Vehicle routing problems (VRPs) have usually been studied with a single objective function defined by the distances associated with the routing of vehicles. The central problem is to design a set of routes to meet the demands of customers at minimum cost. However, in real life, it is necessary to take into account other objective functions, such as social functions, which consider, for example, the drivers' workload balance. This has led to growth in both the formulation of multiobjective models and exact and approximate solution techniques. In this article, to verify the quality of the results, first, a mathematical model is proposed that takes into account both economic and work balance objectives simultaneously and is solved using an exact method based on the decomposition approach. This method is used to compare the accuracy of the proposed approximate method in test cases of medium mathematical complexity. Second, an approximate method based on the Iterated Local Search (ILS) metaheuristic and Decomposition (ILS/D) is proposed to solve the biobjective Capacitated VRP (bi-CVRP) using test cases of medium and high mathematical complexity. Finally, the nondominated sorting genetic algorithm (NSGA-II) approximate method is implemented to compare both medium- and high-complexity test cases with a benchmark. The obtained results show that ILS/D is a promising technique for solving VRPs with a multiobjective approach.

A multi-objective methodology was proposed for solving the green vehicle routing problem with a private fleet and common carrier considering workload equity. The iterated local search metaheuristic, which is adapted to the solution of the problem with three objectives, was proposed as a solution method. A solution algorithm was divided into three stages. In the first, initial solutions were identified based on the savings heuristic. The second and third act together using the random variable neighbourhood search algorithm, which allows performing an intensification process and perturbance processes, giving the possibility of exploring new regions in the search space, which are proposed within the framework of optimizing the three objectives. According to the previous review of the state of the art, there is little related literature; through discussions with the productive sector, this problem is frequent due to increases in demand in certain seasons or a part of the maintenance vehicle fleet departing from service. The proposed methodology was verified using case studies from the literature, which were adapted to the problem of three objectives, obtaining consistent solutions. Where cases were not reported in the literature, these could be used as a reference in future research.

During the past few years, transportation of agricultural products is increasingly becoming a crucial problem in supply chain logistics. In this paper, we present a new mathematical formulation and two solution approaches for an intermodal transportation problem. The proposed bi-objective model is applied to the transportation of agricultural products from Morocco to Europe to minimise both the transportation cost either in the form of uni-modal or intermodal, as well as the maximal overtime to delivery products. The first solution approach is based on a non-dominated sorting genetic algorithm improved by a local search heuristic and the second one is the GRASP algorithm (Greedy Randomised Adaptive Search Procedure) with iterated local search heuristics. They are tested on theoretical and real case benchmark instances and compared with the standard NSGA-II. Results are analysed and the efficiency of algorithms is discussed using some performance metrics.