On Capacitated Vehicle Routing

We consider the capacitated vehicle routing problem (VRP): a fixed fleet of delivery vehicles of uniform capacity must service at minimal transit cost from a common depot known customer demand for a single commodity. This problem is modeled as a side-constrained traveling salesman problem (TSP). Among the additional constraints are the vehicle capacity restrictions, analogous to TSP subtour elimination constraints. We present several variants of a branch-and-cut algorithm for this VRP model, with separation methodology for the capacity restrictions based on the TSP polyhedral relaxation. Specifically, when standard procedures fail to separate a candidate point, we attempt to separate it via decomposition into a convex combination of TSP tours; if successful, the tours present in this decomposition are examined for violated capacity restrictions, and if not, the Farkas Theorem provides a hyperplane separating the point from the TSP polytope. Computational results are given for an implementation within the parallel branch-and-cut framework COMPSys; the platform is the IBM SP2 of the Cornell Theory Center. This research was partially supported by NSF Grants DMS89-20550 and DMS-9527124. School of OR&IE, Cornell University, Ithaca, NY 14853 Department of Mathematical Sciences, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598 School of OR&IE, Cornell University, Ithaca, NY 14853 ([email protected])