Journal of Cleaner Production 113 (2016) 807e821
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Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro
Cooperative strategies for sustainability in a decentralized supply chain with competing suppliers Gang Xie* Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 February 2015 Received in revised form 25 October 2015 Accepted 7 November 2015 Available online 18 November 2015
In today's global market, organizations increasingly recognize that they must address the issue of sustainability in their operations. In addition, the decision-making processes surrounding sustainable supply chain management are raising a wide range of theories and claims about how best to address the issue. In this study, mathematical modeling is used to analyze managerial decision-making in terms of improving sustainability in a decentralized supply chain with two competing suppliers. Firstly, the concept of managerial decision-making for competing suppliers is introduced. Next, the mechanism used in the selection of cooperative strategies is described, and the decisions related to demand, energy efficiency and profits are analyzed in different scenarios of cooperative strategy combinations. Also, lump sum transfer contracts are designed for supply chain coordination. An experimental test of an automobile supply chain in China illustrates the impacts of competition intensity on profits, the energy efficiency of environmentally friendly products and consumer surplus. The analysis indicates that the sustainability of the supply chain can be efficiently enhanced through cooperative strategies and parameter adjustments, while tradeoffs should be made by the policy maker before any cooperative strategy combination is advocated. This study extends and complements existing literature with regard to how it is possible to improve sustainability in a competitive environment through cooperative supply chain strategies and parameter adjustments, i.e. enhancing the price of environmentally friendly products, lowering the supplier's share of instinct demand potential and lowering the manufacturer's fixed cost related to energy efficiency. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Sustainability Competition Environmentally friendly products Cooperative strategy
1. Introduction Over the past few decades, sustainability has become an increasingly significant issue for businesses, due to the rapid depletion of natural resources, as well as concerns over wealth disparity and corporate social responsibility (CSR) (Dao et al., an et al., 2016). Accordingly, sustainability is now 2011; Ag widely discussed at a global level by policy makers, practitioners, media and academics (Dowell et al., 2000; Golini et al., 2014). As the interrelationships among society, the environment and economic development are the three generally accepted “pillars” of sustainability (Elkington, 1994), in this study sustainability refers to the integration of energy efficiency (environment), consumer surplus (society) and the profits of organizations (economy).
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[email protected]. http://dx.doi.org/10.1016/j.jclepro.2015.11.013 0959-6526/© 2015 Elsevier Ltd. All rights reserved.
In the field of environmental protection, global standards are bringing new challenges to firms, markets and industries, all of which need to address energy saving and pollution reduction issues (Friedler, 2010; Zabaniotou and Andreou, 2010). In order to reduce greenhouse gas emissions without drastically changing lifestyles, the current trend is to develop strategies to enhance energy efficiency (Dixon et al., 2010; Wirl, 2008). This concern regarding energy efficiency has resulted in legislation being introduced which expands the responsibility of organizations and increases the organizations' attention on training managers in sustainable management. Concerns regarding energy efficiency have also led to the development of theories to support sustainable managerial decision making (Xie, 2015). As a consequence, cleaner production methods and more environmentally friendly products (EFPs) are advocated for sustainable development (Chen, 2001; Narayanaswamy et al., 2003; Seuring, 2011). In this study, environmental performance is measured by the industry energy efficiency of the EFPs, and higher industry energy efficiency means better environmental performance.
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The impact of manufacturing organizations on the natural environment and social equity should not be studied from an isolated perspective, but rather by explicitly recognizing the upstream and downstream organizations in a supply chain (Klassen and Vachon, 2003; Ciliberti et al., 2008; Vachon and Mao, 2008). The management of supply chains is thus receiving increased prominence and greater scrutiny (Linton et al., 2007; Ahi and Searcy, 2013). In a supply chain, there are continuous flows of materials, funds and information across multiple functional areas, both within and between chain members (Jain et al., 2009). Considering the fact that a supply chain is involved with the product from the initial processing of raw materials right up to delivery of the product to the end user, a focus on supply chains is one step toward the wider adoption and development of sustainability practices (Tsoulfas and cs, 2008; Ashby et al., 2012). Therefore, this Pappis, 2006; Kova study investigates how the various members of a supply chain can make use of cooperative strategies to improve sustainability. In a supply chain, the competition between suppliers often reduces their profits. In particular, when competition intensity increases to the extent where there is no profit for the competing suppliers, they have to withdraw from the market segment. From the perspective of a decentralized supply chain, cooperation between members may allow more effective methods to realize Pareto improvement for the supply chain performance and make progress in achieving sustainability (Govindan, 2013; Xie, 2015). Hence, van Hoof and Thiell (2014) tested a theoretical model of cooperative capacity as a multi-dimensional organizational construct, in order to gauge how to create cleaner production implementation within supply chains. In addition, Xie (2015) investigated the coordination of a supply chain by using the common wholesale pricing and profit sharing (WPPS) schemes, as well as a lump sum transfer contract. However, the case of competing suppliers is not considered in Xie (2015). Unlike most of the existing relevant literature, this study takes an operational view and a quantitative approach. The purpose of this study is to investigate managerial decisionmaking with regard to sustainability improvement in a decentralized supply chain with two competing suppliers. Theoretical models are developed to analyze the supply chain members' decisions in different cooperative strategy combination situations. Moreover, an experimental analysis of an automobile supply chain in China illustrates the impact of competition intensity on profits, the energy efficiency of EFPs and consumer surplus. This study extends and complements existing literature on how it is possible to enhance sustainability in a competitive environment through cooperative supply chain strategies and parameter adjustments. The remainder of this paper is organized as follows: In the next section, existing literature on decision-making for sustainable supply chain management is reviewed. In Section 3, managerial decision-making for competing suppliers is introduced. Then, the methods are proposed in Section 4, and our findings are obtained in Section 5. In Section 6, managerial insights into decision-making for sustainability improvement are discussed. Section 7 reveals our conclusions and limitations and suggests possible directions for future studies. 2. Decision-making for sustainable supply chain management Many models have been designed to cope with sustainable supply chain management (Seuring and Müller, 2008; Seuring, 2013). In order to support the analysis of a supply chain's environmental performance and the resulting decision making, Tsoulfas and Pappis (2008) defined six specific environmental performance indicator groups, including 1) product/process design and
production, 2) packaging, 3) transportation (distribution and recovery) and collection, 4) recycling and disposal, 5) “greening” the internal and external business environment, and 6) other management issues. Considering both the operational costs and social costs caused by the carbon dioxide emissions from operating such a supply chain network, Tseng and Hung (2014) proposed a strategic decision-making model for sustainable supply chain management. The model was used to evaluate carbon dioxide emissions and operational costs under different scenarios in an apparel manufacturing supply chain network. The results showed that the higher the social cost rate of carbon dioxide emissions, the lower the amount of carbon dioxide emissions would be. The results also suggest that legislation which forces an enterprise to bear the social costs of the carbon dioxide emissions resulting from their economic activities is an effective method of reducing carbon dioxide emissions. Front-runner organizations have made efforts to “green” their suppliers. Sustainable supplier relationship management (SSRM) has become a crucial component of companies' sustainability efforts. A firm's corporate image, in terms of its economic, environmental and social behavior, heavily depends on its supply chain and the sustainability performance of each and every chain link, including both primary and second-tier suppliers. In a multiple case study of seven European chemical companies, Leppelt et al. (2013) investigated how firms manage their supplier relations in interdependent situations. The results provided evidence that sustainability leaders intensively invest in SSRM practices in order to manage sustainability, even beyond their corporate boundaries. Additionally, Leppelt et al. (2013) identified corporate strategy alignment, risk perception and the listing of sustainability indices as the key influential factors, which foster and limit a firm's engagement in SSRM. Govindan et al. (2013) explored sustainable supply chain initiatives and examined the problem of identifying an effective model based on the Triple Bottom Line (TBL) approach (economic, environmental and social aspects) for supplier selection operations in supply chains. They presented a fuzzy multi-criteria approach and used triangular fuzzy numbers to express the linguistic values of experts' subjective preferences. A qualitative performance evaluation was performed by using fuzzy numbers to find criteria weights; fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) was then proposed to determine the ranking of suppliers. Also, cooperative strategies have been used to improve supply n et al., 2015). van Hoof and Thiell chain performance (Egels-Zande (2014) investigated the collaboration capacity of 177 suppliers that participated in the Mexican Sustainable Supply Program from 2005 to 2008. The results revealed that cooperative capacity is essential for the effective implementation of cleaner production. Actions leading to cleaner production also provide competitive advantages for sustainable supply chain management. Hsueh (2014) designed a revenue sharing contract which embedded corporate social responsibility (RS-CRS) to realize supply chain coordination. Numerical examples show that an RS-CSR contract can simultaneously achieve the following objectives under proper parameter settings: (1) improve corporate social responsibility (CSR) performance; (2) improve total supply chain profits, and (3) ensure that each partner in the supply chain can benefit from the contract. Xie (2015) investigated the coordination of a supply chain by using common wholesale pricing and profit sharing (WPPS) schemes and a lump sum transfer contract. The observations indicated that a coordinated supply chain is a better choice than a non-coordinated chain in terms of achieving both higher environmental performance and greater consumer surplus. In addition, a manufacturer's involvement can improve the supply chain performance (Xie et al., 2014).
