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Reduction of the bilevel stochastic optimization problem with quantile objective function to a mixed‐integer problem

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  • Stephan Dempe
  • Sergey Ivanov
  • Andrey Naumov

Abstract

The paper is devoted to the stochastic optimistic bilevel optimization problem with quantile criterion in the upper level problem. If the probability distribution is finite, the problem can be transformed into a mixed‐integer nonlinear optimization problem. We formulate assumptions guaranteeing that an optimal solution exists. A production planning problem is used to illustrate usefulness of the model. Copyright © 2017 John Wiley & Sons, Ltd.

Suggested Citation

  • Stephan Dempe & Sergey Ivanov & Andrey Naumov, 2017. "Reduction of the bilevel stochastic optimization problem with quantile objective function to a mixed‐integer problem," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(5), pages 544-554, September.
    • Handle: RePEc:wly:apsmbi:v:33:y:2017:i:5:p:544-554
    DOI: 10.1002/asmb.2254
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    Cited by:

    1. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    2. Natnael Nigussie Goshu & Semu Mitiku Kassa, 2024. "A solution method for stochastic multilevel programming problems. A systematic sampling evolutionary approach," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(1), pages 149-174.
    3. Escudero, Laureano F. & Monge, Juan F. & Rodríguez-Chía, Antonio M., 2020. "On pricing-based equilibrium for network expansion planning. A multi-period bilevel approach under uncertainty," European Journal of Operational Research, Elsevier, vol. 287(1), pages 262-279.

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