Chance Constrained Programming with Exponential Input Coefficients | ||
| The Egyptian Statistical Journal | ||
| Article 3, Volume 61, Issue 1, June 2017, Pages 41-57 PDF (5.06 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.2017.270058 | ||
| Authors | ||
| Nada Hafez* ; Afaf El-Dash; Nagwa Albehery | ||
| Department of Mathematics, Insurance and Applied Statistics, Faculty of Commerce and Business Administration, Helwan University. Egypt. | ||
| Abstract | ||
| In this paper, we consider the chance constrained programming (CCP) technique when at least two of the LHS input coefficients are random with a two-parameter exponential distribution. Two approaches are introduced to transform CCP into deterministic: (i) approach 1 assumes independence between exponential input coefficients, and (ii)approach 2 assumes that random input coefficients are dependent with a correlation coefficient ρ. Approach 1 for independence is an extension of Biswal's approach that deals with m independent two–parameter exponential input coefficients instead of single-parameter ones. Approach 2 of dependence uses the Downton bivariate exponential (DBE) distribution under two cases; the first introduced case assumes that dependent input coefficients have single-parameter exponential marginals, and the second introduced case is an extension of the DBE distribution for two-parameter exponentials. It was shown that the equivalent deterministic transformation of the extension of approach 2 is a generalization of both approach 1 for m=2 when ρ=0 and first case of approach 2 for a single parameter exponential marginal when the second parameter is zero | ||
| Keywords | ||
| Bessel function; Biswal's approach; Non-linear Programming; Probabilistic Programming; Stochastic Programming two; Exponential distribution | ||
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