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Reliability and decomposition techniques to solve certain class of stochastic programming problems

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  • Mínguez, R.
  • Conejo, A.J.
  • García-Bertrand, R.

Abstract

Reliability based techniques has been an area of active research in structural design during the last decade, and different methods have been developed. The same has occurred with stochastic programming, which is a framework for modeling optimization problems involving uncertainty. The discipline of stochastic programming has grown and broadened to cover a wide range of applications, such as agriculture, capacity planning, energy, finance, fisheries management, production control, scheduling, transportation, water management, etc., and because of this, techniques for solving stochastic programming models are of great interest for the scientific community. This paper presents a new approach for solving a certain type of stochastic programming problems presenting the following characteristics: (i) the joint probability distributions of random variables are given, (ii) these do not depend on the decisions made, and (iii) random variables only affect the objective function. The method is based on mathematical programming decomposition procedures and first-order reliability methods, and constitutes an efficient method for optimizing quantiles in high-dimensional settings. The solution provided by the method allows us to make informed decisions accounting for uncertainty.

Suggested Citation

  • Mínguez, R. & Conejo, A.J. & García-Bertrand, R., 2011. "Reliability and decomposition techniques to solve certain class of stochastic programming problems," Reliability Engineering and System Safety, Elsevier, vol. 96(2), pages 314-323.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:2:p:314-323
    DOI: 10.1016/j.ress.2010.09.011
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    References listed on IDEAS

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    1. Matthew Pritsker, 1997. "Evaluating Value at Risk Methodologies: Accuracy versus Computational Time," Journal of Financial Services Research, Springer;Western Finance Association, vol. 12(2), pages 201-242, October.
    2. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    2. Sun, X.T. & Chung, S.H. & Chan, Felix T.S. & Wang, Zheng, 2018. "The impact of liner shipping unreliability on the production–distribution scheduling of a decentralized manufacturing system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 242-269.

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