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Based on the literature review referred to above, the current status of sustainable supply chain management can be synthesized as follows: (1) mathematical modeling is an efficient means to cope with sustainable supply chain management; (2) the management of supplier relationships is a crucial component of any company's sustainability efforts; (3) cooperative strategies can significantly improve supply chain performance; (4) previous studies have not yet analyzed managerial decision-making for sustainability improvement through cooperative strategies in a decentralized supply chain with competing suppliers. Unlike most of the existing relevant literature, this study takes an operational view and a quantitative approach. To the best of our knowledge, the proposed method is the first of its kind to consider the selection of cooperative strategies and parameter adjustments for sustainability improvement in the field of sustainable supply chain management. 3. Managerial decision-making for competing suppliers The purpose of this study is to analyze how to enhance sustainability through the selection of cooperative strategies. Here, sustainability refers to the integration of energy efficiency (environment), consumer surplus (society) and organizations' profits (economy). The main issue faced by the policy maker is how to achieve balance with the various tradeoffs between society, environment and economy. The main optimization problem facing organizations is how to maximize members' profits by setting the optimal energy efficiency of EFPs in different cooperative strategy combinations, under which the equilibrium energy efficiency of EFPs is derived. 3.1. Conceptual model and assumptions In this section, the business flow of the supply chain with competing suppliers is shown in Fig. 1. The two suppliers are independent. For simplicity of analysis, we consider the case where the energy efficiency of environmentally friendly products (EFPs) is decided by the efficiency of the spare parts provided by the suppliers. The supply chain members' profits are influenced by competition intensity, which may change over time. During the evolution of competition intensity, supply chain members may suffer a decline in their equilibrium profits. In particular, when members achieve negative profits, they will almost certainly have to withdraw from the market. Let s1 and s2 be the cooperative strategy combinations of the supply chain, after the decisions of the first mover and the second mover, respectively, are made. The decision sequences of the two suppliers and the corresponding cooperative strategy combinations of the supply chain are described as follows: (i) The two suppliers observe each other's energy efficiency;
The ith supplier
(ii) As the first mover, the ith supplier makes an agreement with the manufacturer on the cooperative strategy to maximize its profit, i.e. s1 is formed; (iii) After observing the actions of the ith supplier and the manufacturer, the second mover, i.e. the jth supplier, also makes an agreement with the manufacturer on the cooperative strategy to maximize its profit, i.e. s2 is formed; (iv) Demand is realized based on the energy efficiency set by the two suppliers and the manufacturer. The notations used in the models are listed in Appendix A. In this study, the energy efficiency xsi and xsj of spare parts are decision variables; other variables are exogenous variables, which are known to all members of the supply chain. Assumption 1. p > wi þ vM and wi > vS þ 3xsi (i, j ¼ 1, 2, i s j). The inequalities ensure that each player in the supply chain makes a positive profit. This assumption is reasonable, because in most cases, the members will withdraw from the market if they make only negative profits (Hsueh, 2014; Formentini and Taticchi, 2016). Assumption 2. In the same market segment, the manufacturer adopts the same price of EFPs, though there is a difference in the energy efficiency of the spare parts provided by the two suppliers. This is reasonable in industries such as the automobile, light bulb and household appliance industries (Xie et al., 2012; Xie, 2015). Assumption 3. The energy efficiency of spare parts can be recognized by both the manufacturer and consumers. This assumption is also reasonable, because the manufacturer can acquire the energy efficiency of the spare parts via sample inspections, and the energy efficiency of EFPs is usually introduced to consumers in products' specifications (Xie et al., 2015). The inequalities in Assumption 1 ensure that each player in a decentralized supply chain makes a positive profit. In this situation, the members will not withdraw from the market. Assumption 2 and Assumption 3 ensure that the function of orders placed by the market segment is decided by the energy efficiency xsi and xsj of spare parts and the price of EFPs. 3.2. Conceptual description of the scenarios In a decentralized supply chain with two competing suppliers, the scenarios of cooperative strategy combinations between the suppliers and the manufacturer can be summarized as follows: 3.2.1. Non-cooperation In a supply chain with non-cooperation (s ¼ NN), the two suppliers initially invest in the energy efficiency of spare parts, but they are non-coordinated with the manufacturer, who does not become involved in improving energy efficiency. Nash's non-cooperative game is implemented between the two suppliers. The decision processes of the players can be described in the following sequential steps:
Order
Energy efficiency Spare part
Manufacturer
Order EFPs
Spare part
Segments of the market
Price
The jth supplier
809
Order
Energy efficiency
Fig. 1. Business flow of the supply chain with competing suppliers.
(i) The two suppliers simultaneously select their energy efficiency; (ii) The manufacturer observes the energy efficiency of the spare parts and places an order with each supplier; (iii) Demand is realized based on the energy efficiency of the EFPs set by the two suppliers. 3.2.2. Cooperation In this section, the decisions made by a supply chain are investigated in three cooperative strategy combinations, including
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manufacturer's involvement, coordination and mixed cooperative strategies.
(iii) Demand is realized based on the energy efficiency set by the two suppliers and the manufacturer.
