The Electric Fleet Size and Mix Vehicle Routing Problem with Time Windows and Recharging Stations

Partial linear recharging strategy for the electric fleet size and mix vehicle routing problem with time windows and recharging stations

A Hybrid Iterative Local Search Algorithm for The Electric Fleet Size and Mix Vehicle Routing Problem with Time Windows and Recharging Stations

Electric vehicles have emerged as a new promising technology guaranteeing sustainable transport activities. To save the environment and avoid our dependence on foreign oil, new laws and regulations concerning the emission of greenhouse gases are made in order to reduce harmful emissions and promote electric vehicles for urban goods distribution. This paper proposes to address the electric Modular Fleet Size and Mix Vehicle Routing Problem with Time Windows, which incorporates electric modules that can be recharged at customer locations. For that purpose, we apply a memetic algorithm that combines a Genetic Algorithm with a Local Search method. Experimental results demonstrate that with the modularity feature, using electric vehicles for freight delivery in cities is interesting economically.

This work deals with the electric Modular Fleet Size and Mix Vehicle Routing Problem with Time Windows, which is an extension of the well-known Vehicle Routing Problem with Time Windows (VRPTW), where the fleet consists of electric modular vehicles (EMVs). An interesting feature of this work is that despite the fact that the vehicles have a limited range, they are allowed sometimes to recharge at certain customer locations in order to continue a tour. To tackle this problem, a comprehensive mathematical formulation is given in order to model the problem and the multiple constraints appeared due to the modularity, electric charging, time windows and capacity issues. Due to the NP-hardness of the problem, a memetic algorithm is designed for determining good quality solutions in reasonable computational times. Extensive computational experiments carried out on some benchmark instances show the effectiveness of both the problem formulation and the memetic algorithm.

This paper introduces the electric Modular Fleet Size and Mix Vehicle Routing Problem with Time Windows (eM-FSMVRPTW), which deals with introducing new types of electric vehicles for urban freight delivery taking into account the possibility of recharging at a customer location. These electric vehicles differ from battery electric vehicles because their modules are autonomous in terms of consumption and electric charging. Therefore, the eM-FSMVRPTW is a completely new problem. Its objective is to minimize the acquisition cost, the total distance travelled and the recharging costs taking into consideration several constraints such as modularity, electric charging, time windows, capacity limit and others. As a solution method, we propose an approach based on a genetic algorithm. The experimental results demonstrate that with the modularity feature, using electric vehicles for freight delivery in urban environment is interesting economically.

Application of a variable neighborhood search algorithm to a fleet size and mix vehicle routing problem with electric modular vehicles

The Heterogeneous-Fleet Electric Vehicle Routing Problem with Nonlinear Charging Functions

Solving the Fleet Size and Mix Vehicle Routing Problem with Time Windows via Adaptive Memory Programming

In this paper, we compare different formulations of the multi-depot fleet size and mix vehicle routing problem (MDFSMVRP). This problem extends the multi-depot vehicle routing problem and the fleet size and mix vehicle routing problem, two logistics problems that have been extensively studied for many decades. This difficult vehicle routing problem combines complex assignment and routing decisions under the objective of minimizing fixed vehicle costs and variable routing costs. We first propose five distinct formulations to model the MDFSMVRP. We introduce a three-index formulation with an explicit vehicle index and a two-index formulation in which only vehicle types are identified. Other formulations are obtained by defining aggregated and disaggregated loading variables. The last formulation makes use of capacity-indexed variables. For each formulation, we summarize known and propose new valid inequalities, including symmetry breaking, lexicographic ordering, routing, and rounded capacity cuts. We then implement branch-and-cut and branch-and-bound algorithms for these formulations, and we fed them into a general purpose solver. We compare the bounds provided by the formulations on a commonly used set of instances in the MDFSMVRP literature, containing up to nine depots and 360 customers, and on newly generated instances. Our in-depth analysis of the five formulations shows which formulations tend to perform better on each type of instance. Moreover, our results have considerably improved available lower bounds on all instances and significantly improved quality of upper bounds that can be obtained by means of currently available methods.

The vehicle routing problem is a traditional combinatorial problem with practical relevance for a wide range of industries. In the literature, several specificities have been tackled by dedicated methods in order to better reflect real-world situations. Following this trend, this article addresses the fleet size and mix vehicle routing problem with time windows in which companies hire a third-party logistics company. The shipping charges considered in this work are calculated using step cost functions, in which values are determined according to the type of vehicle and the total distance traveled, with fixed values for predefined distance ranges. A mixed integer linear programming model is introduced and two sequential insertion heuristics are proposed. The introduced methods are examined through a computational comparative analysis in small-sized instances with known optimal solution, 168 benchmark instances from the literature, and 3 instances based on a real-world problem from the civil construction industry. The numerical experiments show that the proposed methods are efficient and show good performance in different scenarios.

The fleet size and mix vehicle routing problem with time windows (FSMVRPTW) is an important extended type of vehicle routing problem, and it has been proved to be a NP-hard problem in combinatorial optimization, which is difficult or impossible to obtain optimal solutions in large-scale cases. A four-step improved simulated annealing algorithm is proposed, which obtains a good initial solution through the construction of the first three steps and introduces four local search operators to iterate in the fourth step. To evaluate its performance, we test it with Solomon's VRPTW benchmark problems. The computational results demonstrate that the high -quality solutions can be obtained by using the new algorithm within an accepted computational time.

The vehicle routing problem is a traditional combinatorial problem with practical relevance for a wide range of industries. In the literature, several attributes have been tackled by dedicated methods in order to better reflect real-life situations. This article addresses the fleet size and mix vehicle routing problem with time windows in which companies hire a third-party logistics company. The shipping charges considered in this work are calculated using step cost functions, in which values are determined according to the type of vehicle and the total distance traveled, with fixed values for predefined distance ranges. The problem is solved with three different metaheuristic methods: Variable Neighborhood Search (VNS), Greed Randomized Adaptive Search Procedure (GRASP) and a hybrid proposition that combines both. The methods are examined through a computational comparative analysis in 168 benchmark instances from the literature, small-sized instances with known optimal solution, and 3 instances based on a real problem from the civil construction industry. The numerical experiments show that the proposed methods are efficient and show strong performance in different scenarios.

Optimization of electric vehicle recharge schedule and routing problem with time windows and partial recharge: A comparative study for an urban logistics fleet

An alternating direction multiplier method with variable neighborhood search for electric vehicle routing problem with time windows and battery swapping stations

Prize-collecting Electric Vehicle routing model for parcel delivery problem