An Optimal Control Model of the Low-Carbon Supply Chain: Joint Emission Reduction, Pricing Strategies, and New Coordination Contract Design

This paper is contended with the joint emission reduction and pricing decision problems, as well as coordination contract design issue for a class of low-carbon supply chain system. Here, the evolution of emission reduction level is characterized by a linear differential equation. Also, product demand depends on emission reduction level, promotional effort, and retail price in a separable multiplicative way. By considering an optimal control model of the low-carbon supply chain, differential game theory is used to obtain the optimal joint emission reduction efforts, pricing strategies, and the optimal emission reduction level in different decision systems. Subsequently, attention is focused on the design of new coordination contract with the fixed or varied wholesale price such that, under the dynamic decision perspective, supply chain system can realize the win-win situation of economy and ecology, as well as the profits of individual members are Pareto improvement. Finally, several numerical examples are given to show the validity and feasibility of the presented results.