A Cross Decomposition Algorithm for Capacitated Facility Location

We present an implementation of the Cross Decomposition method to solve the capacitated facility location problem. The method unifies Benders Decomposition and Lagrangean relaxation into a single framework that involves successive solutions to a transportation problem and a simple plant location problem. Computational tests on problems with as many as 100 candidate facility locations and 200 customers provide evidence that the approach is superior to several other methods. The specialized Cross Decomposition program is, on a common set of test problems, about ten times faster than several recently developed programs. We also present a simple algorithm to strengthen Benders cuts.