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Technical Note---Preservation of Supermodularity in Parametric Optimization Problems with Nonlattice Structures

Author

Listed:
  • Xin Chen

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801)

  • Peng Hu

    (School of Management, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Simai He

    (Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong)

Abstract

This paper establishes a new preservation property of supermodularity in a class of two-dimensional parametric optimization problems, where the constraint sets may not be lattices. This property and its extensions unify several results in the literature and provide powerful tools to analyze a variety of operations models including a two-product coordinated pricing and inventory control problem with cross-price effects that we use as an illustrative example.

Suggested Citation

  • Xin Chen & Peng Hu & Simai He, 2013. "Technical Note---Preservation of Supermodularity in Parametric Optimization Problems with Nonlattice Structures," Operations Research, INFORMS, vol. 61(5), pages 1166-1173, October.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:5:p:1166-1173
    DOI: 10.1287/opre.2013.1203
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    References listed on IDEAS

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    Cited by:

    1. Long Gao & Jim (Junmin) Shi & Michael F. Gorman & Ting Luo, 2020. "Business Analytics for Intermodal Capacity Management," Manufacturing & Service Operations Management, INFORMS, vol. 22(2), pages 310-329, March.
    2. Xin Chen & Daniel Zhuoyu Long & Jin Qi, 2021. "Preservation of Supermodularity in Parametric Optimization: Necessary and Sufficient Conditions on Constraint Structures," Operations Research, INFORMS, vol. 69(1), pages 1-12, January.
    3. Xin Chen & Peng Hu & Stephen Shum & Yuhan Zhang, 2016. "Dynamic Stochastic Inventory Management with Reference Price Effects," Operations Research, INFORMS, vol. 64(6), pages 1529-1536, December.
    4. Xin Chen & Menglong Li, 2021. "Discrete Convex Analysis and Its Applications in Operations: A Survey," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1904-1926, June.

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