This paper proposes a new cost function based on distance and load of the vehicle for the Capacitated Vehicle Routing Problem. The vehicle-routing problem with this new load-based cost objective is called the Energy Minimizing Vehicle Routing Problem (EMVRP). Integer linear programming formulations with O(n 2) binary variables and O(n2) constraints are developed for the collection and delivery cases, separately. The proposed models are tested and illustrated by classical Capacitated Vehicle Routing Problem (CVRP) instances from the literature using CPLEX 8.0.