The stochastic ordering of mean-preserving transformations and its applications

Wanshan Zhu, Zhengping Wu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)802-809
Number of pages8
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - Dec 16 2014


  • Inventory management
  • Mean-preserving transformation
  • Procurement risk management
  • Stochastic variability
  • Uncertainty modeling

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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