Stochastic Linear Programming
Models, Theory, and Computation
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Book
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Chapter
SLP models with recourse
For various SLP models with recourse, we present in this chapter properties which are relevant for the particular solution methods developed for various model types, to be discussed later on.
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Chapter
Single–stage SLP models
In this chapter we consider stochastic programming problems which represent a single decision stage. The decision is to be made “here and now” and the models do not account for any corrective (recourse) action...
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Chapter
Algorithms
The discussion of algorithms in this chapter is organized according to the framework of different SLP model classes, as presented in the previous chapters. A computer implementation of an algorithm will be cal...
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Chapter
Basics
Linear programs have been studied in many aspects during the last 60 years. They have shown to be appropriate models for a wide variety of practical problems and, at the same time, they became numerically trac...
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Article
Some insights into the solution algorithms for SLP problems
We consider classes of stochastic linear programming problems which can be efficiently solved by deterministic algorithms. For two–stage recourse problems we identify two such classes. The first one consists o...
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Book
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Chapter and Conference Paper
Modeling Support for Multistage Recourse Problems
The purpose of this paper is to discuss modeling aspects concerning multistage stochastic linear recourse problems. We will especially point out the additional features which arise when extending modeling supp...
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Chapter
Stochastic Programming: Achievements and Open Problems
As is well known, many applied problems may be modelled as linear programs of the standard type
(1.1) $$ subject{\kern 1pt} to... -
Article
SLP-IOR: An interactive model management system for stochastic linear programs
In this paper stochastic linear programming (SLP) is considered from the model management point of view. General model management issues specific to SLP are discussed in connection with their implementation in...
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Book and Conference Proceedings
System Modelling and Optimization
Proceedings of the 15th IFIP Conference Zurich, Switzerland, September 2–6, 1991
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Book
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Chapter and Conference Paper
Optimierungsverfahren — Eine Einführung —
Im Rahmen dieser Einführung wollen wir unter einem Optimierungsproblem eine Aufgabe verstehen, die sich folgendermassen formulieren lässt: Für eine vorgegebene Teilmenge C ⊂ ℝn
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Article
Computational methods for solving two-stage stochastic linear programming problems
Approximating a given continuous probability distribution of the data of a linear program by a discrete one yields solution methods for the stochastic linear programming problem with complete fixed recourse. F...
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Book Series
Ökonometrie und Unternehmensforschung / Econometrics and Operations Research
Volume 2 / 1966 to Volume 21 / 1976
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Book
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Chapter
Chance Constrained Programming
Whereas two-stage problems, as we have seen in the last chapter, are rather well-behaved from the viewpoint of optimization theory as far as convexity, continuity and differentiability are concerned, this is i...
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Chapter
Introduction
In view of the fact that sometimes there seems to be a terminological confusion, it might be useful to try to explain what stochastic linear programming is. There are many practical situations for which — at firs...
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Chapter
Prerequisites
Linear Programs are special mathematical programming problems. We understand by a mathematical programming problem in the Euclidean space ℝ n the optimization of a given real-valued...
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Chapter
Distribution Problems
Let us consider the linear program
(1) $$ determine\,\gamma = inf{c^,}x subject\,to Ax = b\,x \geqslant 0 $$ wh...
