Skip to main content
Springer Nature Link
Log in

Multi-depot Electric Vehicle Routing Problem with Half-Open Routes and Rotations: A Mathematical Formulation

  • Conference paper
  • First Online:
Advances in Production Management Systems. Production Management Systems for Volatile, Uncertain, Complex, and Ambiguous Environments (APMS 2024)

Part of the book series: IFIP Advances in Information and Communication Technology ((IFIPAICT,volume 733))

  • 482 Accesses

Abstract

The electrification spreads all around the world with the goal of global net zero emission, especially in transportation sector. As a natural consequence of this phenomenon, many countries and organizations announce their targets relating to the Electric Vehicles (EVs). Although shifting from fossil-fuel towards EVs is a major step forward, there are other precious actions to be taken, one of which is to integrate EVs into scientific studies along with the routing improvements. To this end, we introduce the Multi-Depot Electric Vehicle Routing Problem with Half-Open Routes and Rotations (MDEVRP-HORR) as an extension of the MDEVRP where the rotation refers to set of all routes assigned to an EV. EVs can be recharged at the depots or at the recharging stations along the route with full recharging strategy. The problem is formulated as a 0–1 mixed integer linear program (MILP) and existing procedures are applied to improve the model. The proposed model relaxes the restriction that the departure depot of the first route and arrival depot of the last route of an EV must be the same. It also avoids from creating dummy nodes for recharging stations and replenishment depots. We conducted experimental studies by using small-sized instances from the recent literature due to problem intractability. Out of 36 instances, results reveal that inclusion of half-open routes leads to a cost reduction for 20 instances. Besides, inclusion of both half-open rotations and half-open routes results in cost reduction for 28 instances.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Global EV Outlook 2022, International Energy Agency (IEA). https://iea.blob.core.windows.net/assets/ad8fb04c-4f75-42fc-973a-6e54c8a4449a/GlobalElectricVehicleOutlook2022.pdf. Accessed 05 Oct 2023

  2. Koç, Ç., Jabali, O., Mendoza, J.E., Laporte, G.: The electric vehicle routing problem with shared charging stations. Int. Trans. Oper. Res. 26(4), 1211–1243 (2019)

    Article  MathSciNet  Google Scholar 

  3. Lopez, N.S., Allana, A., Biona, J.B.M.: Modeling electric vehicle charging demand with the effect of increasing EVSEs: a discrete event simulation-based model. Energies 14(13), 3734 (2021)

    Article  Google Scholar 

  4. Gönül, Ö., Duman, A.C.,Güler, Ö.: Electric vehicles and charging infrastructure in Turkey: an overview. Renew. Sustain. Energy Rev. 143 (2021). https://doi.org/10.1016/j.rser.2021.110913

  5. Schneider, M., Stenger, A., Goeke, D.: The electric vehicle-routing problem with time windows and recharging stations. Transp. Sci. 48(4), 500–520 (2014). https://doi.org/10.1287/trsc.2013.0490

    Article  Google Scholar 

  6. Keskin, M., Çatay, B.: Partial recharge strategies for the electric vehicle routing problem with time windows. Transp. Res. Part C: Emerg. Technol. 65, 111–127 (2016)

    Article  Google Scholar 

  7. Paz, J., Granada-Echeverri, M., Escobar, J.: The multi-depot electric vehicle location routing problem with time windows. Int. J. Ind. Eng. Comput. 9(1), 123–136 (2018)

    Google Scholar 

  8. Felipe, Á., Ortuño, M.T., Righini, G., Tirado, G.: A heuristic approach for the green vehicle routing problem with multiple technologies and partial recharges. Transp. Res. Part E: Logist. Transp. Rev. 71, 111–128 (2014)

    Article  Google Scholar 

  9. Keskin, M., Çatay, B.: A matheuristic method for the electric vehicle routing problem with time windows and fast chargers. Comput. Oper. Res. 100, 172–188 (2018)

