The Exploration-Exploitation Tradeoff 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 limitation, referred to as 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? Further, what is the cost imposed by having access only to sales data as opposed to underlying demand samples? We analyze these questions in the context of a well-studied stationary multi-period newsvendor problem in which the decision-maker starts with a prior on the demand distribution. Quite remarkably, we show that, for a broad family of tractable cases, the exploration-exploitation trade-off is negligible for most practical instances; we further articulate the conjunction of conditions that can lead to a non-trivial value. Moreover, we establish that losses stemming from demand censoring are limited, but these are of higher order than those due to ignoring the exploration-exploitation trade-off. In other words, effort to improve information collection about lost sales is more valuable than analytic or computational effort to pin down the optimal policy in the presence of censoring.