An adaptive, distribution-free algorithm for the newsvendor problem with censored demands, with applications to inventory and distribution

Gregory A. Godfrey, Warren Buckler Powell

Research output: Contribution to journalArticle

100 Scopus citations

Abstract

We consider the problem of optimizing inventories for problems where the demand distribution is unknown, and where it does not necessarily follow a standard form such as the normal. We address problems where the process of deciding the inventory, and then realizing the demand, occurs repeatedly. The only information we use is the amount of inventory left over. Rather than attempting to estimate the demand distribution, we directly estimate the Value function using a technique called the Concave, Adaptive Value Estimation (CAVE) algorithm. CAVE constructs a sequence of concave piecewise linear approximations using sample gradients of the recourse function at different points in the domain. Since it is a sampling-based method, CAVE does not require knowledge of the underlying sample distribution. The result is a nonlinear approximation that is more responsive than traditional linear stochastic quasi-gradient methods and more flexible than analytical techniques that require distribution information. In addition, we demonstrate near-optimal behavior of the CAVE approximation in experiments involving two different types of stochastic programs-the newsvendor stochastic inventory problem and two-stage distribution problems.

Original languageEnglish (US)
Pages (from-to)1101-1112
Number of pages12
JournalManagement Science
Volume47
Issue number8
DOIs
StatePublished - Aug 2001

All Science Journal Classification (ASJC) codes

  • Strategy and Management
  • Management Science and Operations Research

Keywords

  • Censored Demands
  • Dynamic Programming Approximations
  • Newsvendor Problem
  • Stochastic Programming

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