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Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution

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  • Bora Tarhan
  • Ignacio Grossmann
  • Vikas Goel

Abstract

In many planning problems under uncertainty the uncertainties are decision-dependent and resolve gradually depending on the decisions made. In this paper, we address a generic non-convex MINLP model for such planning problems where the uncertain parameters are assumed to follow discrete distributions and the decisions are made on a discrete time horizon. In order to account for the decision-dependent uncertainties and gradual uncertainty resolution, we propose a multistage stochastic programming model in which the non-anticipativity constraints in the model are not prespecified but change as a function of the decisions made. Furthermore, planning problems consist of several scenario subproblems where each subproblem is modeled as a nonconvex mixed-integer nonlinear program. We propose a solution strategy that combines global optimization and outer-approximation in order to optimize the planning decisions. We apply this generic problem structure and the proposed solution algorithm to several planning problems to illustrate the efficiency of the proposed method with respect to the method that uses only global optimization. Copyright Springer Science+Business Media, LLC 2013

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  • 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.
    • Handle: RePEc:spr:annopr:v:203:y:2013:i:1:p:141-166:10.1007/s10479-011-0855-x
    DOI: 10.1007/s10479-011-0855-x
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    Cited by:

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    2. Maier, Sebastian & Pflug, Georg C. & Polak, John W., 2020. "Valuing portfolios of interdependent real options under exogenous and endogenous uncertainties," European Journal of Operational Research, Elsevier, vol. 285(1), pages 133-147.
    3. 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.
    4. Sha, Yue & Zhang, Junlong & Cao, Hui, 2021. "Multistage stochastic programming approach for joint optimization of job scheduling and material ordering under endogenous uncertainties," European Journal of Operational Research, Elsevier, vol. 290(3), pages 886-900.
    5. Giovanni Pantuso, 2021. "A node formulation for multistage stochastic programs with endogenous uncertainty," Computational Management Science, Springer, vol. 18(3), pages 325-354, July.
    6. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    7. Majid Taghavi & Kai Huang, 2020. "A Lagrangian relaxation approach for stochastic network capacity expansion with budget constraints," Annals of Operations Research, Springer, vol. 284(2), pages 605-621, January.

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