# Chance-Constrained Programming

@article{Charnes1959ChanceConstrainedP, title={Chance-Constrained Programming}, author={Abraham Charnes and William W. Cooper}, journal={Management Science}, year={1959}, volume={6}, pages={73-79} }

A new conceptual and analytical vehicle for problems of temporal planning under uncertainty, involving determination of optimal sequential stochastic decision rules is defined and illustrated by means of a typical industrial example. The paper presents a method of attack which splits the problem into two non-linear or linear programming parts, i determining optimal probability distributions, ii approximating the optimal distributions as closely as possible by decision rules of prescribed form.

## 2,004 Citations

CHANCE CONSTRAINED PROGRAMS WITH NORMAL DEVIATES AND LINEAR DECISION RULES

- Economics
- 1959

The possibilities of using chance-constrained programming models, in place of queuing models, and the solution of such a model for the leasing of tanker fleets is considered.

Linear Optimal Designs and Optimal Contingency Plans

- Computer Science
- 1990

The formulation and methods for locating potentially good designs and their corresponding optimal contingency plans using a multiple-criteria and multiple-constraint level MC2 simplex method to solve the optimal design problems which have been shown to become amenable to the techniques of decision making under uncertainty.

Multi-Goal Subset Selection Problems under Uncertainty

- Engineering
- 1979

A method for aiding the analysis of management decision problems involving multiple goals and constraints with uncertainties in the input data based on the determination of the alternative decision solution, which minimizes the probabilities that the decision maker's goals and constraint will not be met.

OPTIMAL DECISION RULES FOR THE E MODEL OF CHANCE-CONSTRAINED PROGRAMMING

- Computer Science
- 1965

The general n-period expectation- objective model of chance-constrained programming is presented and certain necessary conditions are established for decision rules to be optimal for such a model.

An experimental solution of the general stochastic programming problem

- Computer Science
- 1978

After reviewing existing approaches to the general stochastic programming problem, an improved experi mental method is proposed. This method uses a va riety of mathematical programming algorithms and…

A Linear Approximation for Chance-Constrained Programming

- Computer Science
- 1987

An approximation formula for chance constraints is presented which can be used in either the single- or multiple-objective case, and will place a bound on the chance constraint at least as tight as the true non-linear form, thus overachieving the chance constraints at the expense of other constraints or objectives.

On decision rules in stochastic programming

- EconomicsMath. Program.
- 1974

The paper surveys the basic results and nonresults for decision rules in stochastic programming. It exhibits some of the difficulties encountered when trying to restrict the class of acceptable rules…

Joint Chance-Constrained Reliability Optimization with General Form of Distributions

- Computer Science
- 2016

The chance-constrained reliability stochastic optimization (CCRSO) problem is described, for which the objective is to maximize the system reliability for the given joint chance constraints where only the resource variables are random in nature and which follow different general form of distributions.

Chance-Constraint-Based Heuristics for Production Planning in the Face of Stochastic Demand and Workload-Dependent Lead Times

- Business
- 2012

While the problem of planning production in the face of uncertain demand has been studied in various forms for decades, there is still no completely satisfactory solution approach. In this chapter we…

## References

Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil

- Business
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Scheduling heating oil production is an important management problem. It is also a complex one. Weather and demand uncertainties, allocation of production between different refineries, joint-and…