Dynamic decision and coordination in a low-carbon supply chain considering the retailer's social preference

https://doi.org/10.1016/j.seps.2021.101010Get rights and content

Highlights

  • A chaotic supply chain system negatively affects the manufacturer's profit.

  • Excessive adjustment parameters destabilize the supply chain system.

  • A retailer's high social preference stabilizes the supply chain system.

  • Social preference cannot change supply chain coordination in decentralized setting.

Abstract

We establish dynamic game models in a low-carbon supply chain consisting of a single manufacturer and a single retailer with social preference. This study investigates the complex dynamic characteristics of pricing decision and carbon abatement strategy in the supply chain and focuses on the impact of the retailer's social preference on pricing decision, carbon emission abatement strategy, profits, supply chain coordination, and complexity of dynamic models. We find that adjustment parameters of pricing and carbon emission abatement should be maintained in a certain range; otherwise, the system will be unstable and even chaotic through period double bifurcation or wave shape chaos. A higher social preference of the retailer is always beneficial to carbon abatement and the manufacturer and helps maintain the stability of the supply chain system. However, the impact on the long-term profitability of the supply chain is related to the state of the system. Compared with the setting of a centralized decision, the optimal carbon abatement strategy and supply chain profit in a decentralized decision are always less than those in a centralized setting, regardless of whether the retailer has social preference. Therefore, a side-payment self-executing contract is designed to coordinate the supply chain and achieve Pareto improvement. The coordination mechanism proposed in this study not only leads to Pareto improvement but also increases the stability of the supply chain system. Finally, this study enlightens management in operating a low-carbon supply chain.

Introduction

The Intergovernmental Panel on Climate Change Special Report on Global Warming of 1.5 °C released in 2018 sends a strong message that extreme weather, rise in sea level, Arctic sea ice loss, and other changes have witnessed the consequences of global warming of 1 °C [1]. As global warming intensifies, dealing with climate change is becoming a major global issue. To enhance competitiveness, members of the supply chain no longer focus on economic benefit but multiple objectives of economic, environmental, and social benefits [2,3].

The supply chain is a complex system comprising many enterprises, and each enterprise unilaterally maximizes its interests while disregarding the marginal interests of other members, resulting in “double marginalization effect.” Therefore, supply chain coordination is vital and can be achieved by adopting an appropriate contract. Currently, the major common side-payment contracts include wholesale price (WP) contract, buyback (BB) contract, revenue sharing (RS) contract, and linear two-part tariff (LTT). By providing a contract, the equilibrium solution of a decentralized decision can achieve the level of a centralized decision. The benefit for a coordination contract is that centralized decision and side-payment benefits both sides and leads to Pareto improvement.

With development in behavioral economics, people gradually realize that decision-makers have social preferences, such as fairness concerns, altruistic preferences, and reciprocal preferences, which make them consider not only their own benefits but also those of others [[4], [5], [6]]. For example, in 2017, to ensure smooth mass production of iPhone 8, Apple purchased high-end production equipment for its supply chain partners [7]. Moreover, Lenovo incorporated its distributors, agents, chain retailers, and other partners into its management system, ensuring an orderly and efficient channel. In 2012, when the global PC market sales fell 8%, Lenovo registered an increase of 10% in sales [8]. Models of the social preference theory introduce human social-affective factors based on psychology and sociology to utility functions to revise the hypothesis of economic man, thus addressing the limitation and narrowness of the traditional hypothesis of economic man and explaining the paradox of many experiments. Thus, there is increased focus on introducing behavioral factors in the operation of the supply chain.

Previous research focuses on the single-period model; however, it is essential to analyze the evolution of the game from a long-term perspective and identify an optimal strategy. Many scholars integrate nonlinear and complex system theories into research on economic systems, thus broadening the scope of the dynamic game [[9], [10], [11]]. Based on this, this study uses nonlinear analysis to investigate the long-term game behavior of pricing decision and carbon abatement level in the supply chain.

