða þ bÞekj a 2
4½eða þ bÞ þ c½eða þ bÞ þ CS e2 b
,
and ¼ xOID j n
2½eða þ bÞ þ c½ðwj vS Þða þ bÞekj a þ eb½ðpvÞða þ bÞeki a 2
4½eða þ bÞ þ c½eða þ bÞ þ CS e2 b
:
Since @2 POID ðxÞ=@ðxOID Þ2 ¼ 2½eða þ bÞ þ c o0 and @2 POID i Sj ðxÞ= i OID 2 @ðxj Þ ¼ 2½eða þ bÞ þ CS o0, the profit functions are strictly concave. When quality improvement is implemented by both chains, and xTID we differentiate Eqs. (5.4) and (5.5) with respect to xTID i j .
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G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
TID TID Let @PTID ¼ 0 and @PTID ¼ 0, so we have i ðxÞ=@xi Mj ðxÞ=@xj 8 TID TID < 2½eða þ bÞ þcxi ebxj ¼ ðpvÞða þ bÞeki a : TID : 2½eða þ bÞ þCM xTID ¼ ðpwj vM Þða þ bÞekj a j ebxi
Then equilibrium solutions of quality are ðpvÞða þ bÞeki a þ ebxTID j
n
xTID ¼ i n
xTID ¼ j n
2½eða þ bÞ þ c
,
ðpwj vM Þða þ bÞ : 2CM
TID 2 Since @2 PTID and @2 PTID i ðxÞ=@ðxi Þ ¼ 2½eða þ bÞ þc o0 Mj ðxÞ= 2 Þ ¼ 2[ e ( a þ b ) þC ] o0, the profit functions are strictly @ðxTID M j concave.
as Proof of Theorem 5.2. From Eq. (5.9), we can transform xTID i n
¼ xTID i n
A BMN 1 N AM ðM þ bÞ þ U þ 2 2e M þ b 2e 2
where A¼(p wj vM)/(2CM), B ¼(p v)(a þ b) ekia, M¼ a þ(c/e) and N ¼p v Ac. n = Obviously, A40. When (B MN)/(2e)r0, i.e. B rMN, @xTID i n increases @b ¼ ðA=2ÞðBMNÞ=½2eðM þ bÞ2 40. Therefore, xTID i in b. Or else, B 4MN, when (A/2)(M þ b) ¼(B MN)/[(2e)(Mþ b)], pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n is minimum. i.e. b ¼ ðBMNÞ=ðeAÞM, xTID i pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi n decreases in b; if As b 40, if b o ðBMNÞ=ðeAÞM, then xTID i pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi TIDn b 4 ðBMNÞ=ðeAÞM, then xi increases in b. References AQSIQ, 2010. Tianjin is trying to realize standardized control on raw milk with life cycle management. /http://www.clii.com.cn/S. Baiman, S., Fischer, P.E., Rajan, M.V., 2000. Information, contracting, and quality costs. Management Science 46, 776–789. Banker, R.D., Khosla, I., Sinha, K.K., 1998. Quality and competition. Management Science 44 (9), 1179–1192. Bernstein, F., Federgruen, A., 2007. Coordination mechanisms for supply chains under price and service competition. Manufacturing Service & Operations Management 9 (3), 242–262. Cachon, G., 2003. Supply chain coordination with contracts, Ch. 6. In: de Kok, A.G., Graves, S.C. (Eds.), Handbooks in Operations Research & Management Science, vol. 11. Elsevier B. V, New York, pp. 13–59. Chambers, C., Kouvelis, P., Semple, J., 2006. Quality-based competition, profitability, and variable costs. Management Science 52 (12), 1884–1895.
Chao, G.H., Iravani, S.M.R., Canan Savaskan, R., 2009. Quality improvement incentives and product recall cost sharing contracts. Management Science 55 (7), 1122–1138. Coughlan, A.T., Wernerfelt, B., 1989. On credible delegation by oligopolists: a discussion of distribution channel management. Management Science 35 (2), 226–239. Ferguson, M., Guide Jr., V.D.R., Souza, G.C., 2006. Supply chain coordination for false failure returns. Manufacturing Service & Operations Management 8 (4), 376–393. Forker, L.B., 1997. Factors affecting supplier quality performance. Journal of Operations Management 15, 243–269. Foster Jr, S.T., 2008. Towards an understanding of supply chain quality management. Journal of Operations Management 26 (4), 461–467. Franca, R.B., Jones, E.C., Richards, C.N., Carlson, J.P., 2010. Multi-objective stochastic supply chain modeling to evaluate tradeoffs between profit and quality. International Journal of Production Economics 127, 292–299. Gans, N., 2002. Customer loyalty and supplier quality competition. Management Science 48 (2), 207–221. Gupta, S., Loulou, R., 1998. Process innovation, product differentiation, and channel structure: strategic incentives in a duopoly. Marketing Science 17 (4), 301–316. Hsieh, C., Liu, Y., 2010. Quality investment and inspection policy in a supplier– manufacturer supply chain. European Journal of Operational Research 202, 717–729. Iyer, G., 1998. Coordinating channels under price and nonprice competition. Marketing Science 17 (4), 338–355. Karipidis, P.I., 2011. Market evaluations of dimensions of design quality. International Journal of Production Economics 129, 292–301. Lin, C., Chow, W.S., Madu, C.N., Kuei, C., Yu, P., 2005. A structural equation model of supply chain quality management and organizational performance. International Journal of Production Economics 96, 355–365. McGuire, T.W., Staelin, R., 1983. An industry equilibrium analysis of downstream vertical integration. Marketing Science 2 (2), 161–191. Moorthy, K.S., 1988. Product and price competition in a duopoly. Marketing Science 7 (2), 141–168. Ren, Z.J., Zhou, Y., 2008. Call center outsourcing: coordinating staffing level and service quality. Management Science 54 (2), 369–383. Reyniers, D.J., Tapiero, C.S., 1995. The delivery and control of quality in supplierproducer contracts. Management Science 41, 1581–1589. Robinson, C.J., Malhotra, M.K., 2005. Defining the concept of supply chain quality management and its relevance to academic and industrial practice. International Journal of Production Economics 96, 315–337. Rong, A., Akkerman, R., Grunow, M., 2011. An optimization approach for managing fresh food quality throughout the supply chain. International Journal of Production Economics 131, 421–429. Singer, M., Donoso, P., Traverso, P., 2003. Quality strategies in supply chain alliances of disposable items. Omega 31, 499–509. Tagaras, G., Lee, H.L., 1996. Economic models for vendor evaluation with quality cost analysis. Management Science 42, 1531–1543. TOYOTA, 2010. ETCS: technology proven in over 40 million Toyota vehicles. /http://www.toyota.com/recall/S. Xie, G., Yue, W., Wang, S., Lai, K.K., 2011. Quality investment and price decision in a risk-averse supply chain. European Journal of Operational Research 214 (2), 403–410. Zhu, K., Zhang, R.Q., Tsung, F., 2007. Pushing quality improvement along supply chains. Management Science 53 (3), 421–436.
