In this paper, we consider chance constrained programming (CCP) technique when at least two of the LHS input coefficients are random with 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 correlation coefficient ρ.
Approach 1 for independence is an extension of Biswal's approach deals with m independent two – parameter exponential input coefficients instead of single-parameter ones. Approach 2 of dependence uses 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 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 single parameter exponential marginal when the second parameter is zero