Mathematical Model for the Electric Vehicle Routing Problem Considering the State of Charge of the Batteries

Abstract

In recent decades, scientific interest has grown in tackling the vehicle routing problem with a sustainable approach (Green VRP). There are numerous studies in the literature addressing environmental problems from the point of view of efficient planning that allows visualizing the benefits associated with the use of the new technologies in electric vehicles. This paper focuses on the electric vehicle routing problem and considers the batteries’ state of charge (SoC). The problem considers a set of customers, where each one has a specific demand and a time window. Deliveries are performed through a homogeneous fleet of electric vehicles with a fixed charging capacity and limited autonomy. In particular, when the vehicle is traveling, it consumes an amount of energy proportional to the distance it travels; therefore, it must visit battery recharging stations to continue and complete its route. The objective is to determine the performed routes with the minimum cost (time), while seeking to visit the recharging stations as many times as possible. In this way, overcharging and deep discharges are avoided by protecting the battery from degradation. In this paper, four models are proposed: the first model requires that the battery be fully charged in the stations; the second model allows partial recharging; the third formulation limits deep discharge; and a fourth formulation adheres to a limitation associated with overcharging and tries to keep the battery in its most comfortable place. The efficiency of the proposed formulations is tested in structured instances of different sizes. The results obtained show the efficiency of the formulations proposed for the electric vehicle routing problem when considering battery degradation.

The Routing Problem for Electric Truck with Partial Nonlinear Charging and Battery Swapping

“…Consequently, this study distinguishes itself from the existing literature by integrating the EVRP with multiple charging options and nonlinear charging functions. [23] CPLEX -Lee (2021) [29] Exact * Karakatič (2021) [30] Heuristic -Sayarshad and Mahmoodian (2021) [34] Exact -Lam et al (2022) [20] Exact * Cataldo-Díaz et al (2022) [21] Gurobi * Jiang et al (2022) [24] Heuristic 0.12 Akbay et al (2023) [25] Heuristic * Amiri et al (2023) [27] Heuristic -This study Heuristic 0.61…”

“…However, the feasibility of partial charging has been verified in many studies. Cataldo-Díaz et al [21] demonstrated the benefits of partial charging in terms of reducing the total time spent on distribution routes and improving energy utilization efficiency. Felipe et al [22] introduced fast charging, slow charging, and partial charging strategies to the EVRP for the first time.…”

“…• Delay Penalty Costs: the penalty costs paid by ETs for exceeding the latest service time specified by customers during the process of unloading. A specific expression being provided in constraint (21), η i represents delay arrival time at customer i. With per unit delay penalty cost u d , the total delay penalty costs generated on the serving route are then…”

Battery Sharing: A Feasibility Analysis through Simulation

“…In our experiments, battery charge is assumed to be linear with time, as discussed in Zeng et al [36] and Cataldo-Díaz et al [37]. In addition Cataldo-Díaz et al [37] assumed linear recharge at stations, despite the fact that this assumption might not be fully accurate when using high recharging speeds.…”

“…In our experiments, battery charge is assumed to be linear with time, as discussed in Zeng et al [36] and Cataldo-Díaz et al [37]. In addition Cataldo-Díaz et al [37] assumed linear recharge at stations, despite the fact that this assumption might not be fully accurate when using high recharging speeds. Hence, given a battery capacity C, a starting battery power level, and the station disbursed power p, the charging time is computed as follows: time = (C − level)/p…”