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.