Profitable Vehicle Routing Problem with Multiple Trips: Modeling and constructive heuristics

In this paper, we study a new variant of the Vehicle Routing Problem (VRP) which combines two known variants: the Profitable VRP (PVRP) and the VRP with Multiple Trips (VRPMT). This problem may be called as (PVRPMT). The problem´s objective is to maximize the sum of collected profit prior to the customers visit minus the transportation costs. This problem has a very practical interest especially for daily distribution schedules with a short course transportation network and a limited vehicle fleet. A discursive method for profit quantification is suggested so as to make it more realistic. A mixed integer programming formulation of the problem is proposed. In addition, two constructive heuristics and a set of benchmark instances which include small and large size data are provided. Finally, a computational study evaluates and compares the performance of the different proposed methods.