Bounds for probabilistic integer programming problems

Authors:
Darinka Dentcheva;András Prékopa;Andrzej Ruszczyński
Affiliations:
Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ;RUTCOR, Rutgers Center for Operations Research, Rutgers University, 640, Bartholomew Road, Piscataway, NJ;RUTCOR, Rutgers Center for Operations Research, Rutgers University, 640, Bartholomew Road, Piscataway, NJ
Venue:
Discrete Applied Mathematics - Workshop on discrete optimization DO'99, contributions to discrete optimization
Year:
2002

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Abstract

We consider stochastic integer programming problems with probabilistic constraints. The concept of p-efficient points of a probability distribution is used to derive various equivalent problem formulations. Next we introduce new methods for constructing lower and upper bounds for probabilistically constrained integer programs. We also show how limited information about the distribution can be used to construct such bounds. The concepts and methods are illustrated on an example of a vehicle routing problem.