IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i5p804-d763262.html
   My bibliography  Save this article

The Cost-Balanced Path Problem: A Mathematical Formulation and Complexity Analysis

Author

Listed:
  • Daniela Ambrosino

    (Department of Economics and Business Studies, University of Genoa, 16126 Genoa, Italy
    These authors contributed equally to this work.)

  • Carmine Cerrone

    (Department of Economics and Business Studies, University of Genoa, 16126 Genoa, Italy
    These authors contributed equally to this work.)

Abstract

This paper introduces a new variant of the Shortest Path Problem ( S P P ) called the Cost-Balanced Path Problem ( C B P P ). Various real problems can either be modeled as B C P P or include B C P P as a sub-problem. We prove several properties related to the complexity of the C B P P problem. In particular, we demonstrate that the problem is NP-hard in its general version, but it becomes solvable in polynomial time in a specific family of instances. Moreover, a mathematical formulation of the C B P P , as a mixed-integer programming model, is proposed, and some additional constraints for modeling real requirements are given. This paper validates the proposed model and its extensions with experimental tests based on random instances. The analysis of the results of the computational experiments shows that the proposed model and its extension can be used to model many real applications. Obviously, due to the problem complexity, the main limitation of the proposed approach is related to the size of the instances. A heuristic solution approach should be required for larger-sized and more complex instances.

Suggested Citation

  • Daniela Ambrosino & Carmine Cerrone, 2022. "The Cost-Balanced Path Problem: A Mathematical Formulation and Complexity Analysis," Mathematics, MDPI, vol. 10(5), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:804-:d:763262
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/5/804/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/5/804/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Dongqing & Wallace, Stein W. & Guo, Zhaoxia & Dong, Yucheng & Kaut, Michal, 2021. "On scenario construction for stochastic shortest path problems in real road networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    2. Prakash, A. Arun, 2018. "Pruning algorithm for the least expected travel time path on stochastic and time-dependent networks," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 127-147.
    3. Dell'Amico, Mauro & Hadjicostantinou, Eleni & Iori, Manuel & Novellani, Stefano, 2014. "The bike sharing rebalancing problem: Mathematical formulations and benchmark instances," Omega, Elsevier, vol. 45(C), pages 7-19.
    4. He, Fang & Yin, Yafeng & Lawphongpanich, Siriphong, 2014. "Network equilibrium models with battery electric vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 306-319.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Antonin Ponsich & Bruno Domenech & Mariona Vilà, 2023. "Preface to the Special Issue “Mathematical Optimization and Evolutionary Algorithms with Applications”," Mathematics, MDPI, vol. 11(10), pages 1-6, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shi, Ziyi & Xu, Meng & Song, Yancun & Zhu, Zheng, 2024. "Multi-Platform dynamic game and operation of hybrid Bike-Sharing systems based on reinforcement learning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 181(C).
    2. Shafqat Jawad & Junyong Liu, 2020. "Electrical Vehicle Charging Services Planning and Operation with Interdependent Power Networks and Transportation Networks: A Review of the Current Scenario and Future Trends," Energies, MDPI, vol. 13(13), pages 1-24, July.
    3. Wentao Jing & Mohsen Ramezani & Kun An & Inhi Kim, 2018. "Congestion patterns of electric vehicles with limited battery capacity," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-18, March.
    4. Shi, Xiao & Pan, Jian & Wang, Hewu & Cai, Hua, 2019. "Battery electric vehicles: What is the minimum range required?," Energy, Elsevier, vol. 166(C), pages 352-358.
    5. Lei, Chao & Ouyang, Yanfeng, 2024. "Average minimum distance to visit a subset of random points in a compact region," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    6. Wagner, Sebastian & Brandt, Tobias & Neumann, Dirk, 2016. "In free float: Developing Business Analytics support for carsharing providers," Omega, Elsevier, vol. 59(PA), pages 4-14.
    7. Wang, Hongping & Fang, Yi-Ping & Zio, Enrico, 2022. "Resilience-oriented optimal post-disruption reconfiguration for coupled traffic-power systems," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    8. Zhang, J. & Meng, M. & Wang, David, Z.W., 2019. "A dynamic pricing scheme with negative prices in dockless bike sharing systems," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 201-224.
    9. Ke, Jintao & Cen, Xuekai & Yang, Hai & Chen, Xiqun & Ye, Jieping, 2019. "Modelling drivers’ working and recharging schedules in a ride-sourcing market with electric vehicles and gasoline vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 125(C), pages 160-180.
    10. Salazar-González, Juan-José & Santos-Hernández, Beatriz, 2015. "The split-demand one-commodity pickup-and-delivery travelling salesman problem," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 58-73.
    11. Sun, Hao & Yang, Jun & Yang, Chao, 2019. "A robust optimization approach to multi-interval location-inventory and recharging planning for electric vehicles," Omega, Elsevier, vol. 86(C), pages 59-75.
    12. Bulhões, Teobaldo & Subramanian, Anand & Erdoğan, Güneş & Laporte, Gilbert, 2018. "The static bike relocation problem with multiple vehicles and visits," European Journal of Operational Research, Elsevier, vol. 264(2), pages 508-523.
    13. Tran, Cong Quoc & Keyvan-Ekbatani, Mehdi & Ngoduy, Dong & Watling, David, 2021. "Stochasticity and environmental cost inclusion for electric vehicles fast-charging facility deployment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    14. Bi, Huibo & Shang, Wen-Long & Chen, Yanyan & Wang, Kezhi & Yu, Qing & Sui, Yi, 2021. "GIS aided sustainable urban road management with a unifying queueing and neural network model," Applied Energy, Elsevier, vol. 291(C).
    15. Jiang, Zhoutong & Lei, Chao & Ouyang, Yanfeng, 2020. "Optimal investment and management of shared bikes in a competitive market," Transportation Research Part B: Methodological, Elsevier, vol. 135(C), pages 143-155.
    16. Mohammed Elhenawy & Hesham A. Rakha & Youssef Bichiou & Mahmoud Masoud & Sebastien Glaser & Jack Pinnow & Ahmed Stohy, 2021. "A Feasible Solution for Rebalancing Large-Scale Bike Sharing Systems," Sustainability, MDPI, vol. 13(23), pages 1-19, December.
    17. Shaohua Cui & Hui Zhao & Cuiping Zhang, 2018. "Locating Charging Stations of Various Sizes with Different Numbers of Chargers for Battery Electric Vehicles," Energies, MDPI, vol. 11(11), pages 1-22, November.
    18. Nie, Yu (Marco) & Ghamami, Mehrnaz & Zockaie, Ali & Xiao, Feng, 2016. "Optimization of incentive polices for plug-in electric vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 103-123.
    19. Zhang, Ziru & Krishnakumari, Panchamy & Schulte, Frederik & van Oort, Niels, 2023. "Improving the service of E-bike sharing by demand pattern analysis: A data-driven approach," Research in Transportation Economics, Elsevier, vol. 101(C).
    20. Alain Quilliot & Antoine Sarbinowski & Hélène Toussaint, 2021. "Vehicle driven approaches for non preemptive vehicle relocation with integrated quality criterion in a vehicle sharing system," Annals of Operations Research, Springer, vol. 298(1), pages 445-468, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:804-:d:763262. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.