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On the product selection and plant dimensioning problem under uncertainty

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  • Alonso-Ayuso, A.
  • Escudero, L. F.
  • Garín, A.
  • Ortuño, M. T.
  • Pérez, G.

Abstract

We present a two-stage full recourse model for strategic production planning under uncertainty, whose aim consists of determining product selection and plant dimensioning. The main uncertain parameters are the product price, demand and production cost. The benefit is given by the product net profit over the time horizon minus the investment depreciation and operation costs. The Value-at-Risk and the reaching probability are considered as risk measures in the objective function to be optimized as alternatives to the maximization of the expected benefit over the scenarios. The uncertainty is represented by a set of scenarios. The problem is formulated as a mixed 0-1 Deterministic Equivalent Model. The strategic decisions to be made in the first stage are represented by 0-1 variables. The tactical decisions to be made in the second stage are represented by continuous variables. An approach for problem solving based on a splitting variable mathematical representation via scenario is considered. The problem uses the Twin Node Family concept within the algorithmic framework known as Branch-and-Fix Coordination for satisfying the nonanticipativity constraints. Some computational experience is reported.

Suggested Citation

  • Alonso-Ayuso, A. & Escudero, L. F. & Garín, A. & Ortuño, M. T. & Pérez, G., 2005. "On the product selection and plant dimensioning problem under uncertainty," Omega, Elsevier, vol. 33(4), pages 307-318, August.
    • Handle: RePEc:eee:jomega:v:33:y:2005:i:4:p:307-318
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    Cited by:

    1. Laureano Escudero, 2009. "On a mixture of the fix-and-relax coordination and Lagrangian substitution schemes for multistage stochastic mixed integer programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 5-29, July.
    2. Unai Aldasoro & María Merino & Gloria Pérez, 2019. "Time consistent expected mean-variance in multistage stochastic quadratic optimization: a model and a matheuristic," Annals of Operations Research, Springer, vol. 280(1), pages 151-187, September.
    3. Hannes Schwarz & Valentin Bertsch & Wolf Fichtner, 2018. "Two-stage stochastic, large-scale optimization of a decentralized energy system: a case study focusing on solar PV, heat pumps and storage in a residential quarter," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 265-310, January.
    4. Xiao, Tiaojun & Qi, Xiangtong, 2008. "Price competition, cost and demand disruptions and coordination of a supply chain with one manufacturer and two competing retailers," Omega, Elsevier, vol. 36(5), pages 741-753, October.
    5. Laureano Escudero & Araceli Garín & María Merino & Gloria Pérez, 2009. "BFC-MSMIP: an exact branch-and-fix coordination approach for solving multistage stochastic mixed 0–1 problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 96-122, July.
    6. Beltran-Royo, C., 2017. "Two-stage stochastic mixed-integer linear programming: The conditional scenario approach," Omega, Elsevier, vol. 70(C), pages 31-42.
    7. Schwarz, Hannes & Bertsch, Valentin & Fichtner, Wolf, 2015. "Two-stage stochastic, large-scale optimization of a decentralized energy system - a residential quarter as case study," Working Paper Series in Production and Energy 10, Karlsruhe Institute of Technology (KIT), Institute for Industrial Production (IIP).
    8. Xiao, Tiaojun & Yang, Danqin, 2008. "Price and service competition of supply chains with risk-averse retailers under demand uncertainty," International Journal of Production Economics, Elsevier, vol. 114(1), pages 187-200, July.
    9. E. Mijangos, 2015. "An algorithm for two-stage stochastic mixed-integer nonlinear convex problems," Annals of Operations Research, Springer, vol. 235(1), pages 581-598, December.
    10. Escudero, L.F. & Garín, M.A. & Merino, M. & Pérez, G., 2010. "An exact algorithm for solving large-scale two-stage stochastic mixed-integer problems: Some theoretical and experimental aspects," European Journal of Operational Research, Elsevier, vol. 204(1), pages 105-116, July.

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