Elsevier

Computers & Industrial Engineering

Volume 128, February 2019, Pages 807-830
Computers & Industrial Engineering

Modeling carbon regulation policies in inventory decisions of a multi-stage green supply chain: A game theory approach

https://doi.org/10.1016/j.cie.2019.01.009Get rights and content

Highlights

  • Leader-follower game model is used for interaction between a GSC and government.

  • We use carbon cap, carbon tax, carbon trade, and carbon offset as carbon regulations.

  • Multi-stage inventory decisions of coordinated and non-coordinated GSC are studied.

  • The total cost and carbon emission of the GSC are directly affected by carbon regulations.

  • Inventory costs and carbon emission can be decreased by coordinating the GSC.

Abstract

Governments and policymakers around the world put their best efforts to control the pollutions and climate change. Thus, they set various regulations to reduce greenhouse gases and carbon footprints. It is expected that firms should follow these regulations while maintaining their profitability. In this regard, firms can manage their carbon emissions across their supply chain (SC) by inventory management, since operational adjustments may affect the amount of carbon emissions, such as changing the production quantity and the frequency of transportations. This study applies a Stackelberg game between the government and a multi-stage green supply chain (GSC), in which the government’s goal is to maximize social welfare and that of the GSC is to minimize its cost. First, we formulate the inventory cost and carbon emission of a multi-stage GSC under two decision-making structures: non-coordinated and coordinated GSCs. Second, we develop eight bi-level mathematical programming models considering the structure of the GSC and the regulations of the government including carbon cap, carbon tax, carbon trade, and carbon offset. Then two solution approaches will present for solving problems based on the type of the GSC structure. This study examines the effect of coordination and carbon regulations on inventory cost, carbon emission and the objective function of the government.

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.

References (74)

  • H. Ding et al.

    Collaborative mechanism of a sustainable supply chain with environmental constraints and carbon caps

    International Journal of Production Economics

    (2016)
  • C.Y. Dye et al.

    Sustainable trade credit and replenishment decisions with credit-linked demand under carbon emission constraints

    European Journal of Operational Research

    (2015)
  • M. García-Alvarado et al.

    Inventory management under joint product recovery and cap-and-trade constraints

    Journal of Cleaner Production

    (2017)
  • A. Ghosh et al.

    Optimal lot-sizing under strict carbon cap policy considering stochastic demand

    Applied Mathematical Modelling

    (2017)
  • A. Gurtu et al.

    Impact of fuel price and emissions on inventory policies

    Applied Mathematical Modelling

    (2015)
  • A. Hafezalkotob

    Competition of two green and regular supply chains under environmental protection and revenue seeking policies of government

    Computers & Industrial Engineering

    (2015)
  • A. Hafezalkotob

    Competition, cooperation, and coopetition of green supply chains under regulations on energy saving levels

    Transportation Research Part E: Logistics and Transportation Review

    (2017)
  • A. Hafezalkotob

    Modelling intervention policies of government in price-energy saving competition of green supply chains

    Computers & Industrial Engineering

    (2018)
  • Z. Hong et al.

    Optimizing an emission trading scheme for local governments: A Stackelberg game model and hybrid algorithm

    International Journal of Production Economics

    (2017)
  • V. Hovelaque et al.

    The carbon-constrained EOQ model with carbon emission dependent demand

    International Journal of Production Economics

    (2015)
  • G. Hua et al.

    Managing carbon footprints in inventory management

    International Journal of Production Economics

    (2011)
  • Y. Huang et al.

    Coordinating pricing and inventory decisions in a multi-level supply chain: A game-theoretic approach

    Transportation Research Part E: Logistics and Transportation Review

    (2011)
  • Y. Huang et al.

    Green supply chain coordination with greenhouse gases emissions management: A game-theoretic approach

    Journal of Cleaner Production

    (2016)
  • R. Jamshidi et al.

    Multi-objective green supply chain optimization with a new hybrid memetic algorithm using the Taguchi method

    Scientia Iranica

    (2012)
  • M. Khouja

    Optimizing inventory decisions in a multi-stage multi-customer supply chain

    Transportation Research Part E: Logistics and Transportation Review

    (2003)
  • T.C. Kuo et al.

    Do carbon taxes work? Analysis of government policies and enterprise strategies in equilibrium

    Journal of Cleaner Production

    (2016)
  • K.N.F. Leung

    A technical note on “Optimizing inventory decisions in a multi-stage multi-customer supply chain”

    Transportation Research Part E: Logistics and Transportation Review

    (2009)
  • X. Ma et al.

    Optimal procurement decision with a carbon tax for the manufacturing industry

    Computers & Operations Research

    (2018)
  • S.R. Madani et al.

    Sustainable supply chain management with pricing, greening and governmental tariffs determining strategies: A game-theoretic approach

    Computers & Industrial Engineering

    (2017)
  • I. Mallidis et al.

    Design and planning for green global supply chains under periodic review replenishment policies

    Transportation Research Part E: Logistics and Transportation Review

    (2014)
  • Z. Miao et al.

    Remanufacturing with trade-ins under carbon regulations

    Computers & Operations Research

    (2018)
  • M. Nematollahi et al.

    Coordination of social responsibility and order quantity in a two-echelon supply chain: A collaborative decision-making perspective

    International Journal of Production Economics

    (2017)
  • S.H.R. Pasandideh et al.

    Optimization of a multiproduct economic production quantity problem with stochastic constraints using sequential quadratic programming

    Knowledge-Based Systems

    (2015)
  • B. Sarkar et al.

    Effect of variable transportation and carbon emission in a three-echelon supply chain model

    Transportation Research Part E: Logistics and Transportation Review

    (2016)
  • J.B. Sheu

    Bargaining framework for competitive green supply chains under governmental financial intervention

    Transportation Research Part E: Logistics and Transportation Review

    (2011)
  • J.B. Sheu et al.

    Impact of government financial intervention on competition among green supply chains

    International Journal of Production Economics

    (2012)
  • J.B. Sheu et al.

    Alliance or no alliance—Bargaining power in competing reverse supply chains

    European Journal of Operational Research

    (2014)
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