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

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  • Cristian Cataldo-Díaz

    (School of Industrial Engineering, Universidad del Bío-Bío, Concepcion 4030000, Chile)

  • Rodrigo Linfati

    (Department of Industrial Engineering, Universidad del Bío-Bío, Concepcion 4030000, Chile)

  • John Willmer Escobar

    (Department of Accounting and Finance, Universidad del Valle, Cali 760001, Colombia)

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.

Suggested Citation

  • Cristian Cataldo-Díaz & Rodrigo Linfati & John Willmer Escobar, 2022. "Mathematical Model for the Electric Vehicle Routing Problem Considering the State of Charge of the Batteries," Sustainability, MDPI, vol. 14(3), pages 1-26, January.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:3:p:1645-:d:739224
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    References listed on IDEAS

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    1. Ziwen Ling & Christopher R. Cherry & Yi Wen, 2021. "Determining the Factors That Influence Electric Vehicle Adoption: A Stated Preference Survey Study in Beijing, China," Sustainability, MDPI, vol. 13(21), pages 1-22, October.
    2. Tolga Bektaş & Emrah Demir & Gilbert Laporte, 2016. "Green Vehicle Routing," International Series in Operations Research & Management Science, in: Harilaos N. Psaraftis (ed.), Green Transportation Logistics, edition 127, chapter 0, pages 243-265, Springer.
    3. Pelletier, Samuel & Jabali, Ola & Laporte, Gilbert & Veneroni, Marco, 2017. "Battery degradation and behaviour for electric vehicles: Review and numerical analyses of several models," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 158-187.
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    Cited by:

    1. Xinhua Gao & Song Liu & Yan Wang & Dennis Z. Yu & Yong Peng & Xianting Ma, 2024. "Consideration of Carbon Emissions in Multi-Trip Delivery Optimization of Unmanned Vehicles," Sustainability, MDPI, vol. 16(6), pages 1-26, March.
    2. Yong Wang & Jingxin Zhou & Yaoyao Sun & Xiuwen Wang & Jiayi Zhe & Haizhong Wang, 2022. "Electric Vehicle Charging Station Location-Routing Problem with Time Windows and Resource Sharing," Sustainability, MDPI, vol. 14(18), pages 1-31, September.
    3. Abdulaziz Almutairi & Naif Albagami & Sultanh Almesned & Omar Alrumayh & Hasmat Malik, 2023. "Electric Vehicle Load Estimation at Home and Workplace in Saudi Arabia for Grid Planners and Policy Makers," Sustainability, MDPI, vol. 15(22), pages 1-16, November.
    4. Hongwen Han & Luxian Chen & Sitong Fang & Yang Liu, 2023. "The Routing Problem for Electric Truck with Partial Nonlinear Charging and Battery Swapping," Sustainability, MDPI, vol. 15(18), pages 1-29, September.

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