Contents lists available at ScienceDirect
Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe
Quality improvement in competing supply chains Gang Xie a,n, Shouyang Wang a, K.K. Lai b a b
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China Department of Management Sciences, City University of Hong Kong, Hong Kong
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 September 2010 Accepted 28 June 2011 Available online 21 July 2011
In this study, we consider quality improvement in a given segment of the market, shared by two supplier–manufacturer supply chains which offer a given product at the same price but compete on quality. The mechanism on the selection of supply chain structures and quality improvement strategies of the two supply chains is described. In particular, we analyze three possible structure combinations: two integrated supply chains, two decentralized supply chains, and one integrated and one decentralized supply chains. Between the supply chains, Nash’s non-cooperative game is implemented. Numerical experiments illustrate the mechanism and some related issues are discussed. & 2011 Elsevier B.V. All rights reserved.
Keywords: Supply chain Competition Coordination Quality improvement
1. Introduction Supply chain quality is a key component in achieving competitive advantage, and quality management practices are significantly correlated with players’ interactions which influence tangible business results and customer satisfaction levels (Forker, 1997; Baiman et al., 2000; Lin et al., 2005; Bernstein and Federgruen, 2007; Franca et al., 2010; Karipidis, 2011; Rong et al., 2011; Xie et al., 2011). In many industries, competition is shifting from price to quality in specific segments of the market (Gans, 2002; Ren and Zhou, 2008). That is, competitors adopt the same price policy but offer different quality of products in a given market segment. For example, in telecommunications industry, mobile operators China Mobile Limited and China Unicom Limited compete by offering value-added services with different functionalities and quality of service to attract potential customers. In the market for fast food, McDonald’s and KFC compete by providing products with different designs and taste. Also, there are competing pairs such as Coca-Cola and Pepsi-cola in soft drinks market. As the procedure from raw materials to products is not within a single firm but throughout a supply chain, quality of a manufacturer’s products depends on not only its own process quality but also on the quality of its supplier(s) (Reyniers and Tapiero, 1995; Foster Jr, 2008; Robinson and Malhotra, 2005; Hsieh and Liu, 2010). However, there are many quality incidents caused by low quality of raw materials or spare parts. For example, millions of automobiles were recalled by Toyota because of unqualified
n
Corresponding author. Tel.: þ86 10 62545830; fax: þ 86 10 62541823. E-mail address: [email protected] (G. Xie).
0925-5273/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2011.07.007
spare parts from its suppliers in 2009 (TOYOTA, 2010). In China, there were incidents of poisonous powdered milk caused by low quality milk produced by inferior cattle, milk adulterated with melamine and nonstandard production processes used in the milk industry (AQSIQ, 2010). Therefore, quality improvement is an important issue in supply chain quality management. A natural question is whether and what kind of interaction between the manufacturer and its supplier(s) can improve quality of products in a given market segment in a competitive environment. From a supply chain perspective, Singer et al. (2003) derived the conditions under which the supplier and the retailer might devise a mutually beneficial contract that simultaneously increases profit and improves quality. Zhu et al. (2007) considered a buyer who designed a product and owned the brand, but outsourced production to a supplier. Both the buyer and the supplier incurred quality related costs. They explored the roles of different parties in a supply chain in quality improvement, and showed that the buyer’s involvement could have a significant impact on profits of both parties, and of the supply chain as a whole. Chao et al. (2009) proposed a contract with selective root cause analysis which differentiated early failures from late failures to coordinate quality improvement efforts of supply chain members. Different from quality management in a single supply chain, we investigate quality improvement in competing supply chains so as to discover which supply chain structure and quality improvement strategy will be selected by the competing supply chains. With the same price, a higher quality level always brings more consumers in the same market segment. Generally speaking, in the market for a particular product, products with ‘‘high quality, high price’’ are provided for high-end customers, who constitute the most price insensitive segment of the market (Chambers et al., 2006). In a
G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
competitive environment, Nash’s non-cooperative game is usually implemented between competitors (Banker et al., 1998). In a supply chain, coordination between players has an important impact on quality related decisions. Reyniers and Tapiero (1995) modeled the effect of price rebates and after-sales warranty costs on the choice of a supplier from the quality perspective, inspection policy of a manufacturer, and the resultant end product quality. They explored both non-cooperative and cooperative settings and highlighted the importance of strategic and contractual issues in quality management. Forker (1997) linked quality management with process optimization to address both effectiveness and efficiency concerns. The study suggested that system performance was affected by transaction-specific investments in a coordinated relationship. In this study, we consider two supply chain structures—vertical integration and decentralized settings. In a supply chain with vertical integration, the centralized decision-maker can realize coordination within the supply chain (Cachon, 2003; Ferguson et al., 2006; Zhu et al., 2007). In a market segment shared by two competing supply chains, competition intensity can influence equilibrium distribution structures. McGuire and Staelin (1983) investigated the effect of product competition on Nash equilibrium distribution structures in a duopoly where each manufacturer distributes its goods through a single exclusive retailer. The investigation showed that for low degrees of competition, manufacturers preferred to distribute products through a company store; for more highly competitive goods, manufacturers would be more likely to use a decentralized distribution system. In contrast to Coughlan and Wernerfelt (1989) and Gupta and Loulou (1998) found that decentralization did not always imply a unique equilibrium or more profitable than integration. In the context of a channel duopoly, Iyer (1998) showed that a mixed distribution channel, i.e. a channel in which one manufacturer chose coordination while the other chose non-coordination, could achieve equilibrium in markets with weak brand loyalty. The paper closest to ours is Banker et al. (1998), which developed formal