Validating vehicle routing zone construction using Monte Carlo simulation

The primary purpose of this paper is to validate a clustering procedure used to construct contiguous vehicle routing zones (VRZs) in metropolitan regions. Given a set of customers with random demand for pickups and deliveries over the day, the goal of the design problem is to cluster the customers into zones that can be serviced by a single vehicle. Monte Carlo simulation is used to determine the feasibility of the zones with respect to package count and tour time. For each replication, a separate probabilistic traveling salesman problem (TSP) is solved for each zone. For the case where deliveries must precede pickups, a heuristic approach to the TSP is developed and evaluated, also using Monte Carlo simulation. In the testing, performance is measured by overall travel costs and the probability of constraint violations. Gaps in tour length, tour time and tour cost are the measure used when comparing exact and heuristic TSP solutions. To test the methodology, a series of experiments were conducted using data provided by a leading shipping carrier for the Pittsburgh area. Currently, the region is divided into 73 VRZs, compared to 64 indicated by the clustering procedure. The simulation results showed that a redesign would yield approximately $334,360 in annual savings without any noticeable deterioration in service. In addition, when the heuristic TSP model was solved in place of the exact model, the average gap in tour duration increased by only 0.16 hours and 0.2 hours for the cases of 73 clusters and 64 clusters, respectively, indicating a small upward bias. However, runtimes decreased by almost 70%.