Chance Constrained Programming with Joint Constraints

Bruce L. Miller and Harvey M. Wagner
Additional contact information
Bruce L. Miller: Stanford University, Stanford, California
Harvey M. Wagner: Stanford University, Stanford, California

Operations Research, 1965, vol. 13, issue 6, 930-945

Abstract: This paper considers the mathematical properties of chance constrained programming problems where the restriction is on the joint probability of a multivariate random event. One model that is considered arises when the right-handside constants of the linear constraints are random. Another model treated here occurs when the coefficients of the linear programming variables are described by a multinormal distribution. It is shown that under certain restrictions both situations can be viewed as a deterministic nonlinear programming problem. Since most computational methods for solving nonlinear programming models require the constraints be concave, this paper explores whether the resultant problem meets the concavity assumption. For many probability laws of practical importance, the constraint in the first type of model is shown to violate concavity. However, a simple logarithmic transformation does produce a concave restriction for an important class of problems. The paper also surveys the “generalized linear programming” method for solving such problems when the logarithmic transformation is justified. For the second type model, the constraint is demonstrated to be nonconcave.

Date: 1965
References: Add references at CitEc
Citations: View citations in EconPapers (60)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.13.6.930 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:13:y:1965:i:6:p:930-945

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().