Data-Driven Approximation Schemes for Joint Pricing and Inventory Control Models

We study the classic multi-period joint pricing and inventory control problem in a data-driven setting.In this problem, a retailer makes periodic decisions on the prices and inventory levels of an item that she wishes to sell. The retailer's objective is to maximize the expected profit over a finite horizon, by matching the inventory level with a random demand that depends on the price in each period. In reality, the demand functions or the distribution of the random noise are usually difficult to know exactly, whereas past demand data are relatively easy to collect.We propose a data-driven approximation algorithm, which uses the past demand data to solve the joint pricing and inventory control problem. We assume the retailer does not know the noise distributions or the true demand functions; instead she only has access to demand hypothesis sets that contain the true demand functions. We prove the algorithm's sample complexity bound, the number of data samples needed to guarantee a near-optimal profit, is O(T⁶ε ⁻² log T), where T is the number of periods and ε is the absolute difference between the expected profit of the data-driven policy and the expected optimal profit. A simulation study suggests that the data-driven algorithm solves the dynamic program effectively