We are analyzing https://link.springer.com/article/10.1007/s10107-008-0247-4.

Title:
An integer programming approach for linear programs with probabilistic constraints | Mathematical Programming
Description:
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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Keywords {🔍}

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Topics {✒️}

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         headline:An integer programming approach for linear programs with probabilistic constraints
         description: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.
         datePublished:2008-10-10T00:00:00Z
         dateModified:2008-10-10T00:00:00Z
         pageStart:247
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            Calculus of Variations and Optimal Control; Optimization
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            Combinatorics
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            Mathematical Methods in Physics
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      headline:An integer programming approach for linear programs with probabilistic constraints
      description: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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         Integer programming
         Probabilistic constraints
         Chance constraints
         Mixing set
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         90C15
         Calculus of Variations and Optimal Control; Optimization
         Mathematics of Computing
         Numerical Analysis
         Combinatorics
         Theoretical
         Mathematical and Computational Physics
         Mathematical Methods in Physics
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