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A distribution-free risk-reward newsvendor model: Extending Scarf's min-max order formula

Donglei Du(ddu***at***unb.ca)
Qiaoming Han(qmhan***at***nju.edu.cn)
Luis Zuluaga(lzuluaga***at***unb.ca)

Abstract: Scarf's min-max order formula for the distribution-free risk-neutral newsvendor problem is a classical result in the field of inventory management. The min-max order formula provides, in closed-form, the order quantity that maximizes the worst-case expected profit associated with the demand of a single product when only the mean and variance of the product's demand distribution, rather than the full distribution itself, is assumed to be known. It has been a long-standing question whether a similar closed-form order formula exists for the distribution-free risk-reward newsvendor problem; that is, for the order quantity that maximizes the worst-case risk-reward associated with the demand of a single product when only the mean and variance of the product's demand distribution is assumed to be known. The main contribution of this work is to extend Scarf's closed-form order formula to one of the most important risk-reward criteria, namely when the reward is defined by the expected profit, and the risk by the profit's standard deviation. Furthermore, we provide managerial insights associated with this result.

Keywords: Distribution-free, newsvendor, risk-averse, mean-standard deviation, closed-form, min-max rule

Category 1: Applications -- OR and Management Sciences (Supply Chain Management )

Category 2: Robust Optimization

Citation: Working Paper Series #2012-001, University of New Brunswick, Canada

Download: [Postscript][PDF]

Entry Submitted: 03/31/2012
Entry Accepted: 03/31/2012
Entry Last Modified: 03/31/2012

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