models of oligopolistic competition to investigate whether equilibrium levels of quality increased in competition intensity. They considered asymmetric duopolistic competition where the dominant firm’s potential intrinsic demand decreased. The investigation suggested that the relationship between equilibrium quality and competition intensity depended on what increased competition was perceived as. Similar to Banker et al. (1998), we consider quality-based competition in a market segment. Different from the competition between two firms in Banker et al. (1998), we investigate the quality equilibrium that between two supplier–manufacturer supply chains which provide a certain product to a given market segment. Furthermore, we consider the interaction between suppliers and manufacturers in the two supply chains, and the mechanism on the selection of supply chain structure and quality improvement strategy. Extant literature on supply chain quality management has not considered quality improvement in competing supply chains as yet, to the best of our knowledge. In this study, we analyze quality improvement of players in a single segment of market shared by two supplier–manufacturer supply chains. For simplicity of analysis, we consider the case where quality of products is decided by that of raw materials. Initially, the two suppliers invest in quality and there is no quality improvement in the two supply chains. Then, we describe the mechanism on the selection of supply chain structure and quality improvement strategy of each supply chain. Between the two supply chains, Nash’s non-cooperative game is implemented. In an integrated supply chain, decision-making is centralized. In a decentralized supply chain, the manufacturer may invest in quality improvement for maximization of its own profit.
263
Moreover, quality improvement is analyzed under three possible combinations of structures of the two supply chains: two integrated supply chains, two decentralized supply chains, and one integrated and one decentralized supply chains. In each combination of structures of the two supply chains, we consider two possible scenarios of quality improvement strategies: quality improvement by one chain and quality improvement by both chains. Numerical experiments demonstrate the mechanism and some related issues are discussed. The remainder of the paper is organized as follows. In Section 2, we describe the problem of quality decisions and the mechanism on the selection of supply chain structure and quality improvement strategy of the two supply chains. Then, quality improvement within different structure combinations of the two supply chains, including two integrated supply chains, two decentralized supply chains, and one integrated and one decentralized supply chains, are considered in Section 3, Section 4, and Section 5, respectively. The mechanism is illustrated by way of experiments, and some related issues are discussed, in Section 6. Section 7 draws conclusions and suggests some directions for future investigations.
2. Description of the problem In a given market segment, two supply chains maintain the same price but compete for more consumers with respect to quality of their products. Assumptions on the problem are as follows. Assumption 1. In the same market segment, the two competing supply chains adopt the same price but compete on quality. This assumption is possible; for example, in the same segment of the market, Adidas and Nike sell shoes at almost the same price but offer different designs and product features. Assumption 2. The market is divided into segments with respect to price. That is, the market is divided into segments defined by price of products. This assumption is also reasonable because quality is always tagged by price; for example, high quality means high price. Assumption 3. Consumers in the given market segment can recognize the quality of products provided by any of the supply chains. Nowadays, many competitors try to highlight quality characteristics of their products by advertisements. As a result, consumers can know about the quality of products easily. Following the definition of quality in Banker et al. (1998), we use the term ‘‘quality’’ to refer to both design and conformance quality characteristics that are of interest to the consumer when evaluating the product offered by a supply chain. The following notations are used in the model: s combination of quality improvement strategy and supply chain structures in the two competing supply chains (s¼NN, OII, ODD, OID, TII, TDD and TID); xsi quality of raw materials provided by the ith supply chain within s (i,j¼1, 2, iaj); p price per unit of products in the given market segment; wi wholesale price per unit of raw materials in the ith supply chain; e quality related variable cost of a supplier; CM fixed cost related to quality of a manufacturer; CS fixed cost related to quality of a supplier; vM variable production cost per unit for a manufacturer; vS variable production cost per unit for a supplier; ki share of the intrinsic demand potential for the ith supply chain;
264
G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
a demand sensitivity of the ith supply chain’s quality;
(i,j ¼1, 2, iaj) for quality is
b competition intensity denoting the competitive effects of
xNN ¼ i n
quality for the supply chain pair (i,j).
2½eða þ bÞ þ CS ½ðwi vS Þða þ bÞeki aþ eb½ðwj vS Þða þ bÞekj a 4½eða þ bÞ þ CS 2 e2 b
2
:
ð2:3Þ In this study, xsi and xsj are decision variables and other variables are exogenous variables, known to both supply chains. In addition, we assume that p 4wi þvM and wi 4vS þ exsi (i,j¼1, 2, iaj). These inequalities ensure that each player in a decentralized supply chain makes a positive profit. Extending the quality definition in Banker et al. (1998), we assume that the primary demand function for products provided by the ith supply chain is decided by quality xsi and xsj , as follows: Dsi
xsi bðxsj xsi Þ
¼ ki a þ a
ð2:1Þ
where ki þkj ¼1, i, j¼1, 2, iaj. Here, kia is the potential intrinsic demand for the ith supply chain, which is irrespective of quality. In a specific combination s of quality improvement strategy and supply chain structures, demand function Dsi implies three key empirical regularities: (i) Dsi has a positive correlation with the ith supply chain’s quality; (ii) Dsi has a negative correlation with preponderance of xsj over xsi , i.e. xsj xsi ; and (iii) if both supply chains increase their quality by one unit, then sales of both should increase. In a market segment consisting of two competing supply chains (Fig. 1), both suppliers and manufacturers know the distribution of demand, and they organize the required production for meeting the demand. Initially, there is no quality improvement in the two decentralized supply chains, s¼NN, and the competition between them takes place in the following sequential steps: (i) The two suppliers simultaneously select their quality levels; (ii) The two supply chains observe each other’s quality choices; (iii) Demand is realized based on quality levels set by the two supply chains. Profit PNN Si ðxÞ of the ith supplier is NN NN NN NN 2 PNN Si ðxÞ ¼ ðwi vS exi Þ½ki a þða þ bÞxi bxj f CS ðxi Þ :
Proof. See the Appendix.
