The authors study here a problem of scheduling n job types on m parallel machines, when setups are required and the demands for the products are correlated random variables. They model this problem as a chance constrained integer program. Methods of solution currently available-in integer programming and stochastic programming-are not sufficient to solve this model exactly. The authors develop and introduce here a new approach, based on a geometric interpretation of some recent results in Gröbner basis theory, to provide a solution method applicable to a general class of chance constrained integer programming problems. The present algorithm is conceptually simple and easy to implement. Starting from a (possibly) infeasible solution, the authors move from one lattice point to another in a monotone manner regularly querying a membership oracle for feasibility until the optimal solution is found. They illustrate this methodology by solving a problem based on a real system.
