Freshness-keeping Coordination in a Two-echelon Dynamic Supply Chain with Uncertainty: A Stackelberg Game Approach

Freshness index is one of crucial factors that affect demand of perishable products. Since freshness index decays over time with uncertainty, freshness-keeping investment is thus an important decision for supply chains except for selling price. We investigate cooperation problem of dynamic pricing and freshness-keeping investment in a two-echelon perishable supply chain consisting of a distributor and one retailer. The retailer first announces a selling price. Additionally, he also shows a participation rate on freshness-keeping investment that specifies the fraction of the distributor’s freshness-keeping costs that he will support. In response, the distributor determines his optimal wholesale price and freshness-keeping policy. We propose a stochastic model to describe the dynamics of freshness index and formulate the coordination problem as a Stackelberg differential game. Applying stochastic dynamic programming, two types of closed-form equilibrium are analytically obtained. Moreover, we conclude the system condition when the retailer chooses co-op freshness-keeping equilibrium. The results are compared with the corresponding policies in the vertically integrated channel, and we demonstrate that a combination of revenue and freshness-keeping sharing contract can coordinate the chain. The study presents managers with a quantitative instrument to design freshness-keeping coordination.