Corollary 2.2. In case of two decentralized supply chains, quality of products provided by a supply chain increases in wholesale price wi (i,j ¼1, 2, iaj) but decreases in its share ki of potential instinct demand. Proof. Straightforward and, therefore, omitted.
Proposition 2.1. When there are two decentralized supply chains n and quality is decided by the two suppliers, equilibrium solution xNN i
Results stated in Corollary 2.2 indicate that a higher wholesale price wi makes the ith supplier enhance its equilibrium quality to achieve higher demand and profit. However, with increase of share ki of potential intrinsic demand, the ith supplier will decrease its equilibrium quality because reduction of quality cost is more than the decrease of revenue caused by demand reduction. As a result, quality enhancement of products by both supply chains can be realized by raising wholesale price wi and wj of raw materials. For enhancement of equilibrium quality of products provided by a certain supply chain, an efficient way is to reduce the share of its potential intrinsic demand in the given market segment. With the equilibrium solution, we can derive profit PNN Mi ðxÞ of the ith manufacturer NN PNN bxNN : Mi ðxÞ ¼ ðpwi vM Þ½ki a þ ða þ bÞxi j n
price
quality
ð2:4Þ
PNN Mi ðxÞ
and are Generally speaking, only when profits positive, will the players manufacture the products. Then, we continue to analyze decisions of the two competing supply chains on selection of quality improvement strategy and channel structure. Let s1 and s2 be combinations of quality improvement strategies and structures of the two competing supply chains after decisions of the first mover and the second mover, respectively. Decision sequences of the two supply chains are described as follows: (i) The two supply chains observe each other’s quality levels; (ii) As the first mover, the ith supply chain selects its supply chain structure and quality improvement strategy to maximize its profit, i.e. s1 is formed; (iii) After observing actions of the ith supply chain, the second mover, i.e. the jth supply chain, selects its supply chain structure and quality improvement strategy to maximize its profit, i.e. s2 is formed; (iv) Demand is realized based on quality levels set by the two supply chains.
Products
Products
orders Raw materials
n
PNN Si ðxÞ
orders Raw materials
&
ð2:2Þ
This model is similar to other studies which have modeled the selection of quality (Moorthy, 1988; Tagaras and Lee, 1996; 2 Banker et al., 1998). Fixed costs f þ CS ðxNN i Þ are increasing and NN convex in quality level xi . Therefore, Proposition 2.1 and Corollary 2.2 summarize our findings on quality of products before quality improvement.
quality
&
price
Fig. 1. Business flow of two competing supply chains.
G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
For the first mover i (i,j ¼1, 2, iaj), selection of supply chain structure and quality improvement strategy s and formation of s1 can be described as follows: s1 ¼ s ¼
arg s A fNN,OII,ODD,OIDg
max Psi ðxÞ:
ð2:5Þ
After observing actions of the first mover i, the second mover j selects its supply chain structure and quality improvement strategy, and s2 can be described as s2 ¼ s ¼
arg s A fNN,OII,ODD,OID,TII,TDD,TIDg
max Psj ðxÞ:
ð2:6Þ
According to Banker et al. (1998), the industry quality provided by the two competing supply chains is x~ s ¼ ððDsi xsi þ Dsj xsj Þ=ðDsi þDsj ÞÞ, and the industry profit is Ps ¼ Psi þ Psj . In the following sections, we analyze quality improvement decisions under different combinations of structures of the two competing supply chains: two integrated supply chains (II), two decentralized supply chains (DD), and one integrated and one decentralized supply chains (ID), where centralized decision-making is realized in an integrated supply chain but the manufacturer invests in quality improvement only for maximization of its own profit. In all the three combinations of structures, Nash’s noncooperative game is implemented between two supply chains.
3.2. Quality improvement by two chains When both two supply chains invest in quality improvement, s¼TII, competition between the two supply chains takes place in the following sequential steps: (i) The two supply chains observe each other’s quality levels; (ii) The two supply chains implement quality improvement; (iii) Demand is realized based on quality levels set by the two supply chains. Profit PTII i ðxÞ of the ith supply chain is TII TII TII TII 2 NN 2 PTII Þ CS ðxNN Þ2 : i ðxÞ ¼ ðpvexi Þ½ki a þ ða þ bÞxi bxj f c½ðxi Þ ðxi i n
Then, Proposition 3.1 and Corollary 3.2 summarize our findings. Proposition 3.1. When coordination is realized in both supply chains, the ith supply chain implements quality improvement but the jth supply chain does not, and equilibrium solutions for quality are n
3. Integrated supply chains
3.1. Quality improvement by one chain
(i) The two supply chains observe each other’s quality levels; (ii) The ith supply chain implements quality improvement while the jth supply chain does not; (iii) Demand is realized based on quality levels set by the two supply chains. When the ith supply chain finds that its profit will be enhanced n n by improving quality level from xNN to xOII , it will attempt to invest i i in quality improvement. As the jth manufacturer does not invest in quality improvement, equilibrium quality of the jth supply chain n n will change from xNN to xOII . With channel coordination, profit j j POII ðxÞ of the ith supply chain after quality improvement is i OII OII OII OII 2 NN 2 POII Þ CS ðxNN Þ2 i ðxÞ ¼ ðpvexi Þ½ki a þ ða þ bÞxi bxj f c½ðxi Þ ðxi i n
n
ð3:1Þ where c ¼ minfCM ,CS g and v¼vM þvS. In the jth supply chain, the jth supplier will select a quality level that maximizes profit POII j ðxÞ of the jth supply chain as follows:
a
4½eða þ bÞ þ c½eða þ bÞ þCS e2 b
2
,
and ¼ xOII j n
OII OII 2 þ bÞxOII j bxi f CS ðxj Þ :
ð3:2Þ
In the following subsection, we continue to analyze the case where both supply chains implement quality improvement.
