An Integer Programming Approach for Linear Programs with Probabilistic Constraints

Linear programs with joint probabilistic constraints (PCLP) are known to be highly intractable due to the non-convexity of the feasible region. We consider a special case of PCLP in which only the right-hand side is random and this random vector has a finite distribution. We present a mixed integer...

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Bibliographic Details
Published inInteger Programming and Combinatorial Optimization Vol. 4513; pp. 410 - 423
Main Authors Luedtke, James, Ahmed, Shabbir, Nemhauser, George
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2007
Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Integer programming
probabilistic constraints
stochastic programming
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ISBN9783540727910
3540727914
ISSN0302-9743
1611-3349
DOI10.1007/978-3-540-72792-7_31

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Summary:Linear programs with joint probabilistic constraints (PCLP) are known to be highly intractable due to the non-convexity of the feasible region. We consider a special case of PCLP in which only the right-hand side is random and this random vector has a finite distribution. We present a mixed integer programming formulation and study the relaxation corresponding to a single row of the probabilistic constraint, yielding two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. We present computational results that indicate that by using our strengthened formulations, large scale instances can be solved to optimality.
ISBN:9783540727910
3540727914
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-540-72792-7_31