2010

Change-constrained stochastic programming problem with normal, t and skew normal, skew t distributions

In this paper, a change constrained optimization programming problem is studied under the assumption that the model coe¢ cients in the inequalities defned as random variables are independent and assumed to be Normal, t; Non Normal Skew distributions; Skew Normal and Skew t distributions. The Hulkursar method transform the stochastic programming problem into a non-linear deterministic problem is used in the study. The most common distribution in CCSP is the Normal Distribution; but the real world problems always may not include normality.Therefore; in the practice stage, an application that the aij technologic coefficient and the bi right side values in the inequalities have both Normal, t; Skew Normal and Skew t distributions is given. Finally the obtained results have been compared.

Keywords:

Change Constrained Stochastic Programming, Skewness, Skew Normal Distribution Skew t Distribution,

PDF

___

Azzalini, A., A class of distributions which includes the normal ones, Scandinavian Journal of Statistics,12 (1985), 171–178.
Azzalini, A., Further results on a class of distributions which includes the normal ones. Statistica, 46(2) (1986), 199-208.
Azzalini, A and Capitanio, A, Distributions generated by perturbation of symmetry wtih emphasis on a multivariate skew t distribution, Journal of the Royal Statistical Society, Series B ( Statistical Methodology), 65(2) (2003), 367-389.
Azzalini, A., The skew-normal distribution and related multivariate families (with discussion), Scandinavian Journal of Statistics, 32 (2005),159–188.
Arslan, O., A review on the univariate skew t-distributions, Far EAST Journal of Theoretical Statistics 34(1) (2011),17-34.
Atalay,K. and Apaydin,A., Gamma distribution approach in change-constrained stochastic programming model, Journal of Inequalities and Applications 1(108) (2011) , 3-13.
Azzalini, A.,The Skew Normal and related families. Cambridge University Press, (2014).
Charnes, A. and Cooper, W.W., Chance constrained programming, Management Science, 6 (1959), 73- 79.
Gupta, A.K., Chang, F.C. and Huang, W.C., Some skew symmetric models, Random Operators and Stochastic Equations, 10 (2) (2002), 133-140.
Gupta, A.K., Multivariate skew t distributions, Statistics: A Journal of Theoretical and Applied Statistics, 37(4) (2003), 359-363.
Hulsurkar et al., Fuzzy programming approach to multi-objective stochastic linear programming problems, Fuzzy Sets and Systems 88 (1997), 173-181.
Stancu-Minasian, I.M. and Wets, M.J., A research bibliography in stochastic programming, Oper.Res. 24 (6) (1976), 955-1975.
Lin, T.I., Lee, J.C. and Yen, S.Y. ,Finite mixture modelling using the skew normal distribution, Statistica Sinica, 17(3) (2007), 909-927.
O’Hagan, A. and Leonard, T., Bayes estimation subject to uncertainty about parameter constraints, Biometrika,63(1) (1976), 201-203.
Yılmaz, M., Edgeworth series pproximation for chi-square type chance constraints, Communications Faculty of Sciences University of Ankara Series A1, 56(2) (2007), 27–37.
Yılmaz, M. Edgeworth series approximation for gamma type chance constraints, Selcuk Journal of Applied Mathematics, 10(1) (2009), 75–89.
Yılmaz, M and Potas N., Solutions to change-constrained programming problems with exponential random variables by edgeworth approximatin, Chaos Complexity Leadership Springer Proceedings in Complexity. (2016),1-22.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics-Cover

ISSN: 1303-5991
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 1948
Yayıncı: Ankara Üniversitesi

Arşiv