The Exploration-Exploitation Trade-off in the Newsvendor Problem

Abstract

When an inventory manager attempts to construct probabilistic models of demand based on past data, demand samples are almost never available: only sales data can be used. This demand censoring introduces an exploration-exploitation trade-off as the ordering decisions impact the information collected. Much of the literature has sought to understand how operational decisions should be modified to incorporate this trade-off. We ask an even more basic question: When does the exploration-exploitation trade-off matter? To what extent should one deviate from a myopic policy that takes the optimal decision for the current period without consideration for future periods? We analyze these questions in the context of a well-studied stationary multiperiod newsvendor problem in which the decision maker starts with a prior on parameters characterizing the demand distribution. We show that, under very general conditions in both perishable and nonperishable settings, the myopic policy will almost surely learn the optimal decision one would have taken with knowledge of the unknown parameters. Furthermore, in the perishable setting, we analyze finite time performance for a broad family of tractable cases. Through a combination of analytical parametric bounds and exhaustive exact analysis, we show that the myopic optimality gap is negligible for many practical instances. Funding: The third author was partially supported by the National Science Foundation [Grant CMMI-1235023]. Supplemental Material: The online supplement is available at https://doi.org/10.1287/stsy.2022.0093 .