Elsevier

Journal of Cleaner Production

Volume 151, 10 May 2017, Pages 286-302
Journal of Cleaner Production

Pricing decision of a two-echelon supply chain with one supplier and two retailers under a carbon cap regulation

https://doi.org/10.1016/j.jclepro.2017.03.011Get rights and content

Abstract

This study considers a two-echelon make-to-order supply chain consisting of one supplier and two retailers under carbon cap regulation. We analyze the pricing decision process in a decentralized system from a game theoretical perspective and find the optimal pricing strategy for the wholesale prices of the supplier and the retail prices of two retailers. Our framework involves various operational strategies, including consistent and inconsistent wholesale prices for the supplier and consistent and inconsistent retail prices for the two retailers. We analyze and compare the performance of strategy combinations and find that the combination of a consistent wholesale price and an inconsistent retail price with a transfer payment mechanism is the best pricing decision to achieve Pareto improvement for supply chain members. We also provide the appropriate range of a carbon cap for the policy maker to effectively reduce carbon emissions. Finally, several numerical examples illustrate the impacts of a carbon cap on profits and carbon emissions in different pricing models.

Introduction

Over the past few decades, the greenhouse effect and global warming have attracted increasingly wide attention. In 1995, the Intergovernmental Panel on Climate Change(IPCC) pointed out that the rise in the earth surface temperature was caused mainly by the increase of greenhouse gas(GHG) concentrations in the atmosphere(IPCC, 1995). In other words, it is generally believed that one of the main driving forces of global warming is the increase of GHG (e.g., carbon emissions). Supply chain activities are major source of GHG emissions such as carbon dioxide. Today, it is recognized that only by sharply reducing carbon emissions will the greenhouse effect be gradually slowed down (Houghton et al., 1996). With a low carbon economy becoming a new trend worldwide, consumers are more sensitive to low carbon products due to the increasing awareness of environmental problems. Therefore, supply chain operations optimization considering the carbon footprint is a significant research field.

Global warming, the popularity of a low-carbon economy in international society, and increased public awareness about environmental issues are encouraging regions and countries to reduce carbon emissions. The IPCC proposed that we should achieve at least a 50% reduction in global carbon emissions by 2050 (Parry et al., 2007). In 1997, 37 European Union members and industrialized countries signed the Kyoto Protocol, which defined the carbon emission reduction obligations of developed countries and required many of the gathered countries to focus on GHG emission abatement. As of May 2008, 181 countries have accepted the protocol. On April 22, 2016, the Paris Agreement, which made arrangements for global action on climate after 2020, was signed by 175 countries on the first day of open signing. The agreement promised to contain the global temperature increase in the range of 2 °C. Ban Ki-moon called on governments and all sectors of society to fully implement the Paris Agreement and take immediate actions to reduce GHG emissions. For the purpose of environmental protection, countries have increasingly begun to focus on the relationship between carbon emissions and the economic, and these countries have reached an agreement to reduce carbon emissions by adopting carbon emission regulations, which aim to achieve at least a 50% reduction by 2050 (the International Energy Agency, 2008). Carbon emission regulations, such as carbon tax, carbon cap, cap and trade, were presented by the Congressional Budget Office of the Congress of the United States in a comprehensive study have been gradually applied all over the world.

In addition, many scholars have focused their research on the relationship between government regulation and corporate behavior. Their research could provide regulation implications and significant managerial inspirations that would be beneficial to government agencies and enterprises. In particular, government agencies could meet their environmental targets without influencing the sustainable development of the economy by formulating effective carbon emission reduction regulations on the basis of this research, and firms could improve their financial performances by making appropriate operational decisions that are supported by this research. That is, an enterprise could adjust its production, inventory, and transportation operations within the constraints of carbon emission regulations. In recent years, the research about cap-and-trade and carbon tax regulations has received widespread attention both in empirical and theoretical studies. Unlike many economists, who prefer tax or cap-and-trade regulations, environmental groups favor carbon cap regulations, and they regard the former regulations as “licenses to pollute.” For instance, the US Environmental Protection Agency used a cap regulation between the years 1970 and 1990 to control SO2 emissions (Popp, 2001).