2½eða þ bÞ þc½ðpvÞða þ bÞekj a þ eb½ðpvÞða þ bÞeki a 4½eða þ bÞ þ c½eða þ bÞ þCS e2 b
2
: ð3:5Þ
When coordination is realized and quality improvement is n implemented by both supply chains, equilibrium solution xTII i (i,j ¼1, 2, i aj) for quality is xTII ¼ i n
When only one supply chain invests in quality improvement, s¼OII, competition between the two supply chains takes place in the following sequential steps:
e
2½eða þ bÞ þCS ½ðpvÞða þ bÞeki a þ eb½ðpvÞða þ bÞekj a
ð3:4Þ
In a given market segment with two integrated supply chains, decision-making for quality improvement is centralized in each supply chain. The objective of quality improvement for the central decision-maker is to maximize profit of the supply chain. We consider two cases of quality improvement strategies: quality improvement by one chain in Section 3.1 and quality improvement by two chains in Section 3.2, as follows.
xOII j Þ½kj a þð
n
ð3:3Þ
xOII ¼ i
POII j ðxÞ ¼ ðpv
265
2½eða þ bÞ þc½ðpvÞða þ bÞeki a þ eb½ðpvÞða þ bÞekj a 4½eða þ bÞ þ c2 e2 b
2
: ð3:6Þ
Proof. See the Appendix.
&
Corollary 3.2. In structure combination II, equilibrium quality of products provided by a supply chain increases in price p but decreases in its share ki (i,j ¼1, 2, iaj) of potential intrinsic demand. Proof. Straightforward and, therefore, omitted.
&
From Corollary 3.2, we can find that in structure combination II of two integrated supply chains, enhancement of equilibrium quality of products provided by both supply chains can be realized by raising price of products. For enhancement of equilibrium quality of products provided by a supply chain, an efficient way is to reduce the share of its potential intrinsic demand in the given market segment.
4. Decentralized supply chains Different from integrated supply chains, in the case of two decentralized supply chains (DD), manufacturers invest in quality improvement for maximizing their own profits.
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4.1. Quality improvement by one chain
and
When only one supply chain invests in quality improvement, s¼ODD, competition between the two supply chains takes place in the following sequential steps:
xODD ¼ j
(i) The two supply chains observe each other’s quality levels; (ii) The ith manufacturer implements quality improvement while the jth manufacturer does not; (iii) Demand is realized based on quality levels set by the two supply chains. In the ith supply chain, the manufacturer invests in quality improvement to maximize its own profit. Profit of the ith manufacturer is ODD PODD bxODD CM ½ðxODD Þ2 ðxNN Þ2 , Mi ðxÞ ¼ ðpwi vM Þ½ki a þ ða þ bÞxi i j i n
ð4:1Þ For the jth supply chain, profit of the jth supplier is
PODD ðxÞ ¼ ðwj vS Sj
e
xODD Þ½kj a þ ð j
a
ð4:2Þ After quality improvement is implemented by the ith manufacturer, profit of the ith supplier is
PODD ðxÞ ¼ ðwi vS exODD Þ½ki a þ ða þ bÞxODD bxODD f CS ðxNN Þ2 , Si i i j i n
n
n
ð4:3Þ and profit of the jth manufacturer is ODD PODD bxODD : Mj ðxÞ ¼ ðpwj vM Þ½kj a þða þ bÞxj i n
NN PODD Mi ðxÞ Z PMi ðxÞ
n
n
ð4:8Þ
Or else, if quality improvement is implemented by both chains, n then equilibrium solution xTDD (i, j ¼1, 2, iaj) of quality is i xTDD ¼ i n
ðpwi vM Þða þ bÞ : 2CM
ð4:9Þ
Proof. See the Appendix.
&
Corollary 4.2. In structure combination DD, in a supply chain with quality improvement, quality of products increases in price p and competition intensity b but decreases in wholesale price wi. However, in a supply chain without quality improvement, quality of products increases in wholesale price wj but decreases in its share kj of potential intrinsic demand. &
From Corollary 4.2, we can obtain managerial insights as follows: in structure combination of two decentralized supply chains, enhancement of equilibrium quality of products provided by both supply chains can be realized by raising price of products and lowering wholesale price of the first mover. For enhancement of equilibrium quality of products provided by a supply chain without quality improvement, an efficient way is to raise wholesale price wj and to reduce its share kj in potential intrinsic demand in the market segment.
ð4:4Þ
PODD ðxÞ Z PNN Si Si ðxÞ
and are Only if conditions met, will manufacturer Mi invest in quality and supplier Si will agree to quality improvement. 4.2. Quality improvement by two chains When both supply chains invest in quality improvement, s¼TDD, competition between the two supply chains takes place in the following sequential steps: (i) The two supply chains observe each other’s quality levels; (ii) The two manufacturers implement quality improvement; (iii) Demand is realized based on quality levels set by the two supply chains. Profit of the ith manufacturer is
PTDD Mi ðxÞ ¼ ðpwi vM Þ½ki a þð
ðwj vS Þða þ bÞekj a þ ebxODD i 2½eða þ bÞ þ CS
Proof. Straightforward and, therefore, omitted.
þ bÞxODD bxODD f CS ðxODD Þ2 : j i j
n
n
a þ bÞxTDD bxTDD CM ½ðxTDD Þ2 ðxNN Þ2 : i i j i n
5. One integrated and one decentralized supply chains In structure combination of one integrated and one decentralized supply chains (ID), the ith supply chain is vertically integrated and the jth supply chain is a decentralized setting. In this case, we consider two cases: quality improvement by one supply chain and quality improvement by two supply chains. 5.1. Quality improvement by one chain When only one supply chain invests in quality improvement, s¼OID, competition between the two supply chains takes place in the following sequential steps: (i) The ith supply chain invests in quality improvement with coordination while the jth supply chain does not; (ii) The two supply chains observe each other’s choice of quality levels; (iii) Demand is realized based on the quality levels.
