Stochastic Decomposition

Higle, Julia L.; Sen, Suvrajeet

doi:10.1007/978-1-4615-4115-8

Cited by 124 publications

(23 citation statements)

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“…The algorithm presented in Section 2.2 corresponds to the basic SD algorithm of Higle and Sen (1996). Such authors also suggest additional concepts to improve performance of the algorithm.…”

Section: Methodsmentioning

confidence: 99%

“…The two main algorithms for stochastic linear programming with fixed recourse are the L-shaped method (Birge & Louveaux, 1988 and the stochastic decomposition (SD) algorithm (Higle & Sen, 1991, 1996:…”

Section: Slpwr Algorithmsmentioning

confidence: 99%

“…For that reason, the estimation of the lower bound of Q(x) is based on expectation. The algorithm presented here corresponds to the basic version provided by Higle and Sen (1996). Sen (1991, 1996) assume complete recourse (no feasibility cuts are needed) and provide a simplification involving a restricted solution set for the dual of the second stage problem in order to decrease the computational effort.…”

Section: Sd Algorithmmentioning

confidence: 99%

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Improving convergence of the stochastic decomposition algorithm by using an efficient sampling technique

Ponce-Ortega

Rico-Ramı́rez

Hernández-Castro

et al. 2004

Computers & Chemical Engineering

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Section: Methodsmentioning

confidence: 99%

Section: Slpwr Algorithmsmentioning

confidence: 99%

Section: Sd Algorithmmentioning

confidence: 99%

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Improving convergence of the stochastic decomposition algorithm by using an efficient sampling technique

Ponce-Ortega

Rico-Ramı́rez

Hernández-Castro

et al. 2004

Computers & Chemical Engineering

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“…However, it is not too difficult to prove that H(x) is, under fairly mild conditions, a convex function (Birge and Louveaux, 1997;Kall and Wallace, 1994), which paves the way to computational algorithms based on statistical sampling. An example is the stochastic decomposition algorithm of (Higle and Sen, 1996). However, the common practical approach is to approximate the underlying continuous distribution of the parameters by a discrete one, represented by a finite set S of scenarios.…”

Section: General Structure Of Two-stage Stochastic Linear Programsmentioning

confidence: 99%

Stochastic Programming Models for Manufacturing Applications

Alfieri

Brandimarte

2005

Design of Advanced Manufacturing Systems

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Stochastic programming models have been proposed for capacity planning problems in different environments, including energy, telecommunication networks, distribution networks, and manufacturing systems. In this chapter we give an introductory tutorial to stochastic linear programming models, with emphasis on modeling techniques, rather than specialized solution methods. We consider two-stage and multi-stage stochastic programming models with recourse for manufacturing related applications, such as production planning and capacity planning with uncertainty on demand. We stress the importance of proper model formulation from two points of view: the first one is building strong mixed-integer formulations; the second one is generating scenario trees in order to suitably represent uncertainty while keeping them to a manageable size. We also compare the stochastic programming approach to traditional dynamic programming and to robust optimization.

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“…For this method, we need ed in §3.1. Other techniques closely related to the stochastic approach for s ethod [75][76][77], chance-constrained method [4,78], simulation based techniques [79][80][81], two stage method [61] and multistage method [82].…”

Section: Smentioning

confidence: 99%

Multiobjective Stochastic Linear Programming: An Overview

Adeyefa¹,

Luhandjula²

2011

AJOR

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Many Optimization problems in engineering and economics involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimization, probability theory and multicriteria decision analysis are interwoven to address situations where the presence of several objective functions and the stochastic nature of data are under one roof in a linear optimization context. In this way users of these models are not bound to caricature their problems by arbitrarily squeezing different objective functions into one and by blindly accepting fixed values in lieu of imprecise ones.

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Stochastic Decomposition

Cited by 124 publications

References 0 publications

Improving convergence of the stochastic decomposition algorithm by using an efficient sampling technique

Improving convergence of the stochastic decomposition algorithm by using an efficient sampling technique

Stochastic Programming Models for Manufacturing Applications

Multiobjective Stochastic Linear Programming: An Overview

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