Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse

Higle, Julia L.; Sen, Suvrajeet

doi:10.1287/moor.16.3.650

Cited by 386 publications

(207 citation statements)

References 11 publications

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“…In order to address the computational challenge, a number of methods have been proposed for the solution of two-stage stochastic programming problems (Ruszczyński, 1997), such as Benders decomposition (Benders, 1962;Van Slyke & Wets, 1969), stochastic decomposition (Higle & Sen, 1991), subgradient decomposition (Sen, 1993;Sen and Huang, 2009), disjunctive decomposition (Ntaimo, 2010), and nested decomposition (Archibald et al, 1999). Among these methods, Benders decomposition (Benders, 1962), also called the L-shaped method, has become the major approach to tackle stochastic programming problems because of its ease of implementation.…”

Section: Introductionmentioning

confidence: 99%

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

You

Grossmann

2011

Ann Oper Res

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Section: Introductionmentioning

confidence: 99%

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

You

Grossmann

2011

Ann Oper Res

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“…If separability is too strong of an approximation, a powerful technique is to use Benders' decomposition (see Higle and Sen 1991;Birge and Louveaux 1997;or Powell 2007, Chapter 11). At time t, iteration n we would solve a problem with the form…”

Section: Multiple Entities Simple Attributesmentioning

confidence: 99%

Feature Article—Merging AI and OR to Solve High-Dimensional Stochastic Optimization Problems Using Approximate Dynamic Programming

Powell

2010

INFORMS Journal on Computing

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W e consider the problem of optimizing over time hundreds or thousands of discrete entities that may be characterized by relatively complex attributes, in the presence of different forms of uncertainty. Such problems arise in a range of operational settings such as transportation and logistics, where the entities may be aircraft, locomotives, containers, or people. These problems can be formulated using dynamic programming but encounter the widely cited "curse of dimensionality." Even deterministic formulations of these problems can produce math programs with millions of rows, far beyond anything being solved today. This paper shows how we can combine concepts from artificial intelligence and operations research to produce practical solution methods that scale to industrial-strength problems. Throughout, we emphasize concepts, techniques, and notation from artificial intelligence and operations research to show how these fields can be brought together for complex stochastic, dynamic problems.

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“…For stochastic linear programs, i.e. when the secondstage problem is linear, the convexity of the second-stage value function along with this decomposability property has been exploited to develop a number of decomposition-based algorithms [4,11,13,19,25] as well as gradient-based algorithms [8,23].…”

Section: Computational Challengesmentioning

confidence: 99%

Dynamic Capacity Acquisition and Assignment under Uncertainty

Ahmed

Garcia

2003

Annals of Operations Research

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Given a set of m resources and n tasks, the dynamic capacity acquisition and assignment problem seeks a minimum cost schedule of capacity acquisitions for the resources and the assignment of resources to tasks, over a given planning horizon of T periods. This problem arises, for example, in the integrated planning of locations and capacities of distribution centers (DCs), and the assignment of customers to the DCs, in supply chain applications. We consider the dynamic capacity acquisition and assignment problem in an environment where the assignment costs and the processing requirements for the tasks are uncertain. Using a scenario based approach, we develop a stochastic integer programming model for this problem. The highly non-convex nature of this model prevents the application of standard stochastic programming decomposition algorithms. We use a recently developed decomposition based branch-andbound strategy for the problem. Encouraging preliminary computational results are provided.

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Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse

Cited by 386 publications

References 11 publications

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

Feature Article—Merging AI and OR to Solve High-Dimensional Stochastic Optimization Problems Using Approximate Dynamic Programming

Dynamic Capacity Acquisition and Assignment under Uncertainty

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