Inventory, Discounts, and the Timing Effect

We introduce and analyze a model that explicitly considers the timing effect of intertemporal pricing—the concept, found in practice, that demand during a sale is increasing in the time since the last sale. We present structural results that characterize the interaction between the decision to hold a sale and the inventory-ordering decision. We show that the 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 the cost of holding inventory and delaying sales. In our computational analysis, we find that compared to a fixed-price policy, we see an average gain in profit of almost 5% from optimally varying promotion and inventory decisions accounting for intertemporal demand, and we find that this potential profit gain increases as demand variability decreases. We also develop a heuristic based on deterministic pricing and find that it performs well relative to the optimal policy.