A Chance Constrained Multiple Choice Programming Algorithm.

A multiple choice programming problem is considered where the elements of the activity matrix can be random variables or random vectors. The truncated block enumeration method of multiple choice programming is described and used in the development of the algorithm. Efficient use of inequalities computed from the means and variances affected by blockpivoting assures fast convergence to a sub optimal solution. The solution will satisfy each constraint with the required marginal probabilities, but the 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. Sample solutions of an elementary stochastic menu problem illustrate the working of the options and the meaning of possible interpretations of chance constraints. Author