A two-item inventory-dependent demand model with return and all-units discount

Abstract

In this paper, we propose a two-item inventory model with deterministic demands, return and all-units discount. We consider a retailer who sells two products, where demands of these two products are deterministic and have inventory-dependent demand feature in the sense that demands are related to the number of inventory available at certain time. In developing our model, we assume that supplier offers quantity discount to the retailer, these two products have different constant deterioration rates and retailer can return some of unsold products at some costs near the end of the period. The objective of the model is to find the optimal return time and the optimal ordering quantity that minimizes the total cost for the retailer. In dealing with this model, we consider two replenishment policies, namely the individual and joint replenishment policy. Some numerical examples are given to illustrate our model and to compare the individual and joint replenishment policies by considering quantity discount or not in terms of their total costs. We found that joint replenishment policy by considering quantity discount mostly gives the minimum total cost.