Mathematical Programming

, Volume 93, Issue 2, pp 195–215 | Cite as

Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra

  • Andrzej Ruszczyński


 We consider stochastic programming problems with probabilistic constraints involving random variables with discrete distributions. They can be reformulated as large scale mixed integer programming problems with knapsack constraints. Using specific properties of stochastic programming problems and bounds on the probability of the union of events we develop new valid inequalities for these mixed integer programming problems. We also develop methods for lifting these inequalities. These procedures are used in a general iterative algorithm for solving probabilistically constrained problems. The results are illustrated with a numerical example.


Programming Problem Specific Property Integer Programming Iterative Algorithm Mixed Integer 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Andrzej Ruszczyński
    • 1
  1. 1.Rutgers University, Department of Management Science and Information Systems, Piscataway, NJ 08854, USA, e-mail: rusz@rutcor.rutgers.eduUS

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