Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra

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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.

Original languageEnglish (US)
Pages (from-to)195-215
Number of pages21
JournalMathematical Programming, Series B
Issue number2
StatePublished - Dec 2002

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)


  • Integer programming
  • Stochastic programming
  • Valid inequalities

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