Chance-Constrained Programming

Charnes, A.; Cooper, W. W.

doi:10.1287/mnsc.6.1.73

Cited by 2,286 publications

(958 citation statements)

References 3 publications

Supporting

Mentioning

945

Contrasting

Unclassified

Order By: Relevance

“…The concept of chance-constrained programming (CCP), which was introduced by Charnes and Cooper [5], is adopted to solve the FIR model (4). CCP deals with uncertainty by specifying the desired levels of confidence for which the constraints hold.…”

Section: Input Relaxation Congestion Model In Fuzzy Deamentioning

confidence: 99%

An input relaxation model for evaluating congestion in fuzzy DEA

Kheirollahi

Hessari

Charles

et al. 2017

Croat. Oper. Res. Rev.

View full text Add to dashboard Cite

Abstract. This paper develops a BCC input relaxation model for identifying input congestion as a severe form of inefficiency of decision-making units in fuzzy data envelopment analysis. The possibility approach is presented to obtain the models equivalent to fuzzy models. We use a one-model approach to determine input congestion based on the BCC input relaxation model. A numerical example is given to illustrate the proposed model and identify the congestion with precise and imprecise data. The proposed model is also used to determine the congestion in 16 hospitals using four fuzzy inputs and two fuzzy outputs with a symmetrical triangular membership function.

show abstract

Section: Input Relaxation Congestion Model In Fuzzy Deamentioning

confidence: 99%

An input relaxation model for evaluating congestion in fuzzy DEA

Kheirollahi

Hessari

Charles

et al. 2017

Croat. Oper. Res. Rev.

View full text Add to dashboard Cite

show abstract

“…25 The main idea of chance constrained programming is to optimize the critical value of the fuzzy objective with certain confidence level subject to some chance constraints. Let D be the given integral upper bound of the spanning trees.…”

Section: Chance-constrained Programming Models Of Dcfmstmentioning

confidence: 99%

Diameter Constrained Fuzzy Minimum Spanning Tree Problem

Nayeem

Pal

2013

IJCIS

View full text Add to dashboard Cite

In this paper, we have studied the constrained version of the fuzzy minimum spanning tree problem. Costs of all the edges are considered as fuzzy numbers. Using the m λ measure, a generalization of credibility measure, the problem is formulated as chance-constrained programming problem and dependent-chance programming problem according to different decision criteria. Then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers. Furthermore, a fuzzy simulation based hybrid genetic algorithm is designed to solve the proposed models using Prüfer like code representation of labeled trees.

show abstract

Section: Acknowledgementsmentioning

confidence: 99%

“…It was shown that the objective function increases, if the specified Introduction 3 constraints have to be satisfied with a higher probability. Examples of application of the CCP technique can also be found in [18][19][20].An alternative approach to the above optimization technique, using an Advanced First Order Second Moment Method, was presented by Nikolaidis and Burdisso in [7]. It was called Safety Index Optimization (SIO), because the , constraints were expressed in terms of the safety index that corresponded to the physical constraints.…”

mentioning

confidence: 99%

Integrated analysis and design in stochastic optimization

Maglaras

Nikolaidis

1990

Structural Optimization

View full text Add to dashboard Cite

The new approach is applied to the design of a simple structure. Both methods are robust to a satisfactory degree. The results are compared to those obtained by the safety index approach without integrating the analysis and design processes. The new methods substantially reduce the computational cost of optimization, which indicates that integrated analysis and design has the potential of removing a major obstacle, which is the excessive computational cost, in applying stochastic optimization to real life structural design. AcknowledgementsAcknowlcdgcments iii;"- Introduction Structural optimization has seen remarkable progress in recent years and is now recognized as a practical design tool. The development of the above method was associated with the advancement in several other areas like:• Establishment of finite element methods.• Advancement in computer technology.• Creation of new, more efficient and robust optimization algorithms.• Development of semi-analytical procedures for sensitivity analysis. By semi-analytical we mean that the expressions developed, involved terms, that had to be calculated numerically.Introduction l I-Iowever, it is generally recognized that structural problems are often non-deterministic and, consequently, decisions have to be made in the presence of uncertainties. That gave birth, in the last one-two decades to systematic procedures for decision making under uncertainties, through the concept of reliability.In general, a stochastic programming problem is an optimization problem in.which some or all of the parameters are described by random variables rather than by deterministic quantities. The basic idea of all stochastic programming methods is to convert the probabilistic problem into an equivalent deterministic one.One of the first publications dealing with reliability based optimization design was published by F. Moses and D.E. Kinser [1]. There, techniques for tinding the minimum weight design of a multi-load, multi-element structure with a prescribed level of safety have been described. Any form of frequency distribution for loads and strengths can be treated, but the probabilistic analysis is applicable only to conventional structures, for which there is a valid structural analysis. It was also demonstrated that an overall level of structural safety can be prescribed in terms of a rational criterion, like the probability of failure, and minimum weight structures can be designed to meet the prescribed safety level.Thoft-Christensen and Sorensen [2,3], established a procedure for system reliability based optimization for framed structures, using the beta-unzippinng method for estimating system reliability. Sensitivity derivatives of the safety index of each failure element of the system were calculated using semi-analytical Introduction 2formulas. Feng and Moses [4], derived an optimality criterion for sizing the components of framed structures, that satisfy a system reliability constraint. This criterion, which is a special case of the Kuhn-Tucker conditions, states tha...

show abstract

Chance-Constrained Programming

Cited by 2,286 publications

References 3 publications

An input relaxation model for evaluating congestion in fuzzy DEA

An input relaxation model for evaluating congestion in fuzzy DEA

Diameter Constrained Fuzzy Minimum Spanning Tree Problem

Integrated analysis and design in stochastic optimization

Contact Info

Product

Resources

About