Under a carbon cap regulation, which is a rigid command-and-control regulation, the carbon emissions of a firm cannot exceed an upper bound, which is the carbon cap. The government agency's and/or the firm's goals can both determine the cap, which reflects either government regulations imposed on the firm or a firm's voluntary effort to reduce carbon emissions. In the case of a strict carbon cap model, a firm will suffer from an infinitely large penalty once it exceeds the cap. In general, the cap can be an upper bound of total emissions in its simplest form, and it is always defined by the average emissions over a time unit, such as a year or month. For instance, Technische Anleitung Luft recorded several caps implemented in Germany (Letmathe and Balakrishnan, 2005). The carbon cap will reshape production and sale decisions when the cap is smaller than a certain value; then, the firm should adjust its mode choice. An even smaller cap would result in a dramatic change in operation decisions, whereas a larger cap is the same as if no regulation were implemented. Thus, a carbon cap is necessary to achieve carbon reduction when neither a high carbon price nor a high tax rate is possible. Therefore, assigning a mandatory carbon cap to firms is popular way to control carbon emissions. In practice, two big challenges in the implementation of a strict carbon cap regulation need to be considered carefully. How can an appropriate emissions cap for firms be determined? How should the firms adjust their operation decisions within a strict carbon cap? We will study and solve the above problems in the following analysis.

In this study, we consider a make-to-order supply chain with one supplier and two retailers under a carbon cap regulation. Assuming that the two retailers are totally separated and independent, we first analyze the optimal pricing decisions for the decentralized and centralized models. Then, we compare the profits of the supply chain members. This study contributes to the literature in several aspects. First, it formulates the different pricing models under a carbon cap regulation based on the different ways of setting the supplier's wholesale prices and the retailers' retail prices. Second, it analyzes mathematically how a carbon cap regulation affects the pricing decisions in each model from the perspective of game theory and gives the optimal pricing decision strategies of the supply chain members. Third, it compares the performances of different pricing models and illustrates which model is more preferred with the constraint of a carbon cap regulation.

The remainder of this paper is organized as follows. Section 2 summarizes the relevant literature. Section 3 describes the problem in detail and presents some notations. Section 4 solves the optimal pricing of different models and obtains the corresponding optimal profits in a decentralized system. Section 5 provides a mechanism to coordinate the decentralized systems. Section 6 presents a numerical example to illustrate the previous results. The conclusion and further research are presented in Section 7.

Section snippets

Literature review

Our study is related to three streams of research. The first stream studies firms' operational decisions in a one-supplier, multiple-retailer supply chain; the second stream investigates firms' operational decisions under carbon emission regulations; and the third stream researches firms’ operational decisions in a supply chain under carbon emission regulations, especially carbon cap regulations.

Model description and notations

This study considers the pricing decision process of a two-echelon, make-to-order supply chain consisting of one supplier and two retailers under a carbon cap regulation. The supplier, which is constrained by the carbon cap regulation as the principal source of carbon emissions, organizes the production of a certain type of product according to retailers’ orders and then sells the products to customers through two retailers at the prices p1 and p2 simultaneously. The goal of the supplier is to

Model analysis of the decentralized system

In this section, we model the decision process of the decentralized system as a Stackelberg(leader-follower) game in which the supplier is the leader. In this system, the decision process is that the supplier first determines the wholesale prices w1 and w2, and, then, the two retailers determine their own retail prices p1 and p2 with full consideration of their own wholesale prices.

Under this system, the profit functions of the two retailers and the supplier can be formulated byΠr,1,1(p1)=(p1w1

Centralized system

In the centralized system, the supplier and two retailers determine the retail prices together. The total profit of the system is given byΠc(p1,p2)=(p1cs)·D1(p1,p2)+(p2cs)·D2(p1,p2)=(p1cs)·(a1bp1+cp2)+(p2cs)·(a2bp2+cp1)

The total carbon emissions in the centralized system, that is, the carbon emissions of the supplier, is(D1+D2)·e=(a1+a2bp1bp2+cp1+cp2)·e,

For the centralized system, we have the following conclusion.

Lemma 3

The profit of the system is jointly concave in p1 and p2. The

Numerical example

In this section, we conduct the numerical study, which is composed of two parts. In the first part, we verify the theoretical results that are given above. In the second part, we analyze the effects of the carbon coefficient on the optimal solutions and address the managerial insights.

Conclusions

In this analysis, a make-to-order supply chain with one supplier and two competing retailers is studied under a carbon cap regulation. We first formulated different pricing models and analyzed the respective pricing processes under a carbon cap regulation in a decentralized system using the supplier Stackelberg game, and we found that (1) when a carbon cap restricts carbon emissions, there exists a valid range of carbon caps, so a policy maker can formulate an appropriate carbon cap. Then, we

Acknowledgments

The authors would like to thank the editor-in-chief, the subject editor and the two anonymous referees for their valuable comments and suggestions that significantly improved the quality of the paper.

The work reported in this paper was supported by the National Natural Science Foundation of China (No. 71332003); the Humanity and Social Science Youth Foundation of Ministry of Education of China [grant number 14YJCZH17]; and Shandong Provincial Natural Science Foundation of China [grant number

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