Efficiency in logistics is often affected by the fair distribution of the customers along the routes and the available depots for goods delivery. From this perspective, in this study, the Multi-depot Vehicle Routing Problem (MDVRP), by considering two objectives, is addressed. The two objectives in conflict for MDVRP are the distance traveled by vehicles and the standard deviation of the routes’ length. A significant standard deviation value provides a small distance traveled by vehicles, translated into unbalanced routes. We have used a weighted average objective function involving the two objectives. A Variable Neighborhood Search algorithm within a Chu-Beasley Genetic Algorithm has been proposed to solve the problem. For decision-making purposes, several values are chosen for the weight factors multiplying the terms at the objective function to build up a non-dominated front of solutions. The methodology is tested in large-size instances for the MDVRP, reporting noticeable results for managerial insights.

Vehicle routing problem (VRP) is a classic problem studied in logistic. One of the most important variations within this problem is called Green Vehicle Routing Problem (GVRP), in which environmental aspects are considered when designing product delivery routes. This variant arises due to the high levels of pollution produced by transport vehicles, so it is a variation whose study represents a vital impact nowadays. This project will consider a GVRP and will be developed considering the characteristics of multi-depot (MDVRP) and multi-product (MPVRP) to minimize the costs of assignation of vehicles and CO2 emissions. To solve the problem, this project proposes a hybridization between the classic tabu search (TS) metaheuristic and the PAES algorithm (TS+PAES) to generate the Pareto frontier of both objectives. An integer mixed linear programming model is formulated and developed for each objective function separately to have an optimal point of comparison for the efficiency of the proposed algorithm. Also, the TS+PAES algorithm is compared to the nearest neighbor algorithm for large instances. Two computational experiments were carried out, one for small and the other one for large instances. The experiment for small instances showed that the GAP of each extreme of the frontier compared to the MILP model is on average 0.73%. For large instances, the metaheuristic improves in 0.1% the results presented by the MILP model showing that the metaheuristic provides closer near-optimal solutions in less computational time. Besides, the metaheuristic, in comparison with the nearest neighborhood heuristic, improves in 44.21% the results of emissions and in 3.88% the costs. All these results demonstrate the effectiveness of the metaheuristic.

This article has studied a full truckload transportation problem in the context of an empty return scenario, particularly an order selection and vehicle routing problem with full truckload, multiple depots and time windows (SFTMDVRPTW). The aim is to develop a solution where a set of truck routes serves a subset of selected transportation demands from a number of full truckload orders to maximize the total profit obtained from those orders. Each truck route is a chain of selected demands to serve, originating at a departure point and terminating at an arriving point of trucks in a way that respects the constraints of availability and time windows. It is not mandatory to serve all orders, and only the profitable ones are selected. In this study, we have formulated the SFTMDVRPTW as a mixed-integer linear programming (MILP) model. Finally, Computational results are conducted on a new data set that contains thirty randomly generated problem instances ranging from 16 to 30 orders using the CPLEX software. The findings prove that our model has provided good solutions in a reasonable time.

This paper proposes a metaheuristic algorithm to solve the Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDHFVRP). The problem consists of determining the customers and the vehicles to be assigned to each used depot and the routes to be performed to fulfill the demands of a set of customers. The objective is to minimize the sum of the fixed cost associated with the used vehicles and of the variable traveling costs related to the performed routes. The proposed approach is based on a modified genetic algorithm, which generates an initial population with heuristic solutions obtained from the well-known (LKH) heuristic algorithm for the TSP together with the solution of a mathematical model for the shortest path problem. In addition, two recombination methods and a mutation operator are considered. Computational experiments on benchmark instances show that the proposed algorithm can obtain high-quality solutions within short computing times.

In this paper, the Multi-Depot Electric Vehicle Location Routing Problem with Time Windows (MDVLRP) is addressed. This problem is an extension of the MDVLRP, where electric vehicles are used instead of internal combustion engine vehicles. The recent development of this model is explained by the advantages of this technology, such as the diminution of carbon dioxide emissions, and the support that they can provide to the design of the logistic and energy-support structure of electric vehicle fleets. There are many models that extend the classical VRP model to take electric vehicles into consideration, but the multi-depot case for location-routing models has not been worked out yet. Moreover, we consider the availability of two energy supply technologies: the “Plug-in” Conventional Charge technology, and Battery Swapping Stations; options in which the recharging time is a function of the amount of energy to charge and a fixed time, respectively. Three models are proposed: one for each of the technologies mentioned above, and another in which both options are taken in consideration. The models were solved for small scale instances using C++ and Cplex 12.5. The results show that the models can be used to design logistic and energy-support structures, and compare the performance of the different options of energy supply, as well as measure the impact of these decisions on the overall distance traveled or other optimization objectives that could be worked on in the future.

In this paper, we consider the multi depot heterogeneous vehicle routing problem with time windows in which vehicles may be replenished along their trips. Using the modeling technique in a new-generation solver, we construct a novel formulation considering a rich series of constraint conditions and objective functions. Computation results are tested on an example comes from the real-world application and some cases obtained from the benchmark problems. The results show the good performance of local search method in the efficiency of replenishment system and generalization ability. The variants can be used to almost all kinds of vehicle routing problems, without much modification, demonstrating its possibility of practical use.