Dual decomposition in stochastic integer programming

Carøe, Claus C.; Schultz, Rüdiger

doi:10.1016/s0167-6377(98)00050-9

Cited by 440 publications

(312 citation statements)

References 13 publications

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“…This is an area of future research. In the future we also intend to combine our approaches, polynomial time algorithms and polyhedral studies, into decomposition frameworks for large size stochastic integer programming problems, such as those studied by Carøe (1998) and Sen and Sherali (2006) (among others).…”

Section: Discussionmentioning

confidence: 99%

Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

Guan

Miller

2008

Operations Research

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In 1958, Wagner and Whitin published a seminal paper on the deterministic uncapacitated lot-sizing problem, a fundamental model that is embedded in many practical production planning problems. In this paper we consider a basic version of this model in which demands (and other problem parameters) are stochastic: the stochastic uncapacitated lot-sizing problem (SULS). We define the production path property of an optimal solution for our model and use this property to develop a backward dynamic programming recursion. This approach allows us to show that the value function is piecewise linear and right continuous. We then use these results to show that a full characterization of the optimal value function can be obtained by a dynamic programming algorithm in polynomial time for the case that each non-leaf node contains at least two children.Moreover, we show that our approach leads to a polynomial time algorithm to obtain an optimal solution to any instance of SULS, regardless of the structure of the scenario tree. We also show that the value function for the problem without setup costs is continuous, piecewise linear, and convex, and therefore an even more efficient dynamic programming algorithm can be developed for this special case.

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Section: Discussionmentioning

confidence: 99%

Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

Guan

Miller

2008

Operations Research

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“…(132), (133) and (134)) non-anticipativity (NA) constraints. If these NA constraints are either relaxed or dualized using Lagrangean decomposition, then the problem decomposes into smaller subproblems that can be solved independently for each scenario within an iterative scheme for the multipliers as described in Carøe and Schultz (1999) and in Gupta and Grossmann (2011). In this way, we can effectively decompose and solve the …”

Section: Solution Approachmentioning

confidence: 99%

Multistage stochastic programming approach for offshore oilfield infrastructure planning under production sharing agreements and endogenous uncertainties

Gupta

Grossmann

2014

Journal of Petroleum Science and Engineering

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The paper presents a new optimization model and solution approach for the investment and operations planning of offshore oil and gas field infrastructure. As compared to previous models where fiscal rules and uncertainty in the field parameters are considered separately, the proposed model is the first one in the literature that includes both of these complexities in an efficient manner. In particular, a tighter formulation for the production sharing agreements is used based on our recent work, and correlation among the endogenous uncertain parameters (field size, oil deliverability, water-oil ratio and gas-oil ratio) is considered to reduce the total number of scenarios in the resulting multistage stochastic formulation. To solve large instances, a Lagangean decomposition approach allowing parallel solution of the scenario subproblems is implemented in the GAMS grid computing environment. Computational results on a variety of oilfield development planning examples are presented to illustrate the efficiency of the model and the proposed solution approach.

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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%

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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Dual decomposition in stochastic integer programming

Cited by 440 publications

References 13 publications

Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

Multistage stochastic programming approach for offshore oilfield infrastructure planning under production sharing agreements and endogenous uncertainties

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

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