3.2.2.1. Manufacturer's involvement. When manufacturer's involvement is implemented in a decentralized supply chain with competing suppliers, two cases of cooperative strategy combinations should be considered. Those are the manufacturer's involvement with one supplier and the manufacturer's involvement with two suppliers, as follows: 3.2.2.1.1. Manufacturer's involvement with one supplier. When the two suppliers are non-coordinated with the manufacturer, and the manufacturer invests in the energy efficiency improvement of one supplier (s ¼ ONN), the decision sequences of all players can be described as follows:
3.2.2.3. Mixed cooperative strategies. When one supplier is coordinated with the manufacturer but the other supplier is noncoordinated with the manufacturer, mixed cooperative strategies are adopted. The manufacturer invests in the improvement of the energy efficiency of the non-coordinated supplier (s ¼ ONC), and the decision sequences of all players can be described as follows:
(i) The manufacturer observes the suppliers' energy efficiency; (ii) The manufacturer invests in the energy efficiency improvement of the ith supplier, in order to enhance its own maximum profit; (iii) Demand is realized based on the energy efficiency set by the two suppliers and the manufacturer. 3.2.2.1.2. Manufacturer's involvement in two suppliers. When the two suppliers are non-coordinated with the manufacturer, and the manufacturer invests in improving the energy efficiency of both suppliers (s ¼ TNN), the decision sequences of all three players can be described as follows: (i) The manufacturer observes both suppliers' energy efficiency; (ii) The manufacturer invests in improving the energy efficiency of both suppliers to enhance its own maximum profit; (iii) Demand is realized based on the energy efficiency set by the two suppliers and the manufacturer. 3.2.2.2. Coordination. When coordination is used as a cooperative strategy, two cases (i.e. one coordinated and one non-coordinated supplier, and two coordinated suppliers) are considered. In a decentralized supply chain, the same performance as that of an integrated supply chain can be realized by using a coordination contract. Usually, a contract should satisfy a winewin condition, by supporting the appropriate choice of contract parameters. In this section, the impact of coordination on energy efficiency is investigated, and lump sum transfer contracts for supply chain coordination are designed. 3.2.2.2.1. One coordinated and one non-coordinated suppliers. When one of the suppliers is coordinated with the manufacturer but the other is non-coordinated (s ¼ CN), the decision sequences of the two suppliers are described as follows: (i) The two suppliers observe each other's energy efficiency; (ii) The ith supplier makes an agreement with the manufacturer on coordination, in order to maximize both their profits, while the jth supplier remains non-coordinated with the manufacturer; (iii) Demand is realized based on the energy efficiency set by the two suppliers and the manufacturer. 3.2.2.2.2. Two coordinated suppliers. When the two suppliers are coordinated with the manufacturer (s ¼ CC), their decision sequences can be described as follows: (i) The two suppliers each observe the other's energy efficiency; (ii) Both of the suppliers make an agreement with the manufacturer on coordination to maximize their profits;
(i) The two suppliers each observe the other's energy efficiency; (ii) The jth supplier makes an agreement with the manufacturer on coordination, in order to maximize both their profits, while the ith supplier remains non-coordinated with the manufacturer; (iii) The manufacturer invests in improving the energy efficiency of the ith supplier, in order to enhance its maximum profit; (iv) Demand is realized based on the energy efficiency set by the two suppliers and the manufacturer. The above multiple scenarios of cooperative strategy combinations and their descriptions can be summarized in Table 1. 4. Methods In this section, the decisions made by a supply chain with competing suppliers are introduced. Moreover, an experiment is conducted to illustrate a number of related issues. 4.1. Supply chain decisions The function of orders placed from the market segment is shown as follows:
Dsi ¼ ki a þ axsi b xsj xsi gp
(1)
where ki þ kj ¼ 1, i, j ¼ 1, 2, i s j. Here, kia is the intrinsic demand potential for the ith supplier. The demand function Dsi implies three key empirical regularities: (i) Dsi has a positive correlation with the energy efficiency of the spare parts provided by the ith supplier; (ii) Dsi has a negative correlation with a preponderance of xsj over xsi, i.e. xsj xsi ; and (iii) if both suppliers improve the energy efficiency of their spare parts by one unit, then the sales of both suppliers should increase. In a decentralized supply chain with competing suppliers, the cost is expressed as
i h 2 C s ¼ vS þ vM þ 3xsi ki a þ ða þ bÞxsi bxsj gp þ f þ CS xsi h 2 i þ vS þ vM þ 3xsj kj a þ ða þ bÞxsj bxsi gp þ f þ CS xsj (2) Here, f is the fixed cost which is not related to energy efficiency xsi or xsj. CS ðxsi Þ2 and CS ðxsj Þ2 are fixed costs respectively related to xsi and
xsj ,
and
ðvS þ vM þ 3xsi Þ½ki a þ ða þ bÞxsi bxsj gp
and
ðvS þ vM þ 3xsj Þ½kj a þ ða þ bÞxsj bxsi gp are variable costs. Therefore, Cs is increasing and convex in xsi and xsj . The interaction mechanism in the supply chain can be described as follows:
s1 ¼ s ¼
arg s2fNN;CN;ONNg
maxPsSi þM ðxÞ;
(3)
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Table 1 Scenarios of cooperative strategy combinations and their descriptions. Case
Scenario of analysis
Description
A supply chain with non-cooperation
s ¼ NN
A supply chain using cooperative strategies
s ¼ ONN
The two suppliers are non-coordinated with the manufacturer, and the manufacturer is not involved in improving energy efficiency. The two suppliers are non-coordinated with the manufacturer, and the manufacturer invests in improving the energy efficiency of spare parts provided by one supplier. The two suppliers are non-coordinated with the manufacturer, and the manufacturer invests in improving the energy efficiency of spare parts provided by both suppliers. The manufacturer is not involved in improving energy efficiency, one of the suppliers is coordinated with the manufacturer, but the other is non-coordinated. The manufacturer is not involved in improving energy efficiency, but the two suppliers are coordinated with the manufacturer. There is one coordinated supplier, but the manufacturer invests in improving the energy efficiency of the non-coordinated supplier.
s ¼ CN s ¼ CC s ¼ ONC
where PsSi þM ðxÞ indicates the sum of the profits of both the ith supplier and the manufacturer. After observing the actions of both the ith supplier and the manufacturer, the jth supplier and the manufacturer select their cooperative strategies, and s2 can then be described as:
s2 ¼ s ¼
arg s2fNN;CN;CC;ONN;TNN;ONCg
maxPsSC ðxÞ;
(4)
where PsSC ðxÞ indicates the profit of the whole supply chain. In our six scenarios of analysis, the models and derivations are presented in Appendix B. In the following subsection, profits, energy efficiency and consumer surplus are analyzed through experiments. 4.2. Experimental test For illustration purposes, we conducted a survey of automobile supply chains in China. In April 2013, questionnaires were posted to the corresponding departments of China's six main automobile companies, including SAIC Motor Corporation Limited (SAIC Motor), Dongfeng Motor Corporation, Great Wall Motor Company Limited and BYD Company Limited. Two companies did not want their names mentioned, but all six car companies produce energy saving automobiles. Ultimately, three questionnaires were received. The data collected from the questionnaires enabled us to estimate parameters in the supply chain operations of energy saving automobiles. We then selected a typical supply chain; one in which the automobile manufacturer intends to introduce special energy saving automobiles into the market, and where two main suppliers of engines are competing for orders from the manufacturer. The parameter values are estimated after a comprehensive analysis of the questionnaires and a series of discussions with managers. In this market, competition intensity b is variable, and other parameters are fixed. a ¼ 1000, ki ¼ 0.55, a ¼ 300, wi ¼ 8, wj ¼ 9, p ¼ 30, g ¼ 5, vS ¼ 2, vM ¼ 3, 3 ¼ 3, f ¼ 1000, CS ¼ 3000, CM ¼ 2000 and b 2 [100, 1000]. Here, the units of a, a, g and b are hundreds of automobiles, the units of CS, CM, wi, wj, p, ε, vM, vR and f are thousands of USD, and the units of xsi and xsj are a 10% improvement in energy efficiency compared with a benchmark of automobile fuel consumption. Just like those in Xie (2015), in our study, profits, energy efficiency, and consumer surplus are selected as the performance measuring criteria relating to sustainability. 5. Findings By using the experimental test, we analyze the impacts of competition intensity b on the criteria as follows:
5.1. Profits With different competition intensity b and cooperative strategies, the members in the supply chain may achieve different profits. Firstly, the profits of the ith supplier and the manufacturer when s1 ¼ NN and ONN are compared. The impact of competition intensity b on the equilibrium profits of the ith supplier and the manufacturer is shown in Fig. 2, where curves SiNN, SiONN, MNN ONN* ONN* and MONN indicate PNN* ðxÞ, PNN* ðxÞ, M ðxÞ and PM Si ðxÞ, PSi respectively. Fig. 2 interprets whether the ith supplier and the manufacturer accept the manufacturer's involvement, as shown by ONN* ðxÞ > PNN* ðxÞ > PNN* PONN* M M ðxÞ but PSi Si ðxÞ ð100 b 1000Þ. ONN* Basically, PNN* ðxÞ increase in b, while PNN* M ðxÞ and PM Si ðxÞ and
PONN* ðxÞ decrease in b. Si The sums of the profits of the ith supplier and the manufacturer are then compared when s1 ¼ NN, ONN and CN. The impact of competition intensity b on the maximum profits is shown in Fig. 3, ONN* where curves NN, ONN and CN indicate PNN* Si þM ðxÞ, PSi þM ðxÞ and PCN* Si þM ðxÞ, respectively. Fig. 3 interprets how the ith supplier and the manufacturer select cooperative strategies, as ONN* NN* PCN* Si þM ðxÞ > PSi þM ðxÞ > PSi þM ðxÞ ð100 b 1000Þ.
shown
by
4
2.5
x 10
2
1.5
Profit
s ¼ TNN
1
0.5
0
-0.5 100
200
300
400 SiNN
500 600 Competition intensity SiONN
700
MNN
800
900
1000
MONN
Fig. 2. Profits of the ith supplier and the manufacturer as functions of competition intensity.