ð4:5Þ After quality improvement is implemented, profit of the ith supplier is
PTDD Si ðxÞ ¼ ðwi vS
e
n xTDD Þ½ki a þ ð i
a
n n n þ bÞxTDD bxTDD f CS ðxNN Þ2 : i j i
ð4:6Þ Then, Proposition 4.1 and Corollary 4.2 summarize our findings. Proposition 4.1. When both supply chains are decentralized, if quality improvement is implemented by one chain, then equilibrium solutions of quality are xODD ¼ i n
ðpwi vM Þða þ bÞ , 2CM
ð4:7Þ
Then, profit function of the ith supply chain is
POID ðxÞ ¼ ðpvexOID Þ½ki a þða þ bÞxOID bxOID i i i j Þ2 ðxNN Þ2 CS ðxNN Þ2 f c½ðxOID i i i n
n
ð5:1Þ
while profit function of the jth supplier is OID POID Þ½kj a þða þ bÞxOID bxOID f CS ðxOID Þ2 : Sj ðxÞ ¼ ðwj vS exj j i j
ð5:2Þ As quality of products in the jth supply chain changes from n n xNN to xOID , profit of the jth manufacturer is j j OID POID bxOID : Mj ðxÞ ¼ ðpwj vM Þ½kj a þ ða þ bÞxj i n
n
ð5:3Þ
G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
5.2. Quality improvement by two chains When both supply chains invest in quality improvement, s¼TID, competition between the two supply chains takes place in the following sequential steps: (i) The two supply chains observe each other’s quality levels; (ii) The two supply chains implement quality improvement; (iii) Demand is realized based on quality levels set by the two supply chains. Then, profit function of the ith supply chain is TID TID TID PTID i ðxÞ ¼ ðpvexi Þ½ki a þ ða þ bÞxi bxj 2 NN 2 f c½ðxTID Þ CS ðxNN Þ2 : i i Þ ðxi n
n
ð5:4Þ
Profit function of the jth manufacturer is
PTID Mj ðxÞ ¼
TID TID 2 NN 2 ðpwj vM Þ½kj a þ ða þ bÞxTID Þ j bxi CM ½ðxj Þ ðxj n
ð5:5Þ where profit
TIDn NN n PTID Þ Z PNN Þ Mj ðxj Mj ðxj
PTID Sj ðxÞ
PTID Sj ðxÞ ¼
and
TIDn NN n PTID Þ Z PNN Þ, Sj ðxj Sj ðxj
and
of the jth supplier is
ðwj vS exTID Þ½kj a þða þ bÞxTID bxTID f CS ðxNN Þ2 : j j i j n
n
n
n
267
Corollary 5.4. In structure combination ID, when there is quality improvement by both chains, quality of products increases in price p but decreases in share ki of potential intrinsic demand and wholesale price wj. In particular, quality of products provided by the jth supply chain increases in b. Proof. Straightforward and, therefore, omitted.
&
From Corollary 5.3, we can obtain managerial insights as follows. In structure combination of one integrated and one decentralized supply chains, when the integrated supply chain implements quality improvement while the decentralized supply chain does not, enhancement of equilibrium quality of products provided by both supply chains can be realized by raising price of products and wholesale price of the decentralized chain and reducing their shares in potential intrinsic demand. From Corollary 5.4, we can obtain managerial insights as follows. In structure combination of one integrated and one decentralized supply chains, when both supply chains implement quality improvement, enhancement of equilibrium quality of products provided by both supply chains can be realized by raising price of products and lowering wholesale price of the decentralized chain. In particular, enhancement of equilibrium quality of products provided by the first mover can be realized by reducing its share in potential intrinsic demand in the market segment.
ð5:6Þ Therefore, we have Proposition 5.1, as follows. Proposition 5.1. In structure combination ID, if quality improvement is implemented by only the ith supply chain, s ¼OID, then equilibrium solutions of quality are ¼ xOID i n
2½eða þ bÞ þ CS ½ðpvÞða þ bÞeki a þ eb½ðwj vS Þða þ bÞekj a 4½eða þ bÞ þc½eða þ bÞ þ CS e2 b
2
,
ð5:7Þ and ¼ xOID j n
2½eða þ bÞ þ c½ðwj vS Þða þ bÞekj a þ eb½ðpvÞða þ bÞeki a 4½eða þ bÞ þc½eða þ bÞ þ CS e2 b
2
:
6. Analysis with experiments In this section, we illustrate the mechanism with numerical experiments. In a competitive environment, in order to reflect the impact of competition intensity b on the results, we suppose that b is variable and other parameters are fixed. Let ki ¼0.4, wi ¼wj ¼6, a¼ 1000, a ¼200, p¼ 20, vS ¼1, vM ¼2, e ¼2, f¼ 1000, CS ¼3000, CM ¼2000 and bA[100, 300]. The migration of equilibrium supply chain structures and quality improvement strategy are shown in Fig. 2, where curves s and s1
ð5:8Þ
12000
Or else, if quality improvement is implemented by both supply chains, s¼TID, then equilibrium solutions of quality are
10000
¼ xTID i n
ðpvÞða þ bÞeki a þ ebxTID j 2½eða þ bÞ þ c
,
ð5:9Þ
and xTID j
n
s1=OID
8000
n
6000
s=NN
4000
ðpwj vM Þða þ bÞ ¼ : 2CM
Proof. See the Appendix.
ð5:10Þ
0
&
Let A¼(p wj vM)/(2CM), B ¼(p v)(a þ b) ekia, M¼ a þ(c/e) and N ¼p v Ac. We have Theorem 5.2, as follows: Theorem 5.2.
n When B rMN, xTID pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i
2000
increases in b. Or else, when
10000 9000 8000
decreases in b; if B 4MN, if b o ðBMNÞ=ðeAÞM, then xTID i pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n b 4 ðBMNÞ=ðeAÞM, then xTID increases in b . i
7000
Proof. See the Appendix.
