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Stochastic Bounds on Distributions of Optimal Value Functions with Applications to PERT, Network Flows and Reliability

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  • Gideon Weiss

    (Georgia Institute of Technology, Atlanta, Georgia, and Tel Aviv University, Tel Aviv, Israel)

Abstract

In many classical combinatorial optimization problems, including critical and shortest paths, maximum flow, and network reliability, the introduction of uncertainty considerably complicates the calculation of system performance. In fact, in these contexts, computing system performance exactly can often be an impossible task. Therefore, obtaining (stochastic) bounds on the system's performance becomes an attractive and useful alternative. This paper studies several stochastic bounds that are applicable to these contexts and to a broader set of problems that can be described by the general combinatorial concepts of clutters and blocking clutters. We begin our discussion by defining these unifying concepts and illustrating their specialization in several problem contexts.

Suggested Citation

  • Gideon Weiss, 1986. "Stochastic Bounds on Distributions of Optimal Value Functions with Applications to PERT, Network Flows and Reliability," Operations Research, INFORMS, vol. 34(4), pages 595-605, August.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:4:p:595-605
    DOI: 10.1287/opre.34.4.595
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    Cited by:

    1. Karthik Natarajan & Miao Song & Chung-Piaw Teo, 2009. "Persistency Model and Its Applications in Choice Modeling," Management Science, INFORMS, vol. 55(3), pages 453-469, March.
    2. Vinit Kumar Mishra & Karthik Natarajan & Dhanesh Padmanabhan & Chung-Piaw Teo & Xiaobo Li, 2014. "On Theoretical and Empirical Aspects of Marginal Distribution Choice Models," Management Science, INFORMS, vol. 60(6), pages 1511-1531, June.
    3. Karthik Natarajan & Dongjian Shi & Kim-Chuan Toh, 2014. "A Probabilistic Model for Minmax Regret in Combinatorial Optimization," Operations Research, INFORMS, vol. 62(1), pages 160-181, February.
    4. Li, Xiaobo & Natarajan, Karthik & Teo, Chung-Piaw & Zheng, Zhichao, 2014. "Distributionally robust mixed integer linear programs: Persistency models with applications," European Journal of Operational Research, Elsevier, vol. 233(3), pages 459-473.
    5. Brucker, Peter & Drexl, Andreas & Mohring, Rolf & Neumann, Klaus & Pesch, Erwin, 1999. "Resource-constrained project scheduling: Notation, classification, models, and methods," European Journal of Operational Research, Elsevier, vol. 112(1), pages 3-41, January.
    6. Nicole Megow & Rolf H. Möhring & Jens Schulz, 2011. "Decision Support and Optimization in Shutdown and Turnaround Scheduling," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 189-204, May.
    7. Xuan Vinh Doan & Karthik Natarajan, 2012. "On the Complexity of Nonoverlapping Multivariate Marginal Bounds for Probabilistic Combinatorial Optimization Problems," Operations Research, INFORMS, vol. 60(1), pages 138-149, February.

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