Retail inventory management with stock-out based dynamic demand substitution

We consider an inventory management problem of a product category in a retail setting with Poisson arrival processes, stock-out based dynamic demand substitution, and lost sales. The retailer uses a fixed-review period, order-up-to level system to control the inventory levels. We present a computational method to determine the order-up-to levels that maximizes the expected profit with profit margins, inventory holding and substitution costs subject to service-level constraints. Determining expected sales, average inventory levels, and number of substitutions between all products for given demand rates, substitution probabilities, and order-up-to levels is not tractable when there are more than two products. Therefore we present efficient and accurate approximations to approximately compute the same performance measures. The approximate approaches are then used to solve the optimization problem by using a genetic algorithm. In a computational study, we discuss the impact of profit margins, inventory holding and substitution costs, and service level constraints on the order-up-to levels and the expected profits. We show that a retailer can increase its expected profits by incorporating substitution among different products.