Cell-and-bound algorithm for chance constrained programs with discrete distributions

Chance constrained programing (CCP) is often encountered in real-world applications when there is uncertainty in the data and parameters. We consider in this paper a special case of CCP with finite discrete distributions. We propose a novel approach for solving CCP. The methodology is based on the connection between CCP and arrangement of hyperplanes. By involving cell enumeration methods for an arrangement of hyperplanes in discrete geometry, we develop a cell-and-bound algorithm to identify an exact solution to CCP, which is much more efficient than branch-and-bound algorithms especially in the worst case. Furthermore, based on the cell-and-bound algorithm, a new polynomial solvable subclass of CCP is discovered. We also find that the probabilistic version of the classical transportation problem is polynomially solvable when the number of customers is fixed. We report preliminary computational results to demonstrate the effectiveness of our algorithm.