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A two-stage stochastic integer programming approach as a mixture of Branch-and-Fix Coordination and Benders Decomposition schemes

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Listed:
  • L. Escudero
  • A. Garín
  • M. Merino
  • G. Pérez

Abstract

We present an algorithmic approach for solving two-stage stochastic mixed 0–1 problems. The first stage constraints of the Deterministic Equivalent Model have 0–1 variables and continuous variables. The approach uses the Twin Node Family (TNF) concept within the so-called Branch-and-Fix Coordination algorithmic framework to satisfy the nonanticipativity constraints, jointly with a Benders Decomposition scheme to solve a given LP model at each TNF integer set. As a pilot case, the structuring of a portfolio of Mortgage-Backed Securities under uncertainty in the interest rate path on a given time horizon is used. Some computational experience is reported. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • L. Escudero & A. Garín & M. Merino & G. Pérez, 2007. "A two-stage stochastic integer programming approach as a mixture of Branch-and-Fix Coordination and Benders Decomposition schemes," Annals of Operations Research, Springer, vol. 152(1), pages 395-420, July.
    • Handle: RePEc:spr:annopr:v:152:y:2007:i:1:p:395-420:10.1007/s10479-006-0138-0
    DOI: 10.1007/s10479-006-0138-0
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    References listed on IDEAS

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    1. Schwartz, Eduardo S & Torous, Walter N, 1989. " Prepayment and the Valuation of Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 44(2), pages 375-392, June.
    2. Stanton, Richard, 1995. "Rational Prepayment and the Valuation Mortgage-Backed Securities," The Review of Financial Studies, Society for Financial Studies, vol. 8(3), pages 677-708.
    3. Samer Takriti & John R. Birge, 2000. "Lagrangian Solution Techniques and Bounds for Loosely Coupled Mixed-Integer Stochastic Programs," Operations Research, INFORMS, vol. 48(1), pages 91-98, February.
    4. Pan Kang & Stavros A. Zenios, 1992. "Complete Prepayment Models for Mortgage-Backed Securities," Management Science, INFORMS, vol. 38(11), pages 1665-1685, November.
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    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. Escudero Bueno, Laureano F. & Garín Martín, María Araceli & Pérez Sainz de Rozas, Gloria & Unzueta Inchaurbe, Aitziber, 2010. "Lagrangean decomposition for large-scale two-stage stochastic mixed 0-1 problems," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    5. F. Wu & H. Li & L. Chu & D. Sculli & K. Gao, 2009. "An approach to the valuation and decision of ERP investment projects based on real options," Annals of Operations Research, Springer, vol. 168(1), pages 181-203, April.
    6. Pagès-Bernaus, Adela & Pérez-Valdés, Gerardo & Tomasgard, Asgeir, 2015. "A parallelised distributed implementation of a Branch and Fix Coordination algorithm," European Journal of Operational Research, Elsevier, vol. 244(1), pages 77-85.
    7. 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.
    8. L. F. Escudero & J. F. Monge & D. Romero Morales & J. Wang, 2013. "Expected Future Value Decomposition Based Bid Price Generation for Large-Scale Network Revenue Management," Transportation Science, INFORMS, vol. 47(2), pages 181-197, May.
    9. Fengqi You & Ignacio Grossmann, 2013. "Multicut Benders decomposition algorithm for process supply chain planning under uncertainty," Annals of Operations Research, Springer, vol. 210(1), pages 191-211, November.
    10. Escudero, Laureano F. & Landete, Mercedes & Rodríguez-Chía, Antonio M., 2011. "Stochastic set packing problem," European Journal of Operational Research, Elsevier, vol. 211(2), pages 232-240, June.
    11. L. Aranburu & L. Escudero & M. Garín & G. Pérez, 2012. "A so-called Cluster Benders Decomposition approach for solving two-stage stochastic linear problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 279-295, July.

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