Modeling carbon regulation policies in inventory decisions of a multi-stage green supply chain: A game theory approach
Introduction
The concurrent development of industries and environment has become a new challenge in the world. The emission of greenhouse gases (GHGs), especially carbon, from industrial activities is one of the main issues for the environment and is the primary cause of global warming (Stern, 2006). In recent years, the regulators and governments have paid significant attention to this problem. Consequently, many policies and regulations have formulated. For instance, the Kyoto Protocol had ratified in an international treaty, and as a result, a cap-and-trade system had been established. According to this system, a firm may sell its excess emission from the assigned amount units through the emission trading market. An emission trading system (ETS) is an incentive policy instrument for managing the emission of GHGs (Du, Ma, Fu, Zhu, & Zhang, 2015). Moreover, policymakers have developed other plans to reduce the emission of carbon. For example, the US EPA established carbon emission allowance for power plants at the national level (Kuo, Hong, & Lin, 2016), and some countries such as Australia implemented the carbon taxation scheme (Zakeri, Dehghanian, Fahimnia, & Sarkis, 2015).
In order to meet the requirements of governments, companies require managing their environmental impacts and wastes among all stages of their supply chain (SC) while maintaining the profitability. In this area, firms need to integrate decisions in their strategic plan and evaluate them on a continuous basis, as various methods have developed in the literature to determine performance rate of organization strategies (see Sobhanallahi et al., 2016a, Sobhanallahi et al., 2016b). However, the companies seem more interested in increasing their profits rather than investing in carbon footprint reduction, and thus reducing the emission of carbon has become a critical challenge for companies and governments (Zhao, Liu, Zhang, & Huang, 2017). The green supply chain management (GSCM) can help companies to save energy, reduce pollution and continuously do their business by considering environmental impact and resource efficiency (Hu & Li, 2011). Therefore, integrating green policies with inventory and production systems is vital for business success (Gharaei et al., 2018, Gharaei et al., 2018). A firm needs to manage its carbon footprint across the SC to meet the governments’ regulations. Various methods can deploy in the GSCM to reduce carbon footprints such as redesigning the product or packaging, using new technologies in manufacturing, and using efficient vehicles for product delivery. Meanwhile, many studies showed that inventory management could be very effective for the reduction of carbon emission (see Bouchery et al., 2012, Chen and Monahan, 2010, Hovelaque and Bironneau, 2015). The inventory policy of a firm determines variables which may affect the emission of carbon such as a number of deliveries, order or production quantities and storage amount. As a result, a firm can reduce its emission by operational adjustment and defining environmental inventory policies.
The carbon regulations and the need for profitability of companies will make the interaction between the government and SCs. Therefore, in this study, we formulate this interaction by game theory approach. The government imposes a regulation to control the emission of carbon and a green supply chain (GSC) requires to minimize its chain-wide costs and comply with the requirements of the government. Hence, there is a trade-off between the total cost of the GSC and the amount of the emission of carbon under governmental regulations.
In the real world, a producer may use several players in its SC to release a product to market. An efficient management should consider the complete end-to-end process such as design, procurement, production planning, distribution, and fulfillment (Gharaei & Pasandideh, 2016). In this regard, we consider a multi-stage GSC that there is a manufacturer in its center and contains a number of suppliers, distributors, and retailers. These members incur ordering, transportation, production, and inventory holding costs. Two different structures are applied to the GSC. In the first structure, the members use a coordination mechanism to manage the flow of the products as a centralized network, which is called the coordinated GSC. In the second structure, the members make their decisions separately, which is called the non-coordinated GSC.
On the other hand, in this study, on the reduction of carbon emission, we examine four different regulations, namely carbon cap, carbon tax, carbon trade, and carbon offset, which the government sets them. In the carbon cap framework, the amount of carbon that emitted by a GSC should be less than a certain cap. In a carbon tax scheme, the government determines tax per unit of carbon emission as a penalty for the GSC. According to the carbon trade or the cap-and-trade policy, each carbon emitter can gain an allowance, that is, if firms produce carbon more than their allowance, they should purchase emission from the market as a penalty, but if firms generate carbon less than their allowance, they can sell their surplus emission and gain revenue. Therefore, it is an incentive system to encourage companies in environmental efforts (Zakeri et al., 2015). The last scheme is the carbon offset or the cap-and-offset, in which specific caps are imposed on an emitter and just excess emission is penalized by purchasing emission credits (Schapiro, 2010). Each of these regulations can influence the optimal solution of the GSC in a different way. We propose different mathematical models to examine how firms managing their inventories under each regulation.
By applying the above-mentioned regulations and the structure of the GSC to the problem, the Stackelberg game has found to be a useful tool for formulating interaction between the government and the GSC. The fundamental research questions are as follows:
- 1.
How can the inventory cost and carbon emission of the multi-stage GSC be formulated?
- 2.
How can different carbon emission regulations be modeled and can influence the optimal strategy between members?
- 3.
What should be the Stackelberg equilibrium for these problems?
This paper is organized as follows. The literature is reviewed in Section 2. The assumptions of the problem are discussed in Section 3. The mathematical models of the problem are presented in Section 4. The solution approach described in Section 5. A numerical example for solving the models, exploring different methods, is presented in Section 6. Finally, the conclusion of the study is presented in Section 7.
Section snippets
Literature review
The literature is categorized into three parts. The first part reviews the researches that consider carbon footprints in inventory management. The second part analyzes the existing literature on games between SCs and governments and the third part presents the research gap and contributions of this study.
Problem description
In this study, we consider a multi-stage GSC that operates under the carbon regulations of the government and delivers one type of product to the market. As shown in Fig. 1, at the first stage of the GSC, there are S suppliers, who supply raw materials and send them to a manufacturer. At the next stage, the manufacturer uses the raw materials at a constant rate to produce the finished products. Then, the finished products are delivered to distribution centers that are denoted by D, who
The problem formulation
In this section, we first formulate the cost and the amount of carbon emission at each stage of the GSC. Then, the objective function of the government will formulate and finally, eight mathematical models will develop.
Solution approach
We confront a hierarchical decision-making problem where a leader first makes his decisions at the top level and then the followers make their decisions according to the decision at the top level. In this section, we investigate the solution for each scenario distinctively. First, the non-coordinated scenarios are investigated and then the coordinated ones. We used different approaches to solve non-coordinated and coordinated scenarios. In this regard, we seek to prove convexity of the
Numerical example
We illustrate the applicability of the mathematical models developed previously through the following numerical example. In practice, the input data for modeling the problem can obtain through several sources. Usually, the values of the parameters of the inventory model can be derived from the firms’ formal financial statements. These statements record the firm’s costs and revenues clearly and are available to the government to be audited. Besides, the carbon emissions of firms are measurable
Conclusion
The purpose of this study was to contribute to the field of inventory management of a multi-stage GSC under carbon emission regulations. This paper used to determine the importance of the inventory decisions for compliance the GSC with carbon regulations and also analyzing the effect of these regulations on the cost and carbon emission. Therefore, a mathematical model is developed for inventory cost and carbon emission of a four-echelon GSC based on the non-coordinated and coordinated
Acknowledgement
This paper has been accomplished on the basis of a Ph.D. dissertation by Kourosh Halat supervised by Prof. Ashkan Hafezalkotob at Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran. The authors would like to appreciate the reviewers and editor for their insightful comments.
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