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Regret in the Newsvendor Model with Partial Information

Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Anderson School of Management, University of California at Los Angeles, Los Angeles, California 90095
georgiap{at}mit.edu
groels{at}anderson.ucla.edu

Traditional stochastic inventory models assume full knowledge of the demand probability distribution. However, in practice, it is often difficult to completely characterize the demand distribution, especially in fast-changing markets. In this paper, we study the newsvendor problem with partial information about the demand distribution (e.g., mean, variance, symmetry, unimodality). In particular, we derive the order quantities that minimize the newsvendor's maximum regret of not acting optimally. Most of our solutions are tractable, which makes them attractive for practical application. Our analysis also generates insights into the choice of the demand distribution as an input to the newsvendor model. In particular, the distributions that maximize the entropy perform well under the regret criterion. Our approach can be extended to a variety of problems that require a robust but not conservative solution.

Subject classifications: distribution-free inventory policy; newsvendor model; robust optimization; entropy; value of information; semi-infinite linear optimization.
History: Received November 2005; revision received May 2007; accepted August 2007.