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Technical Note—Perishable Inventory Systems: Convexity Results for Base-Stock Policies and Learning Algorithms Under Censored Demand

Huanan Zhang¹; Xiuli Chao²; Cong Shi²

¹ Harold and Inge Marcus Department of Industrial and Manufacturing Engineering, Pennsylvania State University, University Park, Pennsylvania 16802 · ² Industrial and Operations Engineering, University of Michigan, Michigan 48105

We develop the first nonparametric learning algorithm for periodic-review perishable inventory systems. In contrast to the classical perishable inventory literature, we assume that the firm does not know the demand distribution a priori and makes replenishment decisions in each period based only on the past sales (censored demand) data. It is well known that even with complete information about the demand distribution a priori, the optimal policy for this problem does not possess a simple structure. Motivated by the studies in the literature showing that base-stock policies perform near optimal in these systems, we focus on finding the best base-stock policy. We first establish a convexity result, showing that the total holding, lost sales and outdating cost is convex in the base-stock level. Then, we develop a nonparametric learning algorithm that generates a sequence of order-up-to levels whose running average cost converges to the cost of the optimal base-stock policy. We establish a square-root convergence rate of the proposed algorithm, which is the best possible. Our algorithm and analyses require a novel method for computing a valid cycle subgradient and the construction of a bridging problem, which significantly departs from previous studies. The e-companion is available at https://doi.org/10.1287/opre.2018.1724

DOI

10.1287/opre.2018.1724

Volume

66 (5)

Pages

1276-1286

Language

en

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