Multicommodity vs. Single-Commodity Routing

In most of the literature on vehicle routing problems, a single numeric value expresses the demand of a customer. The typical constraint is that the total demand served by a vehicle cannot exceed the vehicle capacity. It is usually understood that all vehicles can serve all customers. If different commodities require different vehicles, it is assumed that, in a previous phase, it has been decided which vehicles will serve which set of customers. Then, a routing problem is solved, limited to the customers requesting a commodity and to the vehicles assigned to that commodity. In this paper, we study the cost implications from using vehicles dedicated to a single commodity compared with using flexible vehicles capable of carrying any set of commodities. The problem we study has several important applications. A first natural category of applications is the one where different vehicles are available on the market, namely vehicles that are specific for a commodity and vehicles that are flexible and may be used for different commodities. Usually, the flexible vehicles are more expensive than the specific vehicles, and a decision has to be made about whether it is beneficial to invest in the flexible vehicles. A decision can be made only through the evaluation of the reduction of the operational costs due to the availability of the flexible vehicles with respect to the operational costs in case the specific vehicles are used. An example of this category of problems can be observed in waste management, where vehicles are available to collect one kind of waste only, and more expensive vehicles are also available that may collect two different kinds of waste at a time. These latter vehicles have the container divided in two sections. Similar problems are met, for example, when frozen and non-frozen food have to be delivered to the same customers. The question becomes whether it is more beneficial to