Inventory, Periodic Discounts, and the Timing Effect

We consider the joint pricing and inventory control problem for a single product whose demand distribution in each period is determined both by whether or not a sale price is offered in the current period, and the number of periods since the last time the sale price was offered. We show that optimal inventory ordering policy is a state dependent base stock policy; however, the optimal pricing policy can be quite complicated due to both the value and cost of holding inventory and delaying sales. We conduct a computational study to explore the effect of various cost and demand parameters on optimal pricing, ordering, and markdown decisions, propose a simple threshold type policy suggested by relaxation of the model to a make-to-order system, and computationally evaluate the performance of this heuristic.