On one hand, manufacturers in a low-carbon economy invest in carbon emission reduction under the double pressure of the government's total carbon emission limit and increasing environmental awareness of consumers. On the other hand, due to the cognitive deviation of carbon emission reduction, the social attributes of the supply chain members also affect manufacturers' carbon abatement strategies and pricing decisions. In this study, we build dynamic evolutionary game models in a low-carbon supply chain to examine the impact of the retailer's social preference on decisions, profits, and supply chain coordination. Moreover, it examines the complex dynamic characteristics of pricing decision and carbon abatement strategy in the supply chain. The main concerns in this study are as follows.

  • (1)

    How do the retailer's social preferences, especially altruistic and reciprocal preferences, affect optimal prices, carbon abatement levels, profits of decision-makers, and supply chain coordination?

  • (2)

    How does the game evolve in the long run? How does the decision-makers formulate rational decisions and how does the retailer's social preference influence the complexity of the system?

  • (3)

    How can an effective contract be designed to reach a self-executing, equilibrium solution and Pareto improvement in decision-making? How does the social preference of the retailer affect the proposed contract coordination?

This paper is organized as follows. A review of relevant literature is provided in Section 2, and in Section 3, model assumptions and notions are described. Section 4 shows a decentralized supply chain. A single period model is first solved, and then a dynamic model is established. In Section 5, a centralized decision of single period and dynamic models are shown. Section 6 proposes a coordination mechanism to achieve Pareto improvement. Section 7 presents conclusions and managerial insights.

Section snippets

Literature review

We review the literature based on three areas related to our study: (1) optimal decision and contract coordination of low-carbon supply chain; (2) impact of social preference on decisions and coordination of low-carbon supply chain, and (3) application of the complex system theory in the supply chain.

Model assumptions and notation

  • (1)

    We assume that the demand function D=ap+σe, which indicates that the manufacturer's investment in emission reduction stimulates consumers' demand for low-carbon products; similar demand functions have been widely used by scholars [13,15,16], where a represents market size; p represents the retail price of a unit of the product; σ represents the low-carbon preference coefficient of consumers; e represents the carbon emission reduction level, and 0<e<1. We assume that w is the WP per unit of the

Single-period model

The manufacturer first decides on WP and carbon abatement level, then the retailer decides on retail price according to the manufacturer's optimal decisions. The profit functions of the retailer, the manufacturer, and the supply chain are as follows:πr=(ap+σe)(pw)πm=(ap+σe)(wc)ke2/2πsc=(ap+σe)(pc)ke2/2

By substituting Eqs. (3), (4), (2), the utility function of the retailer is acquired:ur=ηr((ap+σe)(wc)ke2/2)+(1ηr)(ap+σe)(pw)

The backward induction is used to solve the game model.

Single period model

In a centralized decision, both sides make decisions to maximize the profit of the supply chain. The first-order partial derivatives of the supply chain profit in Eq. (5) with respect to po and eoare obtained: {πscop=a+c+σe2pπscoe=σ(pc)ke

Hessian matrix is obtained by solving the second-order partial derivatives of the supply chain profit: H=(2πscp22πscpe2πscep2πsce2)=(2σσk)

When 2k>σ2, the Hessian matrix is negative-definite, and πsco is concave and exists a unique optimal

Design of supply chain coordination mechanism

Traditional contract fails to consider the rationality and fairness of the incremental distribution of system revenue effectively and overemphasizes players' spontaneous participation in side-payment contracts. To overcome the above problems, He et al. [45] designed a side-payment self-executing contract in a sequential game. However, the contract proposed in the study of He et al. is based on the assumption that players are completely rational. We improve the contract model in the study of He

Conclusions

In this study, we incorporate altruistic and reciprocal preferences of the retailer into a low-carbon supply chain and build dynamic evolutionary game models under decentralized and centralized decisions. In this research, we investigate the complex dynamic characteristics of models and focus on the impact of the retailer's social preference on decisions, profits, supply chain coordination, and complexity of dynamic models. Finally, we put forth a side-payment self-executing contract to realize

Declaration of competing interest

None.