    Article  MathSciNet  Google Scholar 

  10. Karakatič, S.: Optimizing nonlinear charging times of electric vehicle routing with genetic algorithm. Expert Syst. Appl. 164, 114039 (2021)

    Article  Google Scholar 

  11. Montoya, A., Guéret, C., Mendoza, J.E., Villegas, J.G.: The electric vehicle routing problem with nonlinear charging function. Transp. Res. Part B: Methodol. 103, 87–110 (2017)

    Article  Google Scholar 

  12. Almouhanna, A., Quintero-Araujo, C.L., Panadero, J., Juan, A.A., Khosravi, B., Ouelhadj, D.: The location routing problem using electric vehicles with constrained distance. Comput. Oper. Res. 115, 104864 (2020)

    Article  MathSciNet  Google Scholar 

  13. Schiffer, M., Walther, G.: The electric location routing problem with time windows and partial recharging. Eur. J. Oper. Res. 260(3), 995–1013 (2017)

    Article  MathSciNet  Google Scholar 

  14. Lijun, F., Changshi, L., Zhang, W.: Half-open time-dependent multi-depot electric vehicle routing problem considering battery recharging and swapping. Int. J. Ind. Eng. Comput. 14(1), 129–146 (2023)

    Google Scholar 

  15. Zhou, Z., Ha, M., Hu, H., Ma, H.: Half open multi-depot heterogeneous vehicle routing problem for hazardous materials transportation. Sustainability 13(3), 1262 (2021)

    Article  Google Scholar 

  16. Fan, L.: A two-stage hybrid ant colony algorithm for multi-depot half-open time-dependent electric vehicle routing problem. Complex Intell. Syst. 1–22 (2023)

    Google Scholar 

  17. Wang, Y., Zhou, J., Sun, Y., Wang, X., Zhe, J., Wang, H.: Electric vehicle charging Station location-routing problem with time windows and resource sharing. Sustainability 14(18), 11681 (2022)

    Article  Google Scholar 

  18. Wang, Y., Zhou, J., Sun, Y., Fan, J., Wang, Z., Wang, H.: Collaborative multidepot electric vehicle routing problem with time windows and shared charging stations. Expert Syst. Appl. 219, 119654 (2023)

    Article  Google Scholar 

  19. Ma, B.-S., Hu, D.-W., Sun, Q.: Research on route optimization of pure electric vehicle under joint distribution mode in city. In: 18th COTA International Conference of Transportation Professionals. 2018. American Society of Civil Engineers Reston, VA (2018)

    Google Scholar 

  20. Li, Y., Lim, M.K., Tan, Y., Lee, Y., Tseng, M.-L.: Sharing economy to improve routing for urban logistics distribution using electric vehicles. Resour. Conserv. Recycl. 153, 104585 (2020)

    Article  Google Scholar 

  21. Crevier, B., Cordeau, J.-F., Laporte, G.: The multi-depot vehicle routing problem with inter-depot routes. Eur. J. Oper. Res. 176(2), 756–773 (2007)

    Article  MathSciNet  Google Scholar 

  22. Salhi, S., Petch, R.: A GA based heuristic for the vehicle routing problem with multiple trips. J. Math. Model. Algorithms 6, 591–613 (2007)

    Article  MathSciNet  Google Scholar 

  23. Schneider, M., Stenger, A., Hof, J.: An adaptive VNS algorithm for vehicle routing problems with intermediate stops. OR Spectrum 37, 353–387 (2015)

    Article  Google Scholar 

  24. Schiffer, M., Schneider, M., Laporte, G.: Designing sustainable mid-haul logistics networks with intra-route multi-resource facilities. Eur. J. Oper. Res. 265(2), 517–532 (2018)

    Article  MathSciNet  Google Scholar 

  25. Erdoğan, S., Miller-Hooks, E.: A green vehicle routing problem. Transp. Res. Part E: Logist. Transp. Rev. 48(1), 100–114 (2012)

