On the Distance Constrained Vehicle Routing Problem

We analyze the vehicle routing problem with constraints on the total distance traveled by each vehicle. Two objective functions are considered: minimize the total distance traveled by vehicles and minimize the number of vehicles used. We demonstrate a close relationship between the optimal solutions for the two objective functions and perform a worst case analysis for a class of heuristics. We present a heuristic that provides a good worst case result when the number of vehicles used is relatively small.