The stochastic ordering of mean-preserving transformations and its applications

Wanshan Zhu and Zhengping Wu

European Journal of Operational Research, 2014, vol. 239, issue 3, 802-809

Abstract: The stochastic variability measures the degree of uncertainty for random demand and/or price in various operations problems. Its ordering property under mean-preserving transformation allows us to study the impact of demand/price uncertainty on the optimal decisions and the associated objective values. Based on Chebyshev’s algebraic inequality, we provide a general framework for stochastic variability ordering under any mean-preserving transformation that can be parameterized by a single scalar, and apply it to a broad class of specific transformations, including the widely used mean-preserving affine transformation, truncation, and capping. The application to mean-preserving affine transformation rectifies an incorrect proof of an important result in the inventory literature, which has gone unnoticed for more than two decades. The application to mean-preserving truncation addresses inventory strategies in decentralized supply chains, and the application to mean-preserving capping sheds light on using option contracts for procurement risk management.

Keywords: Uncertainty modeling; Stochastic variability; Mean-preserving transformation; Inventory management; Procurement risk management (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:239:y:2014:i:3:p:802-809

DOI: 10.1016/j.ejor.2014.06.017

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