On Chance Constrained Programming Problems with Joint Constraints

In this paper we consider chance constrained programming problems with joint constraints shown in the literature to be equivalent deterministic nonlinear programming problems. Since most existing computational methods for solution require that the constraints of the equivalent deterministic problem be concave, we obtain a simple condition for which the concavity assumption holds when the right-hand side coefficients are independent random variables. We show that it holds for most probability distributions of practical importance. For the case where the random vector has a multivariate normal distribution, nonexistence of any efficient numerical methods for evaluating multivariate normal integrals necessitates the use of lower bound approximations. We propose an approximation for the case of positively correlated normal random variables.