Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs

Gade, Dinakar; Küçükyavuz, Simge; Sen, Suvrajeet

doi:10.1007/s10107-012-0615-y

Cited by 80 publications

(92 citation statements)

References 35 publications

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“…However, pure cutting-plane algorithms have important applications in the solution of two-stage stochastic MIPs. We refer the reader to the articles by Sen and Higle [35], for a decomposition algorithm based on lift-and-project cuts for two-stage stochastic mixed-binary programs, Gade et al [36], for decomposition algorithms using Gomory cuts for two-stage stochastic pure integer programs, and Ntaimo [37], for a decomposition algorithm for two-stage stochastic mixed-binary programs based on the so-called Fenchel cuts. (A pure cuttingplane algorithm based on Fenchel cuts [38] is shown to be finitely convergent for deterministic MIPs in [39].…”

Section: Discussionmentioning

confidence: 99%

Pure Cutting‐Plane Algorithms and their Convergence

Gade

Küçükyavuz

2011

Wiley Encyclopedia of Operations Research and Management Science

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Section: Discussionmentioning

confidence: 99%

Pure Cutting‐Plane Algorithms and their Convergence

Gade

Küçükyavuz

2011

Wiley Encyclopedia of Operations Research and Management Science

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“…An alternate deterministic equivalent formulation uses coupling first-stage variables that are common for all scenario blocks, yielding a primal decomposable problem that can be solved by schemes such as Benders' when all second-stage variables are continuous. Extensions have been proposed, but these tend to be computationally impractical, especially when both stages have continuous and integer variables [9].…”

Section: A Stochastic Optimization: An Overviewmentioning

confidence: 99%

An efficient approach for solving large stochastic unit commitment problems arising in a California ISO planning model

Parriani

Cong²,

Meyers

et al. 2014

2014 IEEE PES General Meeting | Conference &Amp; Exposition

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We describe our experience in obtaining significant computational improvements in the solution of large stochastic unit commitment problems. The model we use is a stochastic version of a planning model used by the California Independent System Operator, covering the entire WECC western regional grid. We solve daily hour-timestep stochastic unit commitment problems using a new progressive hedging approach that features linear subproblems and guided solves for finding feasible solutions. For stochastic problems with 5 scenarios, the algorithm produces near-optimal solutions with a 6 times improvement in serial solution time, and over 20 times improvement when run in parallel; for previously unsolvable stochastic problems, we obtain near-optimal solutions within a couple of hours. We note that although this algorithm is demonstrated for stochastic unit commitment problems, the algorithm itself is suitable for application to generic stochastic optimization problems.

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“…Gade et al (2014) propose adding Gomory cuts when the integer variables of the subproblem take a fractional value in the LP relaxation. By successively adding cuts, the objective value of the relaxation is strengthened, and dual information becomes available.…”

Section: £mentioning

confidence: 99%

Perspectives in multilevel decision-making in the process industry

Brunaud¹,

Grossmann²

2017

Front. Eng

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Decisions in supply chains are hierarchically organized. Strategic decisions involve the long-term planning of the structure of the supply chain network. Tactical decisions are mid-term plans to allocate the production and distribution of materials, while operational decisions are related to the daily planning of the execution of manufacturing operations. These planning processes are conducted independently with minimal exchange of information between them. Achieving a better coordination between these processes allows companies to capture benefits that are currently out of their reach and improve the communication among their functional areas. We propose a network representation for the multilevel decision structure and analyze the components that are involved in finding integrated solutions that maximize the sum of the benefits of all nodes of the decision network. Although such task is very challenging, significant research progress has been made in each component of this structure. An overview of strategic models, mid-term planning models, and scheduling models is presented to address the solution of each node in the decision network. Coordination mechanisms for converging the integrated solutions are also analyzed, including solving large-scale models, multiobjective optimization, bi-level programming, and decomposition. We conclude by summarizing the challenges that hinder the full integration of multilevel decision making in supply chain management.

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Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs

Cited by 80 publications

References 35 publications

Pure Cutting‐Plane Algorithms and their Convergence

Pure Cutting‐Plane Algorithms and their Convergence

An efficient approach for solving large stochastic unit commitment problems arising in a California ISO planning model

Perspectives in multilevel decision-making in the process industry

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