IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i23p4846-d1292736.html
   My bibliography  Save this article

Vehicle Routing Problem with Time Windows to Minimize Total Completion Time in Home Healthcare Systems

Author

Listed:
  • Payakorn Saksuriya

    (PhD Degree Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Chulin Likasiri

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

We propose a vehicle routing problem with time windows (VRPTW) with compatibility-matching constraints and total completion time as the objective function, with applications in home healthcare routing and scheduling. Mixed integer linear programming is provided with total completion time minimization as the objective function. The solution approach has two objectives, total completion time (primary objective) and total distance (secondary objective). A heuristic is proposed comprising three phases: initializing to find an initial feasible routing (inserting the procedure with a modified K-means algorithm), swapping