A Parallel Cutting-plane Algorithm for the Vehicle Routing Problem with Time Windows

In the vehicle routing problem with time windows a number of identical vehicles must be routed to and from a depot to cover a given set of customers, each of whom has a speciied time interval indicating when they are available for service. Each customer also has a known demand, and a vehicle may only serve the customers on a route if the total demand does not exceed the capacity of the vehicle. The most eeective solution method proposed to date for this problem is due to Kohl, Desrosiers, Madsen, Solomon, and Soumis. Their algorithm uses a cutting-plane approach followed by a branch-and-bound search with column generation, where the columns of the LP relaxation represent routes of individual vehicles. We describe a new implementation of their method, using Karger's randomized minimum-cut algorithm to generate cutting planes. The standard benchmark in this area is a set of 87 problem instances generated in 1984 by M. Solomon; making using of parallel processing in both the cutting-plane generation and the branch-and-bound search, we solve 80 of these examples, including 10 that were previously unsolved in the literature. Our parallel implementation utilizes the TreadMarks distributed shared memory system. A common element in many applications of vehicle routing is the notion of a time-window to specify that a customer's service must begin within a xed period. These windows may arise, for example, from commitments made to customers or from the limited availability of certain resources. Applied case studies involving time-constrained routing can be found in Caseau and Koppstein 9], Cheng and Rich 8], Knight and Hooer 24], Pullen and Webb 30], and elsewhere. Research eeorts in this area have focused on a variety of simpliied models that can be used as building blocks for the creation of tools to solve real-world instances. A survey of this work can be found in Desrosiers, Dumas, Solomon, and Soumis 15]. In our study we treat the vehicle routing problem with time windows (VRPTW) model that was proposed by Solomon 32]. In this model a number of identical vehicles must be