A cutting-plane approach to mixed 0–1 stochastic integer programs

Carøe, Claus C.; Tind, Jørgen

doi:10.1016/s0377-2217(96)00399-2

Cited by 48 publications

(24 citation statements)

References 10 publications

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“…This method uses a transformed space in which tender variables (χ = T x) are used to partition the problem using a hyperrectangular partitioning process. The method by Carøe and Tind (1997) and Carøe (1998) uses disjunctive programming to derive cutting-planes under the EF (problem 3) setting and requires continuous first-stage and mixed-binary second-stage decision variables. An extension of the method for SIP with pure binary first-stage and mixed-binary secondstage decision variables is also proposed.…”

Section: Related Workmentioning

confidence: 99%

“…It should be pointed out that Theorem 3.3 is a more general form of the common-cut-coefficients (C3) theorem (Sen and Higle, 2005) for SIP with fixed recourse. Unlike here where we generate valid inequalities in the y(ω)-space, Carøe and Tind (1997) and Carøe (1998) derive a similar theorem but for generating cuts in the (x, y(ω))-space based on the extensive formulation (3). Thus the method developed in this paper is different from that of Carøe and Tind (1997) and Carøe (1998).…”

Section: Is a Finite Collection Of Appropriately Dimensioned Matricesmentioning

confidence: 99%

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Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse

Ntaimo

2010

Operations Research

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This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse. Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem. A new class of valid inequalities for mixed 0-1 SIP with random recourse is presented. In particular, valid inequalities that allow for sharing cut coefficients among scenario subproblems for SIP with random recourse but deterministic technology matrix and righthand side vector are obtained. The valid inequalities are used to derive a disjunctive decomposition method whose derivation has been motivated by real-life stochastic server location problems with random recourse, which find many applications in operations research. Computational results with large-scale instances to demonstrate the potential of the method are reported.

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Section: Related Workmentioning

confidence: 99%

Section: Is a Finite Collection Of Appropriately Dimensioned Matricesmentioning

confidence: 99%

Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse

Ntaimo

2010

Operations Research

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“…A similar deterministic approach for general mixed integer linear programs is presented in Owen and Mehrotra (2001). We refer to Carøe and Tind (1997) for an extension of lift-andproject cuts of Balas, Ceria, and Cornuéjols (1996) for SIP problems. Let the linear relaxation of problem (P4) be the following problem:…”

Section: Disjunctive Cutsmentioning

confidence: 99%

B&B Frameworks for the Capacity Expansion of High Speed Telecommunication Networks Under Uncertainty

et al. 2005

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The purpose of this paper is to investigate branch and bound strategies and the comparison of branch and cut with pure branch and bound approaches on high speed telecommunication network design under uncertainty. We model the problem as a two-stage stochastic program with discrete firststage (investment) variables. Two formulations of the problem are used. The first one with general integer investment variables and the second one, a variant of the first model, with 0-1 investment variables. We present computational results for three solution approaches: the integer L-shaped (Benders) decomposition, a branch and bound framework and a disjunctive cutting plane method.

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“…An integer L-shaped method introduced in [16] is one of the most commonly used methods to solve this problem. Methods based on lift-andproject cutting planes are used in [17]. Sen and Higle in [18] developed disjunctive cuts for the second stage that maintain the fixed-recourse property.…”

Section: Introductionmentioning

confidence: 99%

Large-scale stochastic power grid islanding operations by line switching and controlled load shedding

2016

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Recently, there has been an increasing concern regarding the security and reliability of power systems due to the onerous consequences of cascading failures. Among many emergency control operations, controlled power grid islanding is a last resort yet powerful method to prevent large-scale blackouts. Islanding operations split the power grid into self-sufficient operational subnetworks and avoid cascading failures by isolating the failed elements of the power system into a non-operational island. In this paper, we consider a two-stage stochastic mixed-integer program to seek the optimal islanding operations under severe contingency states. Line switching and controlled load shedding are the main tools for the islanding operations and load shedding is considered as a measurement to gauge system's inability to respond to disruption. The number of possible extreme contingencies grows exponentially as the size of the grid increases, and this results in a large-scale mixed-integer program, which is a computationally challenging problem to solve. We present an efficient decomposition method to solve this problem for large-scale power systems.

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A cutting-plane approach to mixed 0–1 stochastic integer programs

Cited by 48 publications

References 10 publications

Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse

Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse

B&B Frameworks for the Capacity Expansion of High Speed Telecommunication Networks Under Uncertainty

Large-scale stochastic power grid islanding operations by line switching and controlled load shedding

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