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Reduction of nonanticipativity constraints in multistage stochastic programming problems with endogenous and exogenous uncertainty

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  • F. Hooshmand

    (Amirkabir University of Technology)

  • S. A. MirHassani

    (Amirkabir University of Technology)

Abstract

Multistage stochastic programming (SP) with both endogenous and exogenous uncertainties is a novel problem in which some uncertain parameters are decision-dependent and others are independent of decisions. The main difficulty of this problem is that nonanticipativity constraints (NACs) make up a significantly large constraint set, growing very fast with the number of scenarios and leading to an intractable model. Usually, a lot of these constraints are redundant and hence, identification and elimination of redundant NACs can cause a significant reduction in the problem size. Recently, a polynomial time algorithm has been proposed in the literature which is able to identify all redundant NACs in an SP problem with only endogenous uncertainty. In this paper, however, we extend the algorithm proposed in the literature and present a new method which is able to make the upper most possible reduction in the number of NACs in any SP with both exogenous and endogenous uncertain parameters. Proving the validity of this method is another innovation of this study. Computational results confirm that the proposed approach can significantly reduce the problem size within a reasonable computation time.

Suggested Citation

  • F. Hooshmand & S. A. MirHassani, 2018. "Reduction of nonanticipativity constraints in multistage stochastic programming problems with endogenous and exogenous uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 1-18, February.
    • Handle: RePEc:spr:mathme:v:87:y:2018:i:1:d:10.1007_s00186-017-0600-6
    DOI: 10.1007/s00186-017-0600-6
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    References listed on IDEAS

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    1. Bora Tarhan & Ignacio Grossmann & Vikas Goel, 2013. "Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution," Annals of Operations Research, Springer, vol. 203(1), pages 141-166, March.
    2. F. Hooshmand Khaligh & S.A. MirHassani, 2016. "A mathematical model for vehicle routing problem under endogenous uncertainty," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 579-590, January.
    3. Solak, Senay & Clarke, John-Paul B. & Johnson, Ellis L. & Barnes, Earl R., 2010. "Optimization of R&D project portfolios under endogenous uncertainty," European Journal of Operational Research, Elsevier, vol. 207(1), pages 420-433, November.
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    5. Tore Jonsbråten & Roger Wets & David Woodruff, 1998. "A class of stochastic programs withdecision dependent random elements," Annals of Operations Research, Springer, vol. 82(0), pages 83-106, August.
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    Cited by:

    1. Giovanni Pantuso, 2021. "A node formulation for multistage stochastic programs with endogenous uncertainty," Computational Management Science, Springer, vol. 18(3), pages 325-354, July.
    2. Saeid Nasrollahi & Hasan Hosseini-Nasab & Mohammad Bagher Fakhrzad & Mahboobeh Honarvar, 2023. "A multi-stage stochastic model for designing a linked cross-docking distribution network with heterogeneous trucks," Operational Research, Springer, vol. 23(1), pages 1-41, March.
    3. Escudero, Laureano F. & Garín, M. Araceli & Monge, Juan F. & Unzueta, Aitziber, 2020. "Some matheuristic algorithms for multistage stochastic optimization models with endogenous uncertainty and risk management," European Journal of Operational Research, Elsevier, vol. 285(3), pages 988-1001.

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