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Regret in the Newsvendor Model with Demand and Yield Randomness

Zhi Chen (zhi.chen***at***cityu.edu.hk)
Weijun Xie (wxie***at***vt.edu)

Abstract: This paper studies the fundamental stochastic newsvendor model that aims at finding an optimal order quantity to maximize the expected profit while considering the randomness of both demand and yield. It is usually difficult in practice to describe precisely the joint demand and yield distribution, although partial statistical information and empirical data about this ambiguous distribution are often accessible. We combat the issue of distributional ambiguity by taking a data-driven distributionally robust optimization approach to hedge against all distributions that are sufficiently close to a uniform and discrete distribution of empirical data, where closeness is measured by the type-infinity Wasserstein distance. We adopt the minimax regret decision criterion to assess the optimal order quantity that minimizes the worst-case regret across all hedged distributions. Then we present several properties about the minimax regret model, including optimality condition, regret bound, and worst-case distribution, and we show that the optimal order quantity can be determined via an efficient bisection search. We extend the analysis to the Hurwicz criterion model, which generalizes the popular albeit pessimistic maximin model (maximizing the worst-case expected profit) and its (less noticeable) more optimistic counterpart--the maximax model (maximizing the best-case expected profit). Finally, we present numerical comparisons of our data-driven minimax regret model with data-driven models based on maximax and maximin decision criteria as well as with a minimax regret model based on partial statistical information.

Keywords: demand randomness, yield randomness, minimax regret, Hurwicz criterion, type-infinity Wasserstein distance, data-driven decision making under uncertainty

Category 1: Robust Optimization

Citation: City University of Hong Kong, working paper.

Download: [PDF]

Entry Submitted: 04/17/2020
Entry Accepted: 04/17/2020
Entry Last Modified: 04/19/2020

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