A Simple Heuristic for Joint Inventory and Pricing Problems with Lead Time

We study a joint inventory and pricing problem in a single-stage system with a positive lead time. We consider both additive and multiplicative demand forms. This problem is, in general, intractable due to its computational complexity. We develop a simple heuristic that resolves this issue. The heuristic involves a myopic pricing policy that generates each period’s price as a function of the initial inventory level and a base-stock policy for inventory replenishment. In each period, the firm monitors its so-called price-deflated inventory position and places an order to reach a target base-stock level. The price-deflated inventory position weights the on-hand and pipeline inventory according to a factor that reflects the sensitivity of price to the net inventory level. To assess the effectiveness of our heuristic, we construct an upper bound to the exact system. The upper bound is based on an information-relaxation approach and involves a penalty function derived from our heuristic. We provide a simple procedure to solve the upper bound problem. A numerical study suggests that the proposed heuristic is near-optimal. The heuristic can also be applied to systems with zero lead time, leading to a solution that closely resembles the exact optimal policy derived in the literature. The heuristic enables us to explore the use of price as a lever to balance supply and demand. Our findings indicate that a responsive strategy (that effectively reduces the replenishment lead time) leads to a more stable pricing policy.