闭环供应链竞争下政府补贴效率研究

The Efficiency of Government Subsidy for Closed-Loop Supply Chains

针对产品需求和废旧产品供给为确定性函数的两条可替代产品闭环供应链,假定生产商委托零售商回收废旧产品以进行再制造活动,利用博弈理论构建了两条分散式闭环供应链的竞争决策模型、政府补贴下政府、制造商和零售商的三阶段博弈模型、以及基于经济-环境效益最大化的回收模型,给出了实现经济-环境效益最大化的政府补贴策略。研究表明:政府回收再制造补贴能促使企业提高回收价,提升废旧产品的回收量和回收率、以及闭环供应链和各方的目标收益;基于经济-环境效益最大化制定的补贴政策比三阶段博弈情况更有效,而三阶段博弈情况下政府的补贴政策优于无政府补贴情况,前者比后者更能促进废旧产品的回收,使回收价、回收量和回收率得以提高。最后的算例结果表明了模型的合理性和补贴政策的有效性。敏感性分析表明:每种模式下废旧产品的回收价、回收量和回收率、以及供应链利润均随回收价格弹性系数g的增加而增加、随交叉价格弹性系数h的增加而减少;两种补贴政策下政府的单位回收再制造补贴随价格弹性系数g或单位废旧产品回收的环境效益n的增加而增加、随交叉价格弹性系数h或单位回收收益v的增加而降低。

The recovery and remanufacturing of waste products can help conserve resource, protect environment, and sustain the development of environment and society. Increasing number of enterprises are directing their attention to the operational mode of closed- loop supply chain （CLSC） based on the recovery and remanufacturing of waste product. A CLSC consists of one manufacturer and one retailer working together in the recycling and remanufacturing of waste product. Governments often use law or subsidy to encourage enterprises to make efforts in the recovery and remanufacturing of waste. The purpose of this study is to investigate three CLSC models ： （1） the competition model of two decentralized CLSCs without government subsidy, （2） a three-phase game among government, manufacturers and retailers when government offers subsidy for waste product recovery and remanufacturing, and （3） recovery model based on the maximum benefit of economy and environment. A government subsidy strategy is proposed after understanding the effectiveness of using these three CLSC models to maximize the profit of economy and environment. Firstly, a recovery model based on the maximum profit of economy and environment is set up. The optimal recovery price and recovery quantity are obtained. The model shows that the optimal recovery price ensures fixed-yield ratio based on economy and environment benefit of unit waste product. Secondly, three-phase game model is set up by using the game theory to characterize the competition of government, manufacturers and retailers when each agent tries to maximize their profit. This model is a MPEC （ Mathematical Program with Equilibrium Constrains） model where an EPEC （ Equilibrium Problem with Equilibrium Constrains） model is embedded. The first layer of this model is to solve the object-maximization problem of government. The second layer is the competition equilibrium between two manufacturers and the third layer is the competition equilibrium between two retailers. It shows that two retailers will take cost-plus pricing strategy to determine optimal retail price based on their own cost and take fixed-profit ratio strategy to determine optimal recovery price based on their subsidy yield. Two manufacturers will use the cost-plus pricing strategy to determine optimal wholesale price based on their own cost and use the fixed-yield ratio strategy to determine optimal recovery subsidy based on their recovery yield. Thirdly, the competition equilibrium model of two decentralized CLSCs is set up when government doesn＇t give subsidy to manufacturers for recovery and remanufacturing. The comparison of these three decision models shows that government subsidy for waste product recovery and remanufacturing encourages enterprisers to increase recovery price and leads to higher recovery quantity and recovery rate of waste product. More supply chain benefits of each agent can be obtained. The subsidy policy based on the maximum benefit of economy and environment is more efficient than that based on the three-phase game. However, the latter is more efficient than the situation of having no government subsidy. This study further analyzes the problem of government designing contract that uses the whole system to inspire enterprisers to take recovery and remanufacturing. A government subsidy contract for recovery and remanufacturing is proposed to encourage manufacturers and retailers to make recovery decisions to maximize recovery benefit of economy and environment. Finally, a numerical example is presented to improve the accuracy of these three models and the validity of the government subsidy contracts. Sensitive analysis shows that under each model recovery price, recovery quantity, and recovery rate of waste products and benefits of two CLSCs will increase when recovery price elastic coefficient g increases, or when cross-price elastic coefficient h decreases. The unit subsidy of both subsidy policies for waste product recovery and remanufacturing will increase when recovery price elasticity coefficient g or environment benefit of unit waste products n increases, or when cross-price elastic coefficient h or economy benefit of unit waste products v decreases. In summary, CLSC vs. CLSC competition and the efficiency of government subsidy under CLSC vs. CLSC competition are important issues. This paper makes three contributions. Firstly, we set up three models to understand different competition models of two decentralized CLSCs with or without government subsidy. A government subsidy contract is presented to realize the maximum benefit of economy and environment under CLSC vs. CLSC competition. Finally, a sensitive analysis of model parameters is conducted to understand the dynamics of CLSC competition. Many important implications are drawn from the findings of this study, such as the efficiency problems of government subsidy under stochastic demand, and the responsibility of the third party for the recovery of waste product and multiple CLSCs competition. Future research related to CLSC can focus on customer behavior, carbon emission restrict, and service level of waste product recovery.