Abstract In this paper, we consider the Electric-Vehicle Routing Problem (EVRP) with nonlinear charging time. Due to their limited travel ranges, electric vehicles have to be recharged (possibly multiple times) at specific recharging points, which incurs a routing problem for which the recharging constraint and time have to be addressed. It is well-known that the recharging of the battery of EVs takes considerable time, so it cannot be ignored. Moreover, the recharging time required to travel a given distance is highly nonlinear due to the battery charging mechanism. The goal of this study is to develop an algorithm that minimizes the total travel and charging times without approximation of the charging time function. Our solution approach is based on the segmentation of the vehicle tour. We then construct an extended charging stations network where any path in this network is also a tour in the original network. We develop the branch-and-price method on the extended charging station network to solve the problem to optimality. An extensive computational study on well-known benchmark problems confirms that the proposed approach can solve moderate-sized problems to the optimality.

An Exact Algorithm for the Electric-Vehicle Routing Problem

A review of siting, sizing, optimal scheduling, and cost-benefit analysis for battery swapping stations

Electric vehicle routing models and solution algorithms in logistics distribution: A systematic review

In this paper, we define the standard LRP as a deterministic, static, discrete, single-echelon, single-objective location-routing problem in which each customer (vertex) must be visited exactly once for the delivery of a good from a facility, and in which no inventory decisions are relevant. We review the literature on the standard LRP published since the survey by Nagy and Salhi appeared in 2006. We provide concise paper excerpts that convey the central ideas of each work, discuss recent developments in the field, provide a numerical comparison of the most successful heuristic algorithms, and list promising topics for further research.

A Survey of the Standard Location-Routing Problem

This paper addresses the Electric Vehicle Routing Problem with Simultaneous Pickup and Delivery (EVRP-SPD), in which electric vehicles (EVs) simultaneously deliver goods to and pick up goods from customers. Due to the limited battery capacity of EVs, their range is shorter than that of internal combustion vehicles. In the EVRP, in addition to the depot and the customers, there are also charging stations (CS) because EVs need to be charged when their battery is empty. The problem is formulated as an integer linear model, and an efficient solution is proposed to minimize the total distance traveled. To create a feasible initial solution, Clarke and Wright’s savings algorithm is used. Several variants of variable neighborhood search are tested, and the reduced-variable neighborhood search algorithm is used to find the best solution in a reasonable time. Computer experiments are performed with benchmark instances to evaluate the effectiveness of our approach in terms of solution quality and time. The obtained results show that the proposed method can achieve efficient solutions in terms of solution quality and time in all benchmark instances.

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Variable Neighborhood Search Algorithms to Solve the Electric Vehicle Routing Problem with Simultaneous Pickup and Delivery

In this paper, a battery swap station location and routing problem with time windows and a mixed fleet of electric and conventional vehicles (BSS–MF–LRPTW) is proposed. This problem is motivated by a real-life logistics application by extending the existing electric vehicle battery swap stations location routing problem (BSS–EV–LRP). The BSS–MF–LRPTW aims to simultaneously determine the locations of battery swap stations (BSSs) and the routing plan of a mixed fleet under the driving range, the load capacity limitation, and time windows. An integer programming (IP) model is developed for the proposed BSS–MF–LRPTW. As there are a large number of variables and complicating constraints of the IP model, we break it up into the master problem and the subproblem, based on Danzig–Wolfe decomposition. To enhance the tractability of the problem, we follow up with a heuristic branch-and-price algorithm with an adaptive selection scheme (HBP-ASS), which integrates the exact policy with a heuristic strategy. The HBP-ASS develops heuristic versions of the dynamic programming algorithm by designing seven operators for heuristic label extension and dominance. An adaptive selection scheme is presented to decide which operator is employed. The performance of the proposed HBP-ASS is evaluated based on an extensive computational study. The results show that the HBP-ASS can obtain the exact solution to small-scale instances much more quickly than commercial branch-and-bound/cut solvers such as CPLEX. Also, for all tested cases, the HBP-ASS can find better solutions to large-scale instances within a shorter time than the existing heuristics – adaptive large neighborhood search. Furthermore, sensitivity analyses are carried out to provide managerial insights.

Solving the battery swap station location-routing problem with a mixed fleet of electric and conventional vehicles using a heuristic branch-and-price algorithm with an adaptive selection scheme

The invention relates to the technical field of logistics transportation, in particular to a battery swap station site selection and hybrid fleet path planning method and system. The method comprisesthe steps of obtaining alternative data information; constructing an integer programming model for joint decision of site selection of the battery swap station and distribution of the electric vehicleand fuel vehicle hybrid fleet; reconstructing the integer programming model into a main problem model and a sub problem model; for the model, an accurate branch pricing algorithm with an adaptive selection mechanism is designed, and seven acceleration solving operators are designed, so that adaptive calling of the operators for different enterprise distribution scenes is realized, and the solvingspeed is increased. And meanwhile, a precise label is adopted to expand a complete search solution space to obtain an optimal solution. The optimal distribution scheme and the optimal station building scheme can be quickly provided for large-scale hybrid fleet distribution systems of different enterprises under the condition of self-building a battery swap station, and real-time optimal scheduling of the enterprises is realized.

Zhang Zongcheng

Papers

Solving the battery swap station location-routing problem with a mixed fleet of electric and conventional vehicles using a heuristic branch-and-price algorithm with an adaptive selection scheme

Battery swap station site selection and hybrid fleet path planning method and system