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Estimating the parameters of a fatigue model using Benders’ decomposition

Author

Listed:
  • Enrique Castillo
  • Roberto Mínguez
  • Antonio Conejo
  • Beatriz Pérez
  • Oscar Fontenla

Abstract

This paper shows how Benders decomposition can be used for estimating the parameters of a fatigue model. The objective function of such model depends on five parameters of different nature. This makes the parameter estimation problem of the fatigue model suitable for the Benders decomposition, which allows us to use well-behaved and robust parameter estimation methods for the different subproblems. To build the Benders cuts, explicit formulas for the sensitivities (partial derivatives) are obtained. This permits building the classical iterative method, in which upper and lower bounds of the optimal value of the objective function are obtained until convergence. Two alternative objective functions to be optimized are the likelihood and the sum of squares error functions, which relate to the maximum likelihood and the minimum error principles, respectively. The method is illustrated by its application to a real-world problem. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Enrique Castillo & Roberto Mínguez & Antonio Conejo & Beatriz Pérez & Oscar Fontenla, 2013. "Estimating the parameters of a fatigue model using Benders’ decomposition," Annals of Operations Research, Springer, vol. 210(1), pages 309-331, November.
    • Handle: RePEc:spr:annopr:v:210:y:2013:i:1:p:309-331:10.1007/s10479-011-0891-6
    DOI: 10.1007/s10479-011-0891-6
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    References listed on IDEAS

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    1. E. Castillo & A. Conejo & C. Castillo & R. Mínguez, 2007. "Closed formulas in local sensitivity analysis for some classes of linear and non-linear problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 355-371, December.
    2. Jean-François Cordeau & Federico Pasin & Marius Solomon, 2006. "An integrated model for logistics network design," Annals of Operations Research, Springer, vol. 144(1), pages 59-82, April.
    3. E. Castillo & A. J. Conejo & C. Castillo & R. Mínguez & D. Ortigosa, 2006. "Perturbation Approach to Sensitivity Analysis in Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 49-74, January.
    4. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    5. Ximing Cai & Daene C. McKinney & Leon S. Lasdon & David W. Watkins, 2001. "Solving Large Nonconvex Water Resources Management Models Using Generalized Benders Decomposition," Operations Research, INFORMS, vol. 49(2), pages 235-245, April.
    6. Jean-François Cordeau & François Soumis & Jacques Desrosiers, 2000. "A Benders Decomposition Approach for the Locomotive and Car Assignment Problem," Transportation Science, INFORMS, vol. 34(2), pages 133-149, May.
    7. Jean-François Cordeau & François Soumis & Jacques Desrosiers, 2001. "Simultaneous Assignment of Locomotives and Cars to Passenger Trains," Operations Research, INFORMS, vol. 49(4), pages 531-548, August.
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