Abstract
In this article, a method is developed to transform the chance-constrained programming problem into a deterministic problem. We have considered a chance-constrained programming problem under the assumption that the random variables a ij are independent with Gamma distributions. This new method uses estimation of the distance between distribution of sum of these independent random variables having Gamma distribution and normal distribution, probabilistic constraint obtained via Essen inequality has been made deterministic using the approach suggested by Polya. The model studied on in practice stage has been solved under the assumption of both Gamma and normal distributions and the obtained results have been compared.
Highlights
A chance-constrained stochastic programming (CCSP) models is one of the major approaches for dealing with random parameters in the optimization problems
Hulsurkar et al [5] have studied on a practice of fuzzy programming approach of multi-objective stochastic linear programming problems
Chance-constraint programming in stochastic is expanded to fuzzy concept by their studies. They have presented certain equations with chance constraint in some fuzzy concept identical to stochastic programming. They have suggested a fuzzy simulation method for chance constraints for which it is usually difficult to be changed into certain equations
Summary
A chance-constrained stochastic programming (CCSP) models is one of the major approaches for dealing with random parameters in the optimization problems. Atalay and Apaydin Journal of Inequalities and Applications 2011, 2011:108 http://www.journalofinequalitiesandapplications.com/content/2011/1/108 values with uniform random variable coefficients He presented the main idea related with the stochastic goal programming and chance-constraint linear goal programming. E (dk) + Kuk Var (dk) ≤ bk Solution methods for models constituted by dual and triple combinations of cj, akj and bk coefficients and for the case that cj’s are random variable are different In this article, these are not mentioned [5,19,20,21]. If akj’s which are kth row of coefficients matrix A are independent gamma random variables, chance constraints given in model (2.1) are as follows.
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