ISyE Seminar - Cong Shi
TITLE: Nonparametric Learning Algorithms for Perishable Inventory Systems
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 but makes the replenishment decision 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, in this paper we focus on finding the best base-stock policy. We first establish an important 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 for this class of problems. The analysis of our algorithm requires a novel method of computing the cycle gradient, and the construction of a bridging problem, which significantly departs from previous studies. We also discuss the strongly convex extension, and conduct numerical experiments to demonstrate the effectiveness of our proposed algorithm. This is a joint work with Huanan Zhang and Xiuli Chao (IOE, UMICH).
Cong Shi is an assistant professor in the Department of Industrial and Operations Engineering at the University of Michigan. He is interested in developing algorithmic approaches to inventory and supply chain management, revenue management, and service operations.
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