Chance Constrained Programming with Exponential Input Coefficients

Document Type : Original Article

Authors

Department of Mathematics, Insurance and Applied Statistics, Faculty of commerce and Business Administration, Helwan University

Abstract

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

Keywords