Optimal ordering quantities for substitutable products with stock-dependent demand

Many retailers are trying to increase their product offers to compete for market share. However, the offer of similar products implies that these products may be substitutable to the consumer. In this paper, we study an inventory control problem in which demand is satisfied by using two mutually substitutable products. Since the products are substitutable, in case of a stock-out for one of them, a known fraction of its demand can be satisfied by using the stock of the other product. The demand for each product also depends on the inventory levels of both of the products at a certain time. The orders for both products are placed jointly. Our aim is the determination of the order quantity for each product that maximizes the joint profit function. Some numerical results, which have several interesting managerial insights and implications, are presented and discussed.