4000
n
&
Then, Corollary 5.3 and 5.4 can be derived as follows. Corollary 5.3. In structure combination ID, when there is quality improvement by one chain, quality of products increases in price p and wholesale price wj, but decreases in share ki of potential intrinsic demand. Proof. Straightforward and, therefore, omitted.
&
6000
100 120 140 160 180 200 220 240 260 280 300 s2=TID
s2=OII
s1=OID
5000 3000 2000 1000 0
100 120 140 160 180 200 220 240 260 280 300
Fig. 2. Maximum profits of supply chain i and j as functions of competition intensity and migration of equilibrium supply chain structures.
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G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
16000
1.6
s2=TID
15500
s=NN
1.4
0.8
14000
s2=OII
0.6
13500
0.4
13000
0.2 0
100 120 140 160 180 200 220 240 260 280 300
Fig. 3. Industry profits as functions of competition intensity.
reflect the impacts of competition intensity b on maximum profits of the ith supply chain before and after the migration; curves s1 and s2 reflect the impacts of competition intensity b on maximum profits of the jth supply chain before and after the migration. When s¼NN, there is no quality improvement and both supply chains are decentralized. For the first mover i, according to Eq. (2.5), there is s1 ¼ OID ¼ arg max Psi ðxÞ, bA[100,300].
1.2
After s1 ¼OID is determined by the ith supply chain, the second mover j has to select its own supply chain structure and quality improvement strategy from {OII, TII, OID, TID}. According to Eq. (2.6), s2 ¼ arg max Psj ðxÞ, bA[100,300], and there is
0
s A fNN,ODD,OIDg
TIDj
0.6 0.4 0.2 100 120 140 160 180 200 220 240 260 280 300
1.6 1.4 1.2
As the migration of equilibrium supply chain structures and quality improvement strategies takes place, industry profit becomes the function of competition intensity b in NN, OII and TID (Fig. 3). Comparing industry profits in OII, TID with that in NN, we find 8 TID NN > < P ðxÞ 4 P ðxÞ, b ¼ 100 OII NN P ðxÞ 4 P ðxÞ, b A ½120,160 : > : OII P ðxÞ o PNN ðxÞ, b A ½180,300
OIIj
0.8
s A fOII,TII,OID,TIDg
OII,
NNj
1
(
b ¼ 100 : b A ½120,300
100 120 140 160 180 200 220 240 260 280 300
1.6 1.4
TID,
TIDi
1
14500
s2 ¼
OIIi
1.2
15000
12500
NNi
NN
OII
TID
1 0.8 0.6 0.4 0.2 0
100 120 140 160 180 200 220 240 260 280 300
Fig. 4. The impact of competition intensity on quality of supply chain i, j and industry quality.
Therefore, the following observations can be made:
Competition intensity has a significant impact on profit and
the selection of supply chain structure and quality improvement strategy. Vertical integration (VI) is a dominant strategy for each supply chain in quality improvement. There is a prisoners’ dilemma (for example, when bA[180,300]): though strategy VI brings more profit for the supply chain which adopts it when s1 ¼OID, two supply chains with VI, i.e. s2 ¼ OII, may cause lower profits for both chains than when s¼NN.
When s¼NN, OII and TID, quality levels in different supply chain structures and quality improvement strategies are shown in Fig. 4, where curves si, sj and s reflect the impacts of competition intensity b on quality levels in supply chain i, j and industry quality. From Fig. 4, the following observations can be made:
Generally, quality improvement by both chains can achieve
higher industry quality than quality improvement by one chain. n n As xTID 4 xOII , quality improvement by the manufacturer j j contributes more to quality enhancement than vertical integration.
From these observations, we can also find that competition intensity b may be used to adjust supply chain structure and quality improvement strategy, and thus to improve the quality of products.
7. Conclusions and future work In this paper, we have described the mechanism on the selection of supply chain structure and quality improvement strategy of two competing supply chains which share a given segment of the market for a given product. Prices of products provided by the two supply chains are the same, and competition between them is based on quality of products. In each supply chain, the supplier provides raw materials, which are processed by the manufacturer into products for the given market segment. Quality of products is decided by that of raw materials. We analyze three possible structure combinations of the two supply chains in the given market segment: two integrated supply chains, two decentralized supply chains, and one integrated and one decentralized supply chains. The study provides valuable insights into the mechanism that leads to quality enhancement
G. Xie et al. / Int. J. Production Economics 134 (2011) 262–270
and the selection of supply chain structure and quality improvement strategy by competing supply chains. In future work, quality determined by both raw materials and production process and quality determined by competition among supply chains with uncertain demand are expected to be worth further studying.
combination II as xTII ¼ i n
2½eða þ bÞ þc½ðpvÞða þ bÞeki a þ eb½ðpvÞða þ bÞekj a
We sincerely thank the referees for their valuable suggestions and comments. This work was supported by the National Natural Science Foundation of China (Nos. 70871107, 70731003) and China Postdoctoral Science Foundation (Grant no. 20060400103), and Main Direction Program of Knowledge Innovation of Chinese Academy of Sciences (No. KACX1-YW-0906).
2
:
Proof of Proposition 4.1. When quality improvement is implemented by one chain, we differentiate Eqs. (4.1) and (4.2) with ODD and xODD , respectively. Let @PODD ¼ 0 and respect to xODD Mi ðxÞ=@xi i j
ðxÞ=@xODD ¼ 0. There are @PODD Sj j 8 < ðpwi vM Þða þ bÞ2CM xODD ¼0 i ebxODD ¼ ðwj vS Þða þ bÞekj a : 2½eða þ bÞ þCS xODD j i
:
Then, we can derive equilibrium solutions in supply chain structure combination DD as
Appendix
¼ xODD i
ðpwi vM Þða þ bÞ , 2CM
¼ xODD j
ðwj vS Þða þ bÞekj a þ ebxODD i : 2½eða þ bÞ þ CS
n
Proof of Proposition 2.1. We differentiate Eq. (2.2) with respect NN to xNN and let @PNN ¼ 0. The first-order conditions charSi ðxÞ=@xi i acterizing equilibrium quality are NN ¼ ðwi vS Þða þ bÞeki a: 2½eða þ bÞ þ CS xNN i ebxj
Then, we can derive the equilibrium solution for quality as follows: n
4½eða þ bÞ þ c2 e2 b
TII 2 Since @2 PTII i ðxÞ=@ðxi Þ ¼ 2½eða þ bÞ þc o 0, the profit function is strictly concave.
