A Chance Constrained Multiple Choice Programming Algorithm

This paper considers multiple choice programming problems in which the elements of the activity matrix can be normally distributed random variables or random vectors. The truncated block enumeration method of multiple choice programming is described and used in the development of an algorithm to solve problems of this type. Deterministic inequalities computed from the means and variances are employed by the block pivoting algorithm to assure fast convergence to a (sub)optimal solution. The solution will satisfy each constraint with the required marginal probabilities, but a lower bound of the joint probabilities is also computed. As an option, problems can be solved when the lower bound of the joint probability that all the constraints are satisfied is specified alone.