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2.4
1000
x 10
500
2.3 0
2.2 -500
Profit
Profit
2.1
2
-1000
-1500
1.9 -2000
1.8 -2500
1.7 -3000 100
1.6 100
200
300
400
500 600 Competition intensity NN
700
800
900
200
300
400
1000
500 600 Competition intensity
SiTNN
ONN
CN
SjTNN
700 SjCN
800
900
1000
SiONC
Fig. 5. Profits of the non-coordinated suppliers as functions of competition intensity.
Fig. 3. Sum of the profits of the ith supplier and the manufacturer as functions of competition intensity.
Moreover, the profits of the whole supply chain are compared when s2 ¼ CN, CC and ONC. The impact of competition intensity b on the equilibrium profits of Ps* SC ðxÞ is shown in Fig. 4, where curves CC* ONC* CN, CC and ONC indicate PCN* ðxÞ, respecSC ðxÞ, PSC ðxÞ and PSC tively. Fig. 4 interprets how the jth supplier and the manufacturer select cooperative strategies, and shows that the supply chain can achieve the highest profit when s2 ¼ CC (100 b 1000). The impacts of competition intensity b on the profits of the non-coordinated suppliers are shown in Fig. 5, where curves ðxÞ, PTNN* ðxÞ, PCN* SiTNN, SjTNN, SjCN, SiONC indicate PTNN* Si Sj Sj ðxÞ
(
(
PTNN* ðxÞ > 0; 100 b 400 Sj PTNN* ðxÞ < 0; Sj (
and
500 b 1000
,
PCN* Sj ðxÞ > 0; 100 b 200 PCN* Sj ðxÞ < 0; 300 b 1000
ðxÞ > 0; 100 b 600 PONC* Si . PONC* ðxÞ < 0; 700 b 1000 Si
5.2. Energy efficiency From the perspective of profits, the above analysis shows that the equilibrium cooperative strategy combination is s ¼ CC. The question, then, is whether s ¼ CC can also bring the highest industry s* s* s* s* s* s* s* energy efficiency e x . Here, e x ¼ ðDs* i xi þ Dj xj Þ=ðDi þ Dj Þ. The
respectively. Fig. 5 indicates that non-coordinated
impact of competition intensity b on the equilibrium industry en-
suppliers may suffer negative profits under certain circum( PTNN* ðxÞ > 0; 100 b 400 Si stances, as shown by , PTNN* ðxÞ < 0; 500 b 1000 Si
s* ergy efficiency e x is shown in Fig. 6, where curves NN, TNN, CN, CC
and
PONC* ðxÞ, Si
2.3
NN*
and ONC indicate e x
TNN*
,e x
CN*
,e x
CC*
,e x
ONC*
and e x
, respectively. As
1.8
x 10
1.6 2.25
1.4 1.2
Energy efficiency
Profit
2.2
2.15
1 0.8 0.6
2.1
0.4 2.05
2 100
0.2 0 100 200
300
400
500 600 Competition intensity CN
CC
700
800
900
200
300
400
1000
NN
500 600 Competition intensity TNN
CN
700 CC
800
900
1000
ONC
ONC
Fig. 4. Profits of the supply chain as functions of competition intensity.
Fig. 6. Industry energy efficiency provided by the supply chain as functions of competition intensity.
G. Xie / Journal of Cleaner Production 113 (2016) 807e821
ONN may cause negative demand as the competition intensity b increases, this cooperative strategy combination is not considered in the following investigation. Fig. 6 indicates which cooperative strategy combination is the most effective in terms of energy efficiency (environment), as 8 TNN* ONC* CC* CN* NN* x >e x >e x >e x >e x ; 100 b 400 x > x > x > x ; 500 b 600 . : TNN* CN* ONC* CC* NN* e x >e x >e x >e x >e x ; 700 b 1000 As stated in Section 3, all members in a decentralized supply chain should have positive profits. Otherwise, the members with negative profits will withdraw from the market segment. As shown in Section 5.1, the non-coordinated suppliers in TNN, CN and ONC realize negative profits when competition intensity b exceeds a critical value. In this situation, if the environment performance is addressed, the policy maker (the government) should provide a subsidy to the suppliers to ensure they are profitable, thus ensuring they will not have to withdraw from the market segment. 5.3. Consumer surplus In addition to the profits of organizations (economy) and energy efficiency (environment), another “pillar” of sustainability, i.e. consumer surplus (society), is also investigated. Here, s* s* s* CSs* ðxÞ ¼ Ds* i xi þ Dj xj . The impact of competition intensity b on the equilibrium consumer surplus CSs* ðxÞ is shown in Fig. 7, where curves NN, TNN, CN, CC and ONC indicate CSNN*, CSTNN*, CSCN*, CSCC* and CSONC*, respectively. Fig. 7 indicates which cooperative strategy combination is the most effective in terms of consumer surplus (society), as shown by 8 < CSTNN* > CSONC* > CSCC* > CSCN* > CSNN* ; 100 b 600 CSTNN* > CSONC* > CSCN* > CSCC* > CSNN* ; 700 b 800 . : TNN* CS > CSCN* > CSONC* > CSCC* > CSNN* ; 900 b 1000 6. Discussion In this section, managerial insights are offered to the policy maker, who can implement policies to improve the sustainability of the supply chain. On the basis of the above analysis, in a decentralized supply chain with competing suppliers, cooperative strategies have significant impacts on sustainability. Also,
3000
2500
Consumer surplus
2000
1500
1000
500
0 100
200
300
400 NN
500 600 Competition intensity TNN
CN
700 CC
800
900 ONC
Fig. 7. Consumer surplus as functions of competition intensity.
1000
813
improvement in the energy efficiency of EFPs can be realized by adjusting parameters, including the price of EFPs, the wholesale price of spare parts, each supplier's share of instinct demand potential and the manufacturer's fixed cost related to energy efficiency. Managerial insights into the selection of cooperative strategy combinations and parameter adjustments are discussed in the following subsections.
6.1. Selection of cooperative strategies In order to support managerial decision-making in sustainable supplier relationship management (SSRM), Leppelt et al. (2013) identified corporate strategy alignment, risk perception and the listing of sustainability indices as the key influential factors, while Govindan et al. (2013) presented a fuzzy multi-criteria approach to determine the ranking of suppliers. However, the two studies named above do not consider how to improve sustainability by cooperation with suppliers, which is illustrated as follows: From Eq. (3) and Fig. 2, because the manufacturer can gain higher profit in ONN than in NN, the manufacturer would naturally prefer to be involved in the investment in energy efficiency improvements. However, as the ith supplier realizes a considerably lower profit in ONN than in NN, the ith supplier will not accept the manufacturer's involvement. In fact, as ONN* NN* PCN* Si þM ðxÞ > PSi þM ðxÞ > PSi þM ðxÞ (100 b 1000), shown in Fig. 3, rather than implementing the cooperative strategy of manufacturer's involvement, the ith supplier and the manufacturer will try to realize coordination between themselves to achieve higher profits, i.e. s1 ¼ CN. After observing the actions of both the ith supplier and the manufacturer, the jth supplier and the manufacturer adjust their cooperative strategy. From Eq. (4) and Fig. 4, to achieve the highest profit (economy) for the supply chain, the jth supplier will also try to realize coordination with the manufacturer, i.e. s2 ¼ CC. These results are similar to those of Hsueh (2014), which suggests that coordination improves total supply chain profits. However, in a decentralized supply chain with competing suppliers, while a cooperative strategy combination brings the highest profit, this does not mean that such a combination can also always achieve the highest energy efficiency. As seen from Fig. 6, the cooperative strategy combination CC is far from the best cooperative strategy combination for energy efficiency (environment). Also, as shown in Fig. 7, rather than CC, TNN is the best cooperative strategy combination for consumer surplus (society). The results are quite different from those proposed by Xie (2015), which suggests that a coordinated supply chain is a better choice than a noncoordinated one in terms of achieving greater energy efficiency and consumer surplus. The reason for this variation in results is that a cooperative strategy with manufacturer's involvement is not investigated in Xie (2015), in which there is only one supplier, and a competitive environment is not considered. From the results of our study, managerial insights are drawn with regard to cooperative strategies for the sustainability of a supply chain. When financial distress or profit sharing is the main problem facing a supply chain, the cooperative strategy combination between players should be adjusted to CC. However, to achieve greater consumer surplus and higher industry energy efficiency, when competition intensity is low, cooperative strategy combinations TNN and ONC, rather than CC, should be chosen. In particular, when competition intensity is rather high, non-coordinated suppliers suffer negative profits, as shown in Fig. 5. In this situation, a subsidy should be provided to the suppliers with negative profits. Otherwise, the non-profitable suppliers will withdraw from the market.
