A Three-Layer Supply Chain EPQ Model for Price- and Stock-Dependent Stochastic Demand with Imperfect Item Under Rework

In this paper, we have developed an integrated supplier-manufacturer-retailer, joint economic lot-sizing model for the items with stochastic demand and imperfect quality. The supplier produces the item (raw material) up to certain time, which is a decision variable, and sends it to the manufacturer. Now, the manufacturer produces the item in small cycles and the production process of manufacturer is imperfect which produces certain number of defective items. A 100 % screening process for detecting the imperfect quality items is conducted, and at the end of each cycle, the imperfect items are accumulated and are reworked by the manufacturer. Thus, ultimately the retailer receives the perfect quality item. We consider that the delivery quantity to the retailer depends on the price and stock-dependent stochastic demand of the retailer. The model considers the impact of business strategies such as optimal time, optimal ordering size of raw material, production rate, etc. in different sectors on collaborating marketing system. An analytical method is applied to optimize the production time and production rate to obtain minimum total cost. Finally, numerical results, which have several interesting managerial insights and implications, and the sensitivity analysis are presented and discussed for illustrative purposes.