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Stochastic multiobjective problems with complementarity constraints and applications in healthcare management

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  • Lin, Gui-Hua
  • Zhang, Dali
  • Liang, Yan-Chao
Abstract
We consider a class of stochastic multiobjective problems with complementarity constraints (SMOPCCs) in this paper. We derive the first-order optimality conditions including the Clarke/Mordukhovich/strong-type stationarity in the Pareto sense for the SMOPCC. Since these first-order optimality systems involve some unknown index sets, we reformulate them as nonlinear equations with simple constraints. Then, we introduce an asymptotic method to solve these constrained equations. Furthermore, we apply this methodology results to a patient allocation problem in healthcare management.

Suggested Citation

  • Lin, Gui-Hua & Zhang, Dali & Liang, Yan-Chao, 2013. "Stochastic multiobjective problems with complementarity constraints and applications in healthcare management," European Journal of Operational Research, Elsevier, vol. 226(3), pages 461-470.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:3:p:461-470
    DOI: 10.1016/j.ejor.2012.11.005
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    References listed on IDEAS

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    1. Thomas P. Lyon, 1999. "Quality Competition, Insurance, and Consumer Choice in Health Care Markets," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 8(4), pages 546-580, December.
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    3. Eila Kankaanpää & Ismo Linnosmaa & Hannu Valtonen, 2011. "Public health care providers and market competition: the case of Finnish occupational health services," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 12(1), pages 3-16, February.
    4. C. Zhang & X. Chen, 2008. "Stochastic Nonlinear Complementarity Problem and Applications to Traffic Equilibrium under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 277-295, May.
    5. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    6. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    7. I. Nishizaki & M. Sakawa, 1999. "Stackelberg Solutions to Multiobjective Two-Level Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 161-182, October.
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    Cited by:

    1. Peng Zhang & Jin Zhang & Gui-Hua Lin & Xinmin Yang, 2018. "Constraint Qualifications and Proper Pareto Optimality Conditions for Multiobjective Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 763-782, March.
    2. Yong Zhao & Wang Chen & Xinmin Yang, 2024. "Adaptive Sampling Stochastic Multigradient Algorithm for Stochastic Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 215-241, January.
    3. Andreani, R. & Júdice, J.J. & Martínez, J.M. & Martini, T., 2016. "Feasibility problems with complementarity constraints," European Journal of Operational Research, Elsevier, vol. 249(1), pages 41-54.

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