Acknowledgements
xNN ¼ i
269
2½eða þ bÞ þ CS ½ðwi vS Þða þ bÞeki a þ eb½ðwj vS Þða þ bÞekj a 4½eða þ bÞ þ CS 2 e2 b
2
:
n
n
ODD 2 Since @2 PODD Þ ¼ 2CM o 0 and @2 PODD ðxÞ=@ðxODD Þ2 ¼ Mi ðxÞ=@ðxi Sj j 2½eða þ bÞ þCM] o0, profit functions are strictly concave. When quality improvement is implemented by both chains, we and let @PTDD differentiate Eq. (4.5) with respect to xTDD Mi ðxÞ= i TDD @xi ¼ 0, so we have
ðpwi vM Þða þ bÞ2CM xTDD ¼ 0, i
NN 2 Since @2 PNN Si ðxÞ=@ðxi Þ ¼ 2½eða þ bÞ þ CS o 0, the profit function is strictly concave with respect to xNN i .
Proof of Proposition 3.1. Differentiating Eqs. (3.1) and (3.2) with respect to xOII and xOII respectively and equating them to zero, we i j obtain the following functions: 8 OII < 2½eða þ bÞ þcxOII i ebxj ¼ ðpvÞða þ bÞeki a : OII : 2½eða þ bÞ þCS xj ebxOII i ¼ ðpvÞða þ bÞekj a
then equilibrium solutions of quality are xTDD ¼ i n
ðpwi vM Þða þ bÞ : 2CM
TDD 2 Þ ¼ 2CM o 0, the profit functions are Since @2 PTDD Mi ðxÞ=@ðxi strictly concave.
Proof of Proposition 5.1. When quality improvement is implemented by one chain, we differentiate Eqs. (5.1) and (5.2) with and xOID , respectively. Let @POID ðxÞ=@xOID ¼ 0 and respect to xOID i i j i
Then, we can derive equilibrium solutions for quality in case of quality improvement by one chain in supply chain structure combination II as ¼ xOII i n
¼ xOII j n
2½eða þ bÞ þ CS ½ðpvÞða þ bÞeki a þ eb½ðpvÞða þ bÞekj a 2
4½eða þ bÞ þ c½eða þ bÞ þ CS e2 b
2½eða þ bÞ þ c½ðpvÞða þ bÞekj a þ eb½ðpvÞða þ bÞeki a 2
4½eða þ bÞ þ c½eða þ bÞ þ CS e2 b
OID ¼ 0. There are @POID Sj ðxÞ=@xj 8 < 2½eða þ bÞ þcxOID ebxOID ¼ ðpvÞða þ bÞeki a i j
: 2½eða þ bÞ þCS xOID ebxOID ¼ ðwj vS Þða þ bÞekj a j i
:
, Then, we derive equilibrium solutions in supply chain structure combination ID as follows:
:
OII 2 and @2 POII Since @2 POII i ðxÞ=@ðxi Þ ¼ 2½eða þ bÞ þc o 0 j ðxÞ= OII 2 @ðxj Þ ¼ 2½eða þ bÞ þ CS o0, the profit function is strictly concave. In the same way, we differentiate Eq. (3.3) with respect to xTII i TII and let @PTII i ðxÞ=@xi ¼ 0. The first-order conditions characterizing equilibrium quality are TII 2½eða þ bÞ þ cxTII i ebxj ¼ ðpvÞða þ bÞeki a:
Then, we can derive equilibrium solutions for quality in case of quality improvement by two chains in supply chain structure
xOID ¼ i n
2½eða þ bÞ þ CS ½ðpvÞða þ bÞeki a þ eb½ðwj vS Þða þ bÞekj a 2
4½eða þ bÞ þ c½eða þ bÞ þ CS e2 b
,
and ¼ xOID j n
2½eða þ bÞ þ c½ðwj vS Þða þ bÞekj a þ eb½ðpvÞða þ bÞeki a 2
4½eða þ bÞ þ c½eða þ bÞ þ CS e2 b
:
Since @2 POID ðxÞ=@ðxOID Þ2 ¼ 2½eða þ bÞ þ c o0 and @2 POID i Sj ðxÞ= i OID 2 @ðxj Þ ¼ 2½eða þ bÞ þ CS o0, the profit functions are strictly concave. When quality improvement is implemented by both chains, and xTID we differentiate Eqs. (5.4) and (5.5) with respect to xTID i j .
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TID TID Let @PTID ¼ 0 and @PTID ¼ 0, so we have i ðxÞ=@xi Mj ðxÞ=@xj 8 TID TID < 2½eða þ bÞ þcxi ebxj ¼ ðpvÞða þ bÞeki a : TID : 2½eða þ bÞ þCM xTID ¼ ðpwj vM Þða þ bÞekj a j ebxi
Then equilibrium solutions of quality are ðpvÞða þ bÞeki a þ ebxTID j
n
xTID ¼ i n
xTID ¼ j n
2½eða þ bÞ þ c
,
ðpwj vM Þða þ bÞ : 2CM
TID 2 Since @2 PTID and @2 PTID i ðxÞ=@ðxi Þ ¼ 2½eða þ bÞ þc o0 Mj ðxÞ= 2 Þ ¼ 2[ e ( a þ b ) þC ] o0, the profit functions are strictly @ðxTID M j concave.
as Proof of Theorem 5.2. From Eq. (5.9), we can transform xTID i n
¼ xTID i n
A BMN 1 N AM ðM þ bÞ þ U þ 2 2e M þ b 2e 2
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