Mathematical Models for the Vehicle Routing Problem by Considering Balancing Load and Customer Compactness

The vehicle routing problem seeking to minimize the traveled distance and the deviation of the total workload is known as the vehicle routing problem with workload balance (WBVRP). In the WBVRP, several elements are considered: (i) the total distance or driving time, (ii) the number of customers to be visited, and (iii) the total weight or amount of delivered goods. We have considered the WBVRP by adding a concept called customer compactness and the visual attractiveness of the routes. The WBVRP allows a similar workload for drivers to improve their well-being and social development. Unbalanced routes could generate high costs due to potential strikes by drivers seeking an equitable workload. We have proposed three mathematical formulations for solving the WBVRP by minimizing the customer compactness and the distance with and without considering workload balancing. The workload balancing is based on the deviation concerning the average load of the routes and considering waiting and driving time. We have tested the efficiency of the proposed models on a synthetic set of instances, analyzing different aspects such as depot location, customer location, and demand. The analysis of the results has been performed considering customer compactness and the visual attractiveness of the obtained solution. Computational experiments on generated random instances show the efficiency of the proposed approaches.