    Article  Google Scholar 

  26. Li, J., Li, Y., Pardalos, P.M.: Multi-depot vehicle routing problem with time windows under shared depot resources. J. Comb. Optim. 31, 515–532 (2016)

    Article  MathSciNet  Google Scholar 

  27. Muñoz-Villamizar, A., Montoya-Torres, J.R., Faulin, J.: Impact of the use of electric vehicles in collaborative urban transport networks: a case study. Transp. Res. Part D: Transp. Environ. 50, 40–54 (2017)

    Article  Google Scholar 

  28. Londoño, A., Gonzalez, W., Giraldo, O., Escobar, J.: A new matheheuristic approach based on Chu-Beasley genetic approach for the multi-depot electric vehicle routing problem. Int. J. Ind. Eng. Comput. 14(3), 555–570 (2023)

    Google Scholar 

  29. Vahedi-Nouri, B., Arbabi, H., Jolai, F., Tavakkoli-Moghaddam, R., Bozorgi-Amiri, A.: Bi-objective collaborative electric vehicle routing problem: mathematical modeling and matheuristic approach. J. Ambient. Intell. Humaniz. Comput. 14(8), 10277–10297 (2023)

    Article  Google Scholar 

  30. Tarantilis, C.D., Zachariadis, E.E., Kiranoudis, C.T.: A hybrid guided local search for the vehicle-routing problem with intermediate replenishment facilities. Informs J. Comput. 20(1), 154–168 (2008)

    Article  MathSciNet  Google Scholar 

  31. Muter, I., Cordeau, J.-F., Laporte, G.: A branch-and-price algorithm for the multidepot vehicle routing problem with interdepot routes. Transp. Sci. 48(3), 425–441 (2014)

    Article  Google Scholar 

  32. Che, A., Wang, W., Mu, X., Zhang, Y., Feng, J.: Tabu-based adaptive large neighborhood search for multi-depot petrol station replenishment with open inter-depot routes. IEEE Trans. Intell. Transp. Syst. 24(1), 316–330 (2022)

    Article  Google Scholar 

  33. Bruglieri, M., Mancini, S., Pezzella, F., Pisacane, O.: A new mathematical programming model for the green vehicle routing problem. Electron. Notes Discret. Math. 55, 89–92 (2016)

    Article  Google Scholar 

  34. Koç, Ç., Karaoglan, I.: The green vehicle routing problem: a heuristic based exact solution approach. Appl. Soft Comput. 39, 154–164 (2016)

    Article  Google Scholar 

  35. Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35(2), 254–265 (1987)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Faculty of Engineering and Natural Sciences, Konya Technical University, Selçuklu/Konya, Turkey

    Hakan Erdeş & Saadettin Erhan Kesen

Authors
  1. Hakan Erdeş
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saadettin Erhan Kesen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hakan Erdeş .

Editor information

Editors and Affiliations

  1. Chemnitz University of Technology, Chemnitz, Germany

    Matthias Thürer

  2. West Saxon University of Applied Sciences Zwickau, Zwickau, Germany

    Ralph Riedel

  3. ZF Friedrichshafen AG, Friedrichshafen, Germany

    Gregor von Cieminski

  4. Tecnológico de Monterrey, Mexico City, Mexico

    David Romero

Rights and permissions

Reprints and permissions

Copyright information

© 2024 IFIP International Federation for Information Processing

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Erdeş, H., Kesen, S.E. (2024). Multi-depot Electric Vehicle Routing Problem with Half-Open Routes and Rotations: A Mathematical Formulation. In: Thürer, M., Riedel, R., von Cieminski, G., Romero, D. (eds) Advances in Production Management Systems. Production Management Systems for Volatile, Uncertain, Complex, and Ambiguous Environments. APMS 2024. IFIP Advances in Information and Communication Technology, vol 733. Springer, Cham. https://doi.org/10.1007/978-3-031-71645-4_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-71645-4_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-71644-7

  • Online ISBN: 978-3-031-71645-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships