An integer programming approach for linear programs with probabilistic constraints

Linear programs with joint probabilistic constraints (PCLP) are difficult to solve because the feasible region is not convex. 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 give a mixed-integer programming formulati...

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Bibliographic Details
Published inMathematical programming Vol. 122; no. 2; pp. 247 - 272
Main Authors Luedtke, James, Ahmed, Shabbir, Nemhauser, George L.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.04.2010
Springer
Springer Nature B.V
Subjects
Applied sciences
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Exact sciences and technology
Flows in networks. Combinatorial problems
Full Length Paper
Hierarchies
Inequality
Integer programming
Knapsack problem
Linear programming
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Probability
Production planning
Random variables
Stochastic models
Studies
Systems engineering
Theoretical
Integer programming
Probabilistic constraints
90C11
Chance constraints
90C15
Mixing set
Stochastic programming
Probabilistic approach
Linear programming
Mixed integer programming
Random vector
Combinatorial optimization
Modeling
Knapsack problem
Case study
Mathematical programming
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Summary:Linear programs with joint probabilistic constraints (PCLP) are difficult to solve because the feasible region is not convex. 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 give a mixed-integer programming formulation for this special case and study the relaxation corresponding to a single row of the probabilistic constraint. We obtain 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 which indicate that by using our strengthened formulations, instances that are considerably larger than have been considered before can be solved to optimality.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-008-0247-4