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In existing literature, while different kinds of models are applied, it is evident that the social side of sustainability is not taken into account (Seuring, 2013). In contrast, we consider the three “pillars” of sustainability, i.e. environment, society and economy in this study. Our conclusion is that there is no single best cooperative strategy combination for all three criteria. Therefore, tradeoffs should be made by the policy maker before any cooperative strategy combination is advocated, which in turn proves the partial view in Seuring and Müller (2008) that tradeoffs among the environmental and economic dimensions are most often taken as a starting point for building the models. Tseng and Hung (2014) suggest that the reduction of carbon dioxide emissions can be achieved by enacting legislation which would force an enterprise to bear the social costs of the carbon dioxide emissions resulting from their economic activities. However, such legislation could also cause economic loss. This study presents cooperative strategies which may improve both environmental performance and economic performance. For instance, compared with the environmental performance and the economic performance when s ¼ NN, both of them (economy and environment) improve when s ¼ CC. Besides cooperative strategies, parameter adjustment is another approach used to achieve energy efficiency improvement in different scenarios of cooperative strategy combinations, which we discuss in the following subsection. 6.2. Parameter adjustment From the propositions and corollaries in Appendix B, we find that in a supply chain with competing suppliers, the energy efficiency of EFPs can be improved by lowering the manufacturer's fixed cost related to energy efficiency. As a consequence, the policy maker can prompt a manufacturer to lower the manufacturer's fixed cost related to energy efficiency by providing financial support (for technology innovation) to the manufacturer. In particular, the energy efficiency of spare parts provided by one supplier can be improved by lowering the share of the supplier's instinct demand potential. In addition, the energy efficiency of EFPs is closely related to the price of EFPs for the segments of market and the wholesale price of spare parts to suppliers. With regard to price, enhancing the price of EFPs leads to higher energy efficiency in all scenarios. However, in the case of two non-coordinated suppliers s ¼ NN, ONN or TNN, the improvement in the energy efficiency of the spare parts provided by a non-coordinated supplier can be realized by enhancing the wholesale price to the supplier. The above results are similar to those found by Xie et al. (2015). However, when the manufacturer's involvement is implemented to a non-coordinated supplier, the improvement in the energy efficiency of the supplier's spare parts can be realized by lowering the wholesale price to the supplier. As a consequence, the energy efficiency can be improved by making parameter adjustments, i.e. enhancing the price of EFPs, lowering the supplier's share of instinct demand potential and lowering the manufacturer's fixed cost related to energy efficiency. In contrast to the Tsoulfas and Pappis (2008) study, which defines six specific environmental performance indicators to support the decisions of supply chains in the presence of environmental considerations, we develop mathematical models and derive new ways to improve environment performance by means of parameter adjustments. 7. Conclusions This paper extends and complements existing studies in how to enhance sustainability through cooperative strategies in a supply
chain with competing suppliers. The mechanism used in the selection of cooperative strategies is described, and the decisions of supply chain members are derived under different scenarios. In addition, an experimental analysis illustrates the impacts of competition intensity on profits, the energy efficiency of EFPs and consumer surplus. Managerial insights into the improvement of energy efficiency, profits and consumer surplus are discussed. This study makes an important contribution to existing sustainability and supply chain literature, which until now has not investigated how to improve sustainability in a competitive environment through cooperative supply chain strategies, has lacked any mathematical modeling of supply chain sustainability and competition analysis, and which has focused more on case analysis and monopolistic scenarios. Our key managerial insights can be summarized as follows: First, profits, the energy efficiency of EFPs and the consumer surplus of the supply chain can be efficiently enhanced by cooperative strategies, which may lead to negative profits for non-coordinated suppliers. This finding suggests that the policy maker should sometimes subsidize suppliers, for reasons of improved environment performance. Second, there is no single best cooperative strategy combination for all three “pillars” of sustainability, i.e. energy efficiency (environment), consumer surplus (society) and the profits of organizations (economy). A tradeoff should be made by the policy maker before a cooperative strategy combination is advocated. Third, energy efficiency can be improved by making parameter adjustments, i.e. enhancing price, lowering the supplier's share of instinct demand potential and lowering the manufacturer's fixed cost related to energy efficiency. One of the limitations of our paper is that this study focuses on the case of two competing suppliers. In fact, there are usually more than two suppliers. In such cases, new models can be developed to analyze managerial decision-making for sustainability improvement. Moreover, the results of our experimental analysis are decided by parameters, which change over time. As a consequence, the results of our experimental analysis may be inapplicable when the parameters change. This study may be a subject of future research. Dynamic managerial decision-making models that are able to integrate the selection of a cooperative strategy combination phase with the monitoring and continuous analysis of that selection can be investigated. In future work, the topics expected to be worthy of further study include risk management in a sustainable supply chain, the regulation of a sustainable supply chain with uncertain demand and risk management in competing supply chains. Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 71372176) and The Royal Academy of Engineering for research exchanges with China and India scheme. Appendix A The following notations are used in the model: s The cooperative strategy combination of the manufacturer's involvement in energy efficiency improvement and the coordination between the two suppliers and the manufacturer (s, s1, s2 ¼ NN, ONN, TNN, CN, CC, ONC); s1 The cooperative strategy combination of the supply chain after decisions of the first mover; s2 The cooperative strategy combination of the supply chain after decisions of the second mover;
G. Xie / Journal of Cleaner Production 113 (2016) 807e821
xsi The energy efficiency of spare parts provided by the ith supplier within s (i, j ¼ 1, 2, i s j), which is also a measure of energy saving improvement compared with a benchmark; p Price per unit of the EFPs in a given market segment; wi Wholesale price per unit of spare parts to the ith supplier (i, j ¼ 1, 2, i s j);
xNN* ¼ i
Proposition 1. When there are two non-coordinated suppliers, the equilibrium solutions xNN* and xNN* for energy efficiency of EFPs are: i j
4½3ða þ bÞ þ CS 2 32 b2
;
(6)
and
3b½3gp þ ða þ bÞðwi vS Þ 3ki a þ 2½3ða þ bÞ þ CS 3gp þ ða þ bÞ wj vS 3kj a 4½3ða þ bÞ þ CS 2 32 b2
3 The suppliers' variable cost related to energy efficiency; CS The suppliers' fixed cost related to energy efficiency; CM The manufacturer's fixed cost related to energy efficiency; ki Share of the intrinsic demand potential for the ith supplier (i, j ¼ 1, 2, i s j); a Demand sensitivity to energy efficiency of the spare parts; b Competition intensity denoting the competitive effects of energy efficiency for the supplier pair (i, j); g Demand sensitivity to price of the EFPs.
:
(7)
Proof of Proposition 1. From Eq. (5), first-order partial derivative NN is obtained as follows: of PNN Si ðxÞ with respect to xi
. NN vPNN ¼ 2½3ða þ bÞ þ CS xNN þ 3bxNN þ 3gp Si ðxÞ vxi i j þ ða þ bÞðwi vS Þ 3ki a NN ¼ 0, there is Let vPNN Si ðxÞ=vxi
2½3ða þ bÞ þ CS xNN 3bxNN ¼ 3gp þ ða þ bÞðwi vS Þ 3ki a i j
Appendix B The decisions made by the supply chain are investigated under the six scenarios of analysis, and equilibrium solutions for the en-
xNN* ¼ i
Then, Proposition 1 and Corollary 2 summarize our findings on the energy efficiency of an EFP when s ¼ NN.
