Heuristic approaches to vehicle routing with backhauls and time windows

The vehicle routing problem with backhauls and time windows (VRPBTW) involves the pickup and delivery of goods at different customer locations, with earliest and latest time deadlines, and varying demands. The demands are serviced using capacitated vehicles with limited route time. Moreover, all deliveries (linehauls) must be done before the pick-ups (backhauls). The objective of the problem is to service all customers while minimizing the number of vehicles and distance travelled while not violating the capacity and route time constraints of the vehicles, and the time window constraint at each customer. In this paper, we describe a route construction heuristic for the VRPBTW, as well as different local search heuristics to improve the initial solution. The heuristics were tested on 45 problems obtained from the literature, consisting of 25, 50 and 100-customer problems for which the optimal solutions are known in most cases. The solutions produced by the heuristics are within 2.5% of the optimal solutions on average.