Distance discount in the green vehicle routing problem offered by external carriers

Abstract

This study suggested a model for the Green Vehicle Routing Problem (GVRP) regarding distance discount strategy. For the first time,we defined distance discount strategy based on intervals for a vehicle routing problem. The proposed model attempts to minimize the total cost of the system by selecting the different vehicles and paths that have time and fuel constraints while external carriers offer the distance discount. This model is formulated by mixed-integer linear programming and classified as NP-hard. The feasibility of this issue depends on the location of customers and fuel stations. Two metaheuristic algorithms such as tabu search (TS) and simulated annealing (SA) have been developed beside the exact method, and the efficiency of our metaheuristic methods have been examined through 40 benchmark instances of different sizes and 16 randomly generated numerical instances. Computational results show superior performance of the simulated annealing in comparison with the tabu search for test problems and the cost efficiency owing to the distance discount from the organization's outlook.