Multi-attribute label matching algorithms for vehicle routing problems with time windows and backhauls

We consider the class of vehicle routing problems with backhauls and time window constraints. Our motivating application is the land transportation of air-cargo freight forwarders, which requires fast solution times and the ability to handle various operational issues such as heterogeneous vehicles, multiple trips per vehicle, and penalty for early arrival at customer sites. We formulate the problem in the framework of label matching where the labels have multiple attributes representing the states of vehicles at customer locations or possible routes that vehicles may continue to cover. Two optimization-based heuristics are developed. Experimental tests on random problems and real data show that the methods can produce quality solutions quickly and are flexible in incorporating complex constraints.