(SPEPS)
Springer (Berlin [u.a.])
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| edoc-Server der Humboldt-Universität zu Berlin |
| Author(s): | Andrzej Ruszczynski, RUTCOR, Rutgers Center for Operations Research | Title: | Probabilistic programs with discrete distributions and precedence constrained knapsack polyhedra |
| Date of Acceptance: | 05.10.2000 |
| Submission Date: | 02.10.2000 |
| Series Title: |
Stochastic Programming E-Print Series (SPEPS) |
| Editors: | Julie L. Higle; Werner Römisch; Surrajeet Sen |
| Keywords (eng): | Probabilistic Programming, Integer Programming, Valid Inequal |
| Appeared in: |
Mathematical programming 2 (Vol. 93, 2002)
Springer (Berlin [u.a.]) |
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| Abstract (eng): | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 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 inequalities for these mixed integer programs. 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. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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