Integrating Dynamic Pricing with Inventory Decisions Under Lost Sales

Abstract

Inventory-based pricing under lost sales is an important yet notoriously challenging problem in the operations management literature. The vast existing literature on this problem focuses on identifying optimality conditions for a simple management policy while restricting to special classes of demand functions and to the special case of single-period or long-term stationary settings. In view of the existing developments, it seems unlikely to find general, easy-to-verify conditions for a tractable optimal policy in a possibly nonstationary environment. Instead, we take a different approach to tackle this problem. Specifically, we refine our analysis to a class of intuitively appealing policies, under which the price is decreasing in the postorder inventory level. Using properties of stochastic functions, we show that, under very general conditions on the stochastic demand function, the objective function is concave along such price paths, leading to a simple base stock list price policy. We identify the upper and lower boundaries for a candidate set of decreasing price paths and show that any decreasing path outside of this set is always dominated by some inside the set in terms of profit performance. The boundary policies can be computed efficiently through a single-dimensional search. An extensive numerical analysis suggests that choosing boundary policies yields close-to-optimal profit—in most instances, one of the boundary policies indeed generates the optimal profit; even when they are not, the profit loss is very marginal. This paper was accepted by David Simchi-Levi, operations management.