Bounds for probabilistic integer programming problems

Darinka Dentcheva; András Prékopa; Andrzej Ruszczyski

doi:10.1016/S0166-218X(01)00329-8

Bounds for probabilistic integer programming problems

Darinka Dentcheva, András Prékopa, Andrzej Ruszczyski

Rutgers Business School, Management & Information Systems

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

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.

Original language	English (US)
Pages (from-to)	55-65
Number of pages	11
Journal	Discrete Applied Mathematics
Volume	124
Issue number	1-3
DOIs	https://doi.org/10.1016/S0166-218X(01)00329-8
State	Published - Dec 15 2002

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

Keywords

Column generation
Integer programming
Probabilistic constraints
Stochastic programming

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10.1016/S0166-218X(01)00329-8

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AU - Prékopa, András

AU - Ruszczyski, Andrzej

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N2 - 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.

AB - 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.

KW - Column generation

KW - Integer programming

KW - Probabilistic constraints

KW - Stochastic programming

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Bounds for probabilistic integer programming problems

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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