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Distributionally robust maximum probability shortest path problem

Author

Listed:
  • Rashed Khanjani-Shiraz

    (University of Tabriz)

  • Ali Babapour-Azar

    (University of Tabriz)

  • Zohreh Hosseini-Noudeh

    (University of Tabriz)

  • Panos M. Pardalos

    (University of Florida)

Abstract

In this study, we discuss and develop a distributionally robust joint chance-constrained optimization model and apply it for the shortest path problem under resource uncertainty. In sch a case, robust chance constraints are approximated by constraints that can be reformulated using convex programming. Since the issue we are discussing here is of the multi-resource type, the resource related to cost is deterministic; however, we consider a robust set for other resources where covariance and mean are known. Thus, the chance-constrained problem can be expressed in terms of a cone constraint. In addition, since our problem is joint chance-constrained optimization, we can use Bonferroni approximation to divide the problem into L separate problems in order to build convex approximations of distributionally robust joint chance constraints. Finally, numerical results are presented to illustrate the rigidity of the bounds and the value of the distributionally robust approach.

Suggested Citation

  • Rashed Khanjani-Shiraz & Ali Babapour-Azar & Zohreh Hosseini-Noudeh & Panos M. Pardalos, 2022. "Distributionally robust maximum probability shortest path problem," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 140-167, January.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:1:d:10.1007_s10878-021-00747-9
    DOI: 10.1007/s10878-021-00747-9
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    References listed on IDEAS

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    Cited by:

    1. Belleh Fontem, 2023. "Robust Chance-Constrained Geometric Programming with Application to Demand Risk Mitigation," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 765-797, May.
    2. Hosseini-Nodeh, Zohreh & Khanjani-Shiraz, Rashed & Pardalos, Panos M., 2023. "Portfolio optimization using robust mean absolute deviation model: Wasserstein metric approach," Finance Research Letters, Elsevier, vol. 54(C).

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