Acknowledgments

This paper is supported by Post-Funded Project for Research on Philosophy and Social Sciences from Ministry of Education of China (Grant No. 19JHG091). National Natural Science Foundation of China (Grant No. 72061003). National Social Science Foundation of China (Grant No. 20&ZD155).

Ruguo Fan holds a Ph. D in Hydraulic structure. He is a Professor from Economics and Management School, Wuhan University. He has authored several articles, books and chapters focused on complex system management, evolutionary game, and supply chain management. In recent years he published papers on refereed academic journals including Journal of Cleaner Production, Energy Policy, Energy, and etc.

Wuhan, 430072, PR China. Email: [email protected]

References (49)

  • Y.J. Zhou et al.

    Co-op advertising and emission reduction cost sharing contracts and coordination in low-carbon supply chain based on fairness concerns

    J Clean Prod

    (2016)
  • Q.Q. Li et al.

    Price and carbon emission reduction decisions and revenue-sharing contract considering fairness concern

    J Clean Prod

    (2018)
  • J. Dejonckheere et al.

    Measuring and avoiding the bullwhip effect: a control theoretic approach

    Eur J Oper Res

    (2003)
  • X.L. Zhan et al.

    Design and coordination for multi-channel recycling of oligopoly under the carbon tax mechanism

    J Clean Prod

    (2019)
  • F. Zhang et al.

    Dynamic pricing strategy and coordination in a dual-channel supply chain considering service value

    Appl Math Model

    (2018)
  • J.H. Ma et al.

    The impact of variable cost on a dynamic Cournot–Stackelberg game with two decision-making stages

    Commun Nonlinear Sci Numer Simulat

    (2018)
  • L. Xie et al.

    Implications of stochastic demand and manufacturers' operational mode on retailer's mixed bundling strategy and its complexity analysis

    Appl Math Model

    (2018)
  • J. Ma et al.

    Research on the complexity of green innovative enterprise in dynamic game model and governmental policy making

    Chaos, Solit Fractals X

    (2019)
  • A. Göksu et al.

    Synchronization and control of chaos in supply chain management

    Comput Ind Eng

    (2015)
  • J.A. Hołyst et al.

    Chaos control in economical model by time-delayed feedback method

    Physica A

    (2000)
  • G. Mahmoud et al.

    Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control, Chaos

    Solitons Fractals

    (2017)
  • The Intergovernmental Panel on Climate Change

    Special Report on global warming of 1.5°C

    (2018)
  • X. Zhao et al.

    Industrial structure distortion and urban ecological efficiency from the perspective of green entrepreneurial ecosystems

    Socio-Econ. Plan. Sci.

    (2020)
  • Z. Sazvar et al.

    An integrated replenishment-recruitment policy in a sustainable retailing system for deteriorating products

    Soc Econ Plann Sci

    (2020)
  • Cited by (25)

    View all citing articles on Scopus

    Ruguo Fan holds a Ph. D in Hydraulic structure. He is a Professor from Economics and Management School, Wuhan University. He has authored several articles, books and chapters focused on complex system management, evolutionary game, and supply chain management. In recent years he published papers on refereed academic journals including Journal of Cleaner Production, Energy Policy, Energy, and etc.

    Wuhan, 430072, PR China. Email: [email protected]

    Jinchai Lin is currently doing her PhD courses on Management Science and Engineering. She is from Economics and Management School, Wuhan University. Her research interests include complex system management, supply chain management.

    Wuhan, 430072, PR China. Email: [email protected]

    Xianchun Tan is a Ph. D in Machinery Manufacturing and Automation. She is a Researcher from institute of science and technology policy and management, Chinese Academy of Sciences. Her research interests include Low-carbon economics, regional low-carbon development strategy and planning. She published several papers on Energy Procedia, Procedia Environmental Sciences, Resources, Conservation and Recycling, Energy Policy, Applied Energy, and etc.

    Beijing, 100190, PR China. Email: [email protected]

    Kaiwei Zhu is currently a PhD candidate at the Institutes of science and technology policy and management, Chinese Academy of Sciences. His research interests include energy system and Low-carbon economics.

    Beijing, 100190, PR China. Email: [email protected]

    View full text