An Integer Programming Approach for Linear Programs with Probabilistic Constraints James Luedtke Shabbir Ahmed George Nemhauser H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology October 24, 2006 Contact: luedtke@gatech.edu Keywords: Integer programming, branch and cut algorithms Abstract Linear programs with joint probabilistic constraints (PCLP) are known to be highly in- tractable due to the non-convexity of the feasible region. We consider a special case of PCLP in which only the right-hand side is random and this random vector has a finite distribution. We present a mixed integer programming formulation and study the relaxation corresponding to a single row of the probabilistic constraint, yielding two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. We present computational results that indicate that by using our strengthened formulations, large scale instances can be solved to optimality.