Distribution-free Inventory Policy ; Newsvendor Model ; Robust Optimization ; Entropy ; Value of Information ; Semi-infinite Linear Optimization
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, the authors 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 their solutions are tractable, which makes them attractive for practical application. Their 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. This approach can be extended to a variety of problems that require a robust but not conservative solution.