The lexicographical capacitated vehicle routing problem

The objective of the Capacitated Vehicle Routing Problem is to find routes with minimal cost for a homogeneous fleet of vehicles to serve all the customers, without violating the capacity of the vehicles. Usually, in the basic version of the problem a set of identical vehicles, with a known capacity, is available at the depot and additional objective requiring the minimization of the number of used vehicles. If the number of vehicles to be used is fixed, we may require to minimize the maximum load of vehicles. In this paper we examine the CVRP with fixed number of vehicles with equal capacity and two main goals: the first is to minimize the capacity of the vehicles and the second is to minimize the total travel cost. This variant of the CVRP we call the Lexicographical Capacitated Vehicle Routing Problem.