Combined Pricing and Inventory Control Under Uncertainty

TLDR

Demand in each period is independent but depends on price through stochastic demand functions. The paper jointly optimizes pricing and inventory replenishment under demand uncertainty to maximize expected discounted or average profit across finite and infinite horizons, allowing arbitrary price adjustments or only decreases. The authors study a single‑item periodic‑review model with price‑dependent stochastic demand, dynamic pricing based on system state, optional replenishment at period starts, full backlogging, and compute optimal policies via efficient value iteration. Numerical experiments illustrate qualitative features of the optimal strategies and their profit outcomes.

Abstract

This paper addresses the simultaneous determination of pricing and inventory replenishment strategies in the face of demand uncertainty. More specifically, we analyze the following single item, periodic review model. Demands in consecutive periods are independent, but their distributions depend on the item's price in accordance with general stochastic demand functions. The price charged in any given period can be specified dynamically as a function of the state of the system. A replenishment order may be placed at the beginning of some or all of the periods. Stockouts are fully backlogged. We address both finite and infinite horizon models, with the objective of maximizing total expected discounted profit or its time average value, assuming that prices can either be adjusted arbitrarily (upward or downward) or that they can only be decreased. We characterize the structure of an optimal combined pricing and inventory strategy for all of the above types of models. We also develop an efficient value iteration method to compute these optimal strategies. Finally, we report on an extensive numerical study that characterizes various qualitative properties of the optimal strategies and corresponding optimal profit values.