2½3ða þ bÞ þ CS ½3gp þ ða þ bÞðwi vS Þ 3ki a þ 3b 3gp þ ða þ bÞ wj vS 3kj a
vS The suppliers' variable production cost per unit; vM The manufacturer's variable production cost per unit;
xNN* ¼ j
815
Then, equilibrium solutions xNN* and xNN* for the energy effii j ciency of EFPs are derived as follows:
2½3ða þ bÞ þ CS ½3gp þ ða þ bÞðwi vS Þ 3ki a þ 3b 3gp þ ða þ bÞ wj vS 3kj a 4½3ða þ bÞ þ CS 2 32 b2
and
ergy efficiency of EFPs are derived. (1) s ¼ NN
xNN* ¼ j
3b½3gp þ ða þ bÞðwi vS Þ 3ki a þ 2½3ða þ bÞ þ CS 3gp þ ða þ bÞ wj vS 3kj a 4½3ða þ bÞ þ CS 2 32 b2
In the scenario of s ¼ NN, profit PNN Si ðxÞ of the ith supplier is:
NN PNN Si ðxÞ ¼ wi vS 3xi h 2 i NN NN ki a þ ða þ bÞxNN : i bxj gp f CS xi
(5)
:
Corollary 2. In the case of two non-coordinated suppliers, the energy efficiency of the EFPs provided by the ith supplier increases in p and wi (i, j¼1,2, i s j) but decreases in its share ki of the instinct demand potential. Proof: Straightforward and therefore omitted.
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G. Xie / Journal of Cleaner Production 113 (2016) 807e821
With the equilibrium solutions, the profit PNN* M ðxÞ of the manufacturer can be derived as follows:
h i NN* PNN* bxNN* gp M ðxÞ ¼ ðp wi vM Þ ki a þ ða þ bÞxi j i h bxNN* gp : þ p wj vM kj a þ ða þ bÞxNN* j i NN* Only when profits PNN* Si ðxÞ and PM ðxÞ are positive will the supply chain enter into the market and the players manufacture EFPs. In the following section, the decisions made by a supply chain implementing cooperative strategies are investigated.
(2) s ¼ ONN When s ¼ ONN, the profit PONN M ðxÞ of the manufacturer is:
h i ONN PONN bxONN gp M ðxÞ ¼ ðp wi vM Þ ki a þ ða þ bÞxi j 2 2 NN* x CM xONN i i i h bxONN gp : þ p wj vM kj a þ ða þ bÞxONN j i (9) h i kj a þ ða þ bÞxONN PONN ðxÞ ¼ wj vS 3xONN bxONN gp Sj j j i 2 : f CS xONN j (10) Then, Proposition 3 and Corollary 4 summarize our findings on the energy efficiency of the EFP when s ¼ ONN. Proposition 3. When s ¼ ONN, the equilibrium solutions xONN* and i xONN* for energy efficiency of EFPs are: j
(11)
and
xONN* j
3gp þ ða þ bÞ wj vS 3kj a þ 3bxONN* i : ¼ 2½3ða þ bÞ þ CS
xONN* ¼ j
Corollary 4. In the case of s ¼ ONN, the energy efficiency of the EFPs provided by the ith supplier increases in p but decreases in CM and wi, while the energy efficiency of the EFPs provided by the jth supplier increases in p and wj but decreases in CS and its share kj of the instinct demand potential. Proof: Straightforward and therefore omitted. With the equilibrium solutions, we can derive the profit PONN ðxÞ Si of the ith supplier as follows:
PONN* ðxÞ¼ wi vS 3xONN* Si i h i 2 ki aþðaþbÞxONN* bxONN* gpONN* f CS xNN* : i j i Only when profits PONN* ðxÞ, PONN* ðxÞ and PONN* ðxÞ are positive, M Si Sj will the supply chain enter into the market segment and the players manufacture the EFPs. (3) s ¼ TNN When the manufacturer invests in improving the energy efficiency of both suppliers, the profit PTNN M ðxÞ of the manufacturer is
h i TNN PTNN bxTNN gp M ðxÞ ¼ ðp wi vM Þ ki a þ ða þ bÞxi j 2 2 xNN* CM xTNN i i i h bxTNN gp þ p wj vM kj a þ ða þ bÞxTNN j i 2 2 NN* : x CM xTNN j j (14)
(12)
Proof of Proposition 3. From Eqs. (9) and (10), first-order partial ONN ðxÞ with respect to xONN and xONN derivatives of PONN M ðxÞ and PSj i j
Proposition 5 and Corollary 6 then summarize our findings on the energy efficiency of the EFP when s ¼ TNN. Proposition 5. When s ¼ TNN, equilibrium solutions for the energy efficiency of the EFPs are:
are obtained as follows:
. ONN vPONN ¼ aðp wi vM Þ b wi wj 2CM xONN M ðxÞ vxi i . vPONN ðxÞ vxONN ¼ 3bxONN 2½3ða þ bÞ þ CS xONN þ 3gp Sj j i j þ ða þ bÞ wj vS 3kj a ONN ¼ 0 and vPONN ðxÞ=vxONN ¼ 0, there are Let vPONN M ðxÞ=vxi Sj j
(
3gp þ ða þ bÞ wj vS 3kj a þ 3bxONN* i : 2½3ða þ bÞ þ CS
(13)
The profit PONN ðxÞ of the jth supplier is: Sj
aðp wi vM Þ b wi wj ; 2CM
aðp wi vM Þ b wi wj ¼ ; 2CM
and
(8)
xONN* ¼ i
xONN* i
aðp wi vM Þ b wi wj 2CM xONN ¼0 i 3bxONN ¼ 3gp þ ða þ bÞ wj vS 3kj a 2½3ða þ bÞ þ CS xONN j i
Then, equilibrium solutions xONN* and xONN* for the energy efi j ficiency of EFPs are derived as follows:
xTNN* ¼ i
aðp wi vM Þ b wi wj ; 2CM
(15)
a p wj vM b wj wi : 2CM
(16)
and
xTNN* ¼ j
Otherwise, there are no equilibrium solutions. Proof of Proposition 5. From Eq. (13), partial derivatives of TNN and xTNN are obtained as follows: PTNN M ðxÞ with respect to xi j
TNN vPTNN ¼ aðp wi vM Þ b wi wj 2CM xTNN ; M ðxÞ=vxi i
G. Xie / Journal of Cleaner Production 113 (2016) 807e821
TNN vPTNN M ðxÞ=vxj
¼ a p wj vM b wj wi 2CM xTNN ; j
2 TNN ¼ 2CM ; v2 PTNN M ðxÞ=v xi
817
PTNN* ðxÞ ¼ wi vS 3xTNN* Si i h 2 i ki a þ ða þ bÞxTNN* bxTNN* gp f CS xNN* ; i j i (17) PTNN* ðxÞ ¼ wj vS 3xTNN* Sj j h 2 i kj a þ ða þ bÞxTNN* bxTNN* gp f CS xNN* : j i j
2 TNN v2 PTNN ¼ 2CM ; M ðxÞ=v xj
(18) v
2
TNN TNN PTNN vxj M ðxÞ=vxi
¼ 0;
PTNN* ðxÞ, Si
TNN ; xTNN Þ Hessian matrix H of PTNN is M ðxi j
TNN 0 2CM ; HTNN ¼ . To be certain that HTNN is maximum in 0; 2CM
; xTNN* Þ, the Hessian matrix HTNN should be negative definite. ðxTNN* i j That is, (2CM)(2CM) > 0, which is obvious tenable. Therefore, there are unique optimal solutions for the energy efficiency of EFPs. TNN ¼ 0 and vPTNN ðxÞ=vxTNN ¼ 0. Equilibrium Let vPTNN M ðxÞ=vxi M j solutions xTNN* and xTNN* for the energy efficiency of EFPs are i j derived as follows:
aðp wi vM Þ b wi wj ¼ ; 2CM
(4) s ¼ CN When coordination is realized between the ith supplier and the manufacturer, the profit PCN Si þM ðxÞ of the ith supplier and the manufacturer is:
h i CN CN ki a þ ða þ bÞxCN PCN Si þM ðxÞ ¼ p vS vM 3xi i bxj gp 2 2 2 NN* CS xNN* x f c xCN i i i i h CN þ p wj vM kj a þ ða þ bÞxCN j bxi gp (19) where c ¼ min{CS, CM}. The profit PCN Sj ðxÞ of the jth supplier is:
and
xTNN* ¼ j
a p wj vM b wj wi : 2CM
Corollary 6. In the case of s ¼ TNN, the energy efficiency of the EFPs provided by both suppliers increases in p, but decreases in the wholesale price and CM. Proof: Straightforward and, therefore, omitted. With the equilibrium solutions, the profit PTNN* ðxÞ of the ith Si supplier and the profit PTNN* ðxÞ of the jth supplier are derived as Sj follows:
xCN* ¼ i
PTNN* ðxÞ M
Only when profits and are positive, will the supply chain enter the market segment and the players manufacture the EFPs. In the following subsection, another cooperative strategy, i.e. coordination, is investigated as follows.
