Coordination contract in supply chain system with product quality, promotional effort and carbon emission reduction efforts using control theory

The present scholarly work attempts to investigate the optimality of a low-carbon supply chain system. In this chain, the manufacturer and retailer work together under a wholesale price–cost sharing (WP–CS) agreement, where the manufacturer focuses on emission reduction and quality improvement, while the retailer handles promotional efforts. The proposed model is formulated taking variable retailers’ demand rates under the new coordination contract. Here, manufacturer contributes to a fraction of the promotional costs borne by the retailer, while as a return, retailer assists with a part of the quality enhancement and emission reduction costs of manufacturer. Then, to control the efforts of emission reduction and quality improvement over an infinite time horizon, several optimal control problems arise for both centralized and decentralized systems. All these problems are solved by implementing theories of optimal control and the Stackelberg game. The optimality conditions of the proposed system are illustrated numerically for the centralized, decentralized and coordination scenarios. The study finds that coordination contracts give better benefits to both the manufacturer and the retailer than non-coordination strategies.