The vehicle routing problem combined with loading of goods, considering the reduction of fuel consumption, aims at finding the set of routes that will serve the demands of the customers, arguing that the fuel consumption is directly related to the weight of the load in the paths that compose the routes. This study integrates the Fuel Consumption Heterogeneous Vehicle Routing Problem with Two-Dimensional Loading Constraints (2L-FHFVRP). To reduce fuel consumption taking the associated environmental impact into account is a classical VRP variant that has gained increasing attention in the last decade. The objective of this problem is to design the delivery routes to satisfy the customers’ demands with the lowest possible fuel consumption, which depends on the distances of the paths, the assigned vehicles, the loading/unloading pattern and the load weight. In the vehicle routing problem literature, the approximate algorithms have had great success, especially the evolutionary ones, which appear in previous works with quite a sophisticated structure, obtaining excellent results, but that are difficult to implement and adapt to other variants such as the one proposed here. In this study, we present a specialized genetic algorithm to solve the design of routes, keeping its main characteristic: the easy implementation. By contrast, the loading of goods restriction is validated by means of a GRASP algorithm, which has been widely employed for solving packing problems. With a view of confirming the performance of the proposed methodology, we provide a computational study that uses all the available benchmark instances, allowing to illustrate the savings achieved in fuel consumption. In addition, the methodology suggested can be adapted to the version of solely minimizing the total distance traveled for serving the customers (without the fuel consumption) and it is compared to the best works presented in the literature. The computational results show that the methodology manages to be adequately adapted to this version and it is capable of finding improved solutions for some benchmark instances. As for future work, we propose to adjust the methodology to consider the three-dimensional loading problem so that it adapts to more real-life conditions of the industry.

In the classical vehicle routing problem with backhauls (VRPB) the customers are divided into two sets; the linehaul and backhaul customers, so that the distribution and collection services of goods are separated into different routes. This is justified by the need to avoid the reorganization of the loads inside the vehicles, to reduce the return of the vehicles with empty load and to give greater priority to the customers of the linehaul. Many logistics companies have special responsibility to make their operations greener, and electric vehicles (EVs) can be an efficient solution. Thus, when the fleet consists of electric vehicles (EVs), the driving range is limited due to their battery capacities and, therefore, it is necessary to visit recharging stations along their route. In this paper the electric vehicle routing problem with backhauls (EVRPB) is introduced and formulated as a mixed integer linear programming model. This formulation is based on the generalization of the open vehicle routing problem considering a set of new constraints focussed on maintaining the arborescence condition of the linehaul and backhaul paths. Different charging points for the EVs are considered in order to recharge the battery at the end of the linehaul route or during the course of the backhaul route. Finally, a heuristic initialization methodology is proposed, in which an auxiliary graph is used for the efficient coding of feasible solutions to the problem. The operation and effectiveness of the proposed formulation is tested on two VRPB instance datasets of literature which have been adapted to the EVRPB.

In this paper, an optimization model for the Charging Station Location Problem of Electric Vehicles for Freight Transportation CSLP-EVFT is presented. This model aims to determine an optimal location strategy of Electric Vehicle Charging Stations EVCSs and the routing plan of a fleet of electric vehicles under battery driving range limitation, in conjunction with the impact on the power distribution system. Freight transportation is modeled under the mobility patterns followed by the Capacitated Vehicle Routing Problem CVRP for contracted fleet, and Shortest Path SP problem for subcontracted fleet. A linear formulation of the power flow is used in order to consider the impact on the electric grid. Several costs are examined, i.e., EVs routing, installation and energy consumption of EVCSs, and energy losses. Although uncertainties related to temporal variation of some aspects (number of customers and their demands, fleet size, power network nodes and routes) are not addressed, the proposed model represents a useful approach to evaluate multiple scenarios or to be introduced within stochastic optimization. Instead, the mathematical model is studied under the variation of EVs travel range that accounts for the advance of battery technology and sensitivity analysis. Additionally, the problem is reduced to a mixed integer non-linear mathematical model, which is linearized by using multivariable Taylor’s series.

The separate delivery and collection services of goods through different routes is an issue of current interest for some transportation companies by the need to avoid the reorganization of the loads inside the vehicles, to reduce the return of the vehicles with empty load and to give greater priority to the delivery customers. In the vehicle routing problem with backhauls (VRPB), the customers are partitioned into two subsets: linehaul (delivery) and backhaul (pickup) customers. Additionally, a precedence constraint is established: the backhaul customers in a route should be visited after all the linehaul customers. The VRPB is presented in the literature as an extension of the capacitated vehicle routing problem and is NP-hard in the strong sense. In this paper, we propose a mixed integer linear programming formulation for the VRPB, based on the generalization of the open vehicle routing problem; that eliminates the possibility of generating solutions formed by subtours using a set of new constraints focused on obtaining valid solutions formed by Hamiltonian paths and connected by tie-arcs. The proposed formulation is a general purpose model in the sense that it does not deserve specifically tailored algorithmic approaches for their effective solution. The computational results show that the proposed compact formulation is competitive against state-of-the-art exact methods for VRPB instances from the literature.

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.