A Continuous Review Policy for Two Complementary Products with Interrelated Demand

We consider a retailer selling two complementary products. The products are demanded individually or jointly. The retailer uses a continuous review (Q,r) policy to manage the inventory of each product. The customers arrive according to a Poisson process and unmet demands are lost. We aim to calculate the optimal policy parameters which maximize the expected profit rate. A shortage of one product might result in a lost sale of its complementary product, even if this product is in stock. This fact complicates the analysis. We rely on a simulation-based optimization approach to derive the optimal parameters of the (Q,r) policy for each product. Our results reveal that the maximum profit rate is attained when all customers demand both products, i.e., the bundle of complementary products. In addition, we observe that when the demand rate is low, the interaction between product demands has significant impact on the expected profit rate, and this effect becomes even more prominent when the unit lost sale costs are low and the unit holding costs are high. We derive the analytical properties of a single-product inventory system based on which an efficient approximation algorithm is developed