Pricing and Inventory Control in a Supply Chain of Deteriorating Items: A Non-cooperative Strategy with Probabilistic Parameters

This paper determines the pricing, the replenishment cycle, and the number of shipments in a manufacturer–retailer supply chain of the deteriorating items. Generally speaking, deterioration items means products that their value is reduced over time. The relationship between the manufacturer and the retailer is analyzed by non-cooperative Stackelberg game, where the manufacturer is assumed to be the leader and retailer is the follower. It is assumed that inventory policy is non-delayed equal size shipments in which the manufacturer delivers shipments to the retailer in the production period. Also, the deterioration and demand rates are determined by probabilistic distribution function. First, an inventory control model for both the retailer and the manufacturer is formulated. Then, the conditions to obtain the optimal solution under non-cooperative Stackelberg equilibrium are derived. Next, a numerical example is extended by performing a sensitivity analysis and simulation of the model parameters and managerial insights are discussed. The main outcome of this paper is the optimal selling price and inventory control variables. Also, the results indicate that the conditions of inventory system determine the act of the manufacturer as a leader whether use its power against retailer as a follower or have a cooperation with the retailer. Moreover, the retailer’s total profit is more sensitive to the ordering costs than the other parameters and the decision variables of manufacturer significantly depend upon the manufacturer’s holding cost. In addition, the simulation results show the validation of the proposed model.