Routing relatively few customers per route

This paper presents a modification of the well-known Solomon (1987) sequential insertion heuristic I1 for the Vehicle Routing Problem with Time Windows (VRPTW). VRPTW involves servicing customers within a pre-specified service time window by homogeneously capacitated vehicles from a single depot. By using two new measures for the additional time needed to insert a customer in the route, significantly better solutions are obtained for relatively short routes compared to the original Solomon (1987) sequential insertion heuristic I1. Because high-quality initial heuristics often allow local searches and metaheuristics to achieve better solutions more quickly, the new approach is likely to help generating better solutions to practical routing problems.