Research Reports from the Department of Operations
Document Type
Report
Publication Date
1-1-1966
Abstract
In the present thesis, we want to show that a programming problem with joint stochastic constraints can be treated generally and under relatively simple conditions, as a quasi-concave programming problem. In some cases, the same problem may be equivalent to a concave programming problem after a logarithmic transformation. It has been shown by Charnes and Cooper that a stochastic programming problem where each constraint has to be achieved with a given probability, can be put under the form of a deterministic programming problem which is concave under some assumptions [1]. The "joint chance-constraint" formulation presented here is less restrictive and yields a further result. However, the random variables will appear only in the demand vector. An algorithmic method for finding an optimum solution is presented and applied on some numerical examples.
Keywords
Stochastic processes, Operations research, Mathematical optimization, Programming (Mathematics), Nonlinear programming, Algorithms, Constrained optimization
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 47
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Doulliez, Pierre J., "Mathematical Programming with Joint Stochastic Constraints" (1966). Research Reports from the Department of Operations. 288.
https://commons.case.edu/wsom-ops-reports/288