TNN TNN vxi ¼ 0: v2 PTNN M ðxÞ=vxj
xTNN* i
PTNN* ðxÞ Sj
h i CN CN CN kj a þ ða þ bÞxCN PCN Sj ðxÞ ¼ wj vS 3xj j bxi gp 2 : f CS xCN j (20) Then, Proposition 7 and Corollary 8 summarize our findings on the energy efficiency of the EFP when s ¼ CN. Proposition 7. When one supplier is coordinated with the manufacturer but the other is non-coordinated, the equilibrium solutions xCN* and xCN* for energy efficiency of the EFPs are i j
2½3ða þ bÞ þ CS ða þ 3gÞp þ b wj vS aðvS þ vM Þ 3ki a þ 3b 3gp þ ða þ bÞ wj vS 3kj a 4½3ða þ bÞ þ CS ½3ða þ bÞ þ c 32 b2
;
(21)
and
xCN* ¼ j
2½3ða þ bÞ þ c 3gp þ ða þ bÞ wj vS 3kj a þ 3b ða þ 3gÞp þ b wj vS aðvS þ vM Þ 3ki a 4½3ða þ bÞ þ CS ½3ða þ bÞ þ c 32 b2
:
(22)
818
G. Xie / Journal of Cleaner Production 113 (2016) 807e821
Proof of Proposition 7. From Eqs. (19) and (20), first-order partial CN CN and xCN are derivatives of PCN Si þM ðxÞ and PSj ðxÞ with respect to xi j obtained as follows:
. CN CN vPCN ¼ 2½3ða þ bÞ þ cxCN Si þM ðxÞ vxi i þ 3bxj þ ða þ 3gÞp 3ki a aðvS þ vM Þ þ b wj vS ;
should pay the lump sum fee F to the manufacturer. The profits of CN* F and the supplier Si and the manufacturer are PCN Si ¼ PSi CN* CN NN* and PCN PNN* are satisfied. PCN M ¼ PM þ F. Then, PSi PSi M M
Therefore, we propose Corollary 9 as follows:
. CN CN ¼ 3bxCN vPCN Sj ðxÞ vxj i 2½3ða þ bÞ þ CS xj þ 3gp þ ða þ bÞ wj vS 3kj a:
Corollary 9. In a lump sum transfer contract for supply chain co PCN* ordination, in the case of s ¼ CN, when PNN* Si Si , the manu-
CN ¼ 0 and vPCN ðxÞ=vxCN ¼ 0. The equations Let vPCN Si þM ðxÞ=vxi Sj j are as follows:
(
CN 2½3ðaþbÞþcxCN i 3bxj ¼ðaþ3gÞpþb wj vS aðvS þvM Þ3ki a : CN 3bxi þ2½3ðaþbÞþCS xCN j ¼3gpþðaþbÞ wj vS 3kj a
Then, equilibrium solutions xCN* and xCN* for the energy effii j ciency of EFPs are derived as follows:
xCN* ¼ i
facturer should pay a lump sum fee F to the supplier; otherwise, PCN* when PNN* M M , the supplier should pay the lump sum fee F to the manufacturer, where F meets F F F, F ¼ maxfPNN* Si NN* CN* CN* CN* NN* PCN* PNN* Si ; PM PM ; 0g and F ¼ maxfPSi Si ; PM PM ; 0g.
Proof: Straightforward and therefore omitted. (5) s ¼ CC
2½3ða þ bÞ þ CS ða þ 3gÞp þ b wj vS aðvS þ vM Þ 3ki a þ 3b 3gp þ ða þ bÞ wj vS 3kj a 4½3ða þ bÞ þ CS ½3ða þ bÞ þ c 32 b2
;
When coordination is realized between each supplier and the manufacturer, the profit PCC SC ðxÞ of the suppliers and the manufacturer is:
and
xCN* ¼ j
2½3ða þ bÞ þ c 3gp þ ða þ bÞ wj vS 3kj a þ 3b ða þ 3gÞp þ b wj vS aðvS þ vM Þ 3ki a 4½3ða þ bÞ þ CS ½3ða þ bÞ þ c 32 b2
Corollary 8. In the case of s ¼ CN, the energy efficiency of the EFPs provided by the ith supplier increases in p and wj but decreases in its share ki of the instinct demand potential, while the energy efficiency of the EFPs provided by the jth supplier increases in p and wj but decreases in its share kj of the instinct demand potential. Proof: Straightforward and therefore omitted. Due to the complete and symmetric information assumption, lump sum transfer contracts can be used for supply chain coordination. To ensure that suppliers and the manufacturer in a decentralized supply chain all have incentives to accept the coordination contract, the profits of the suppliers and the manufacturer should be no less than those which were in place NN* NN* before coordination, i.e. PCN and PCN M PM . This Si PSi problem can be easily solved by offering a lump sum fee F NN* CN* PCN* ðF F FÞ. Here, F ¼ maxfPNN* Si Si ; PM PM ; 0g and F¼
when the ith supplier earns less with the coordination contract, the manufacturer should pay a lump sum fee F to the supplier. Then, the profits of the supplier Si and the manufacturer are CN* þ F and PCN ¼ PCN* F. Otherwise, the supplier S PCN i M M Si ¼ PSi
maxfPCN* Si
xCC* ¼ i
CN* PNN* Si ; PM
PNN* M ; 0g.
When
PNN* Si
PCN* Si ,
i.e.
h i CC CC ki a þ ða þ bÞxCC PCC SC ðxÞ ¼ p vS vM 3xi i bxj gp 2 2 2 CS xNN* xNN* þ p vS f c xCC i i i h i CC kj a þ ða þ bÞxCC vM 3xCC j j bxi gp f 2 2 2 NN* c xCC x : CS xNN* j j j (23) Proposition 10 and Corollary 11 then summarize our findings on the energy efficiency of EFPs when cooperative strategy combination s ¼ CC. Proposition 10. When both of the suppliers are coordinated with the manufacturer, equilibrium solutions xCC* and xCC* for the energy i j efficiency of EFPs are:
½3ða þ bÞ þ c½3gp þ aðp vS vM Þ 3ki a þ 3b 3gp þ aðp vS vM Þ 3kj a 2½3ða þ bÞ þ c2 232 b2
:
;
(24)
G. Xie / Journal of Cleaner Production 113 (2016) 807e821
819
and
xCC* ¼ j
½3ða þ bÞ þ c 3gp þ aðp vS vM Þ 3kj a þ 3b½3gp þ aðp vS vM Þ 3ki a
( Proof of Proposition 10. From Eq. (23), first-order partial deCC and xCC are obtained as rivatives of PCC SC ðxÞ with respect to xi j follows:
xCC* ¼ i
(25)
2½3ða þ bÞ þ c2 232 b2
CC 2½3ða þ bÞ þ cxCC i 23bxj ¼ 3gp þ aðp vS vM Þ 3ki a CC 23bxCC i þ 2½3ða þ bÞ þ cxj ¼ 3gp þ aðp vS vM Þ 3kj a
;
Then, equilibrium solutions xCN* and xCN* for the energy effii j ciency of EFPs are derived as follows:
½3ða þ bÞ þ c½3gp þ aðp vS vM Þ 3ki a þ 3b 3gp þ aðp vS vM Þ 3kj a 2½3ða þ bÞ þ c2 232 b2
;
and
xCC* j
¼
½3ða þ bÞ þ c 3gp þ aðp vS vM Þ 3kj a þ 3b½3gp þ aðp vS vM Þ 3ki a 2½3ða þ bÞ þ c2 232 b2
. CC CC CC vPCC SC ðxÞ vxi ¼ 2½3ða þ bÞ þ cxi þ 23bxj þ 3gp þ aðp vS vM Þ 3ki a; CC CC CC vPCC SC ðxÞ=vxj ¼ 23bxi 2½3ða þ bÞ þ cxj þ 3gp
þ aðp vS vM Þ 3kj a; 2 CC v2 PCC ¼ 2½3ða þ bÞ þ c; SC ðxÞ=v xi
v
2
PCC SC ðxÞ=v
xCC j
2
¼ 2½3ða þ bÞ þ c;
CC CC v2 PCC SC ðxÞ=vxi vxj ¼ 23b;
CC CC v2 PCC SC ðxÞ=vxj vxi ¼ 23b:
The Hessian matrix HCC of PCC is SC ðxÞ
2½3ða þ bÞ þ c 23b . To be certain that HCC HCC ¼ 23b 2½3ða þ bÞ þ c is maximum in ðxCC* ; xCC* Þ, the Hessian matrix HCC should be i j
negative definite. That is, [3(a þ b) þ c]2 32b2 > 0, i.e. [3(a þ 2b) þ c](3a þ c) > 0, which is obvious tenable. Therefore, there are unique optimal solutions for the energy efficiency of EFPs. CC CC CC Let vPCC SC ðxÞ=vxi ¼ 0 and vPSC ðxÞ=vxj ¼ 0. The equations are as follows:
:
Corollary 11. In the case of two suppliers being coordinated with the manufacturer, the energy efficiency of the EFPs provided by the ith supplier increases in p, but decreases in its share ki of the instinct demand potential. Proof: Straightforward and therefore omitted. Also, exactly as with the contract in Corollary 9, another lump sum transfer contract is proposed in Corollary 12 for supply chain coordination in the case of s ¼ CC as follows: Corollary 12. In a lump sum transfer contract for supply chain coordination in the case of s ¼ CC, when PNN* PCC* Si Si , the manufacturer should pay a lump sum fee F to the ith supplier; otherwise, when PNN* PCC* M M , the supplier should pay the lump sum fee F to the manufacturer, where F meets F F F, F ¼ maxfPNN* Si NN* CC* CC* NN* CC* NN* PCC* Si ; PM PM ; 0g and F ¼ maxfPSi PSi ; PM PM ; 0g.
The same rules should be implemented with the jth supplier. Proof: Straightforward and therefore omitted. (6) s ¼ ONC In the scenario where s ¼ ONC, the profit PONC Si ðxÞ of supplier Si is
h i ONC ki a þ ða þ bÞxONC PONC bxONC gp Si ðxÞ ¼ wi vS 3xi i j 2 : f CS xNN* i (26)
820
G. Xie / Journal of Cleaner Production 113 (2016) 807e821
After energy efficiency improvement is provided to the ith supplier, the profit PONC MþSj ðxÞ of the jth supplier and the manufacturer is:
. ONC v2 PONC v xONC ¼ 3b; MþSj ðxÞ v xi j
h i ONC PONC bxONC gp MþSj ðxÞ ¼ ðpwi vM Þ ki aþðaþbÞxi j 2 2 xNN* CM xONC i i h i kj aþðaþbÞxONC bxONC gp þ pvS vM 3xONC j j i 2 2 2 NN* CS xNN* x : f c xONC j j j
. ONC v xONC ¼ 3b; v2 PONC MþSj ðxÞ v xj i
(27)
Theorem 13. In mixed cooperative strategies, when pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3b < 2 CM ½3ða þ bÞ þ c, there are unique optimal solutions for the energy efficiency of EFPs. Proof of Theorem 13. From Eq. (27), partial derivatives of ONC and xONC are obtained as follows: PONC MþSj ðxÞ with respect to xi j
. ONC vPONC ¼ 2CM xONC þ 3bxONC þ aðp wi vM Þ MþSj ðxÞ vxi i j
2 v2 PONC ðxÞ v xONC ¼ 2½3ða þ bÞ þ c; MþSj j The HONC ¼
Hessian matrix H of PONC is MþSj ðxÞ ONC 3b 2CM . To be certain that HONC is 3b 2½3ða þ bÞ þ c
maximum in ðxONC* ; xONC* Þ, the Hessian matrix HCC should be i j negative definite. Therefore, when 4CM ½3ða þ bÞ þ c 32 b2 > 0, i.e. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3b < 2 CM ½3ða þ bÞ þ c, there are unique optimal solutions for the energy efficiency of EFPs. Proposition 14 and Corollary 15 then summarize our findings on the energy efficiency of the EFPs when s ¼ ONC. Proposition 14. When s ¼ ONC, the equilibrium solutions xONC* and i xONC* for the energy efficiency of EFPs are: j
bðwi vS Þ;
xONC* ¼ i
3b aðp vS vM Þ þ bðwi vS Þ þ 3gp 3kj a þ 2½3ða þ bÞ þ c½aðp wi vM Þ bðwi vS Þ 4CM ½3ða þ bÞ þ c 32 b2
;
(28)
and
xONC* ¼ j
2CM aðp vS vM Þ þ bðwi vS Þ þ 3gp 3kj a þ 3b½aðp wi vM Þ bðwi vS Þ 4CM ½3ða þ bÞ þ c 32 b2
:
ONC ¼ 0 Proof of Proposition 14. Let vPONC MþSj ðxÞ=vxi ONC ONC ¼ 0. The equations are as follows: vPMþSj ðxÞ=vxj
(
(29)
and
3bxONC ¼ aðp wi vM Þ bðwi vS Þ 2CM xONC i j 3bxONC þ 2½3ða þ bÞ þ cxONC ¼ aðp vS vM Þ þ bðwi vS Þ þ 3gp 3kj a i j
. ONC ¼ 3bxONC 2½3ða þ bÞ þ cxONC vPONC MþSj ðxÞ vxj i j þ aðp vS vM Þ þ bðwi vS Þ þ 3gp 3kj a;
v2 PONC MþSj ðxÞ
2 v xONC ¼ 2CM ; i
and xONC* for the energy efThen, equilibrium solutions xONC* i j ficiency of EFPs are derived as follows:
G. Xie / Journal of Cleaner Production 113 (2016) 807e821
xONC* ¼ i
821
3b aðp vS vM Þ þ bðwi vS Þ þ 3gp 3kj a þ 2½3ða þ bÞ þ c½aðp wi vM Þ bðwi vS Þ 4CM ½3ða þ bÞ þ c 32 b2
;
and
xONC* ¼ j
2CM aðp vS vM Þ þ bðwi vS Þ þ 3gp 3kj a þ 3b½aðp wi vM Þ bðwi vS Þ 4CM ½3ða þ bÞ þ c 32 b2
Corollary 15. In the case of s ¼ ONC, the energy efficiency of the EFPs provided by the ith supplier increases in p but decreases in wi and CM, while the energy efficiency of the EFPs provided by the jth supplier increases in p but decreases in c and that supplier's share kj of the instinct demand potential. Proof: Straightforward and therefore omitted. After energy efficiency improvement is implemented for the ith supplier, the profit PONC* ðxÞ of the ith supplier is: Si
h ki a þ ða þ bÞxONC* PONC* ðxÞ ¼ wi vS 3xONC* bxONC* Si i i j 2 i gp f CS xNN* : i
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