A Route Improvement Algorithm for the Vehicle Routing Problem with Time Dependent Travel Times

In urban areas, congestion creates a substantial variation in travel speeds during peak morning and evening hours. This research presents a new solution approach, an iterative route construction and improvement algorithm (IRCI), for the time dependent vehicle routing problem (TDVRP) with hard or soft time windows. Improvements are obtained at a route level; hence the proposed approach does not rely on any type of local improvement procedure. Further, the solution algorithms can tackle constant speed or time-dependent speed problems without any alteration in their structure. A new formulation for the TDVRP with soft and hard time windows is presented. Leveraging on the well known Solomon instances, new test problems that capture the typical speed variations of congested urban settings are proposed. Results in terms of solution quality as well as computational time are presented and discussed. The computational complexity of the IRCI is analyzed and experimental results indicate that average computational time increases proportionally to the square of the number of customers.