Inventory control of fresh food supply chain and its differential game considering fresh-keeping effort

Due to the perishable, fresh, deteriorating characteristics of fresh food, the inventory control of the fresh food supply chain is a strain for management. The fundamental metamorphic inventory model was improved, considering the preservation efforts of supplier and retailer, and prices and freshness factors affecting time-varying demand rate was built. Revenue sharing parameters and cost sharing parameters were considered, and the variational method was used to set up differential game models including jointly managed inventory (JMI) and decentralized inventory management (DIM) under the background of continuous time. Nash equilibrium’s existence of constraint equations was proved and corresponding optimal inventory differential strategies were proposed. Finally, by numerical simulation, preservation efforts, inventory changes and total supply chain profits were explored under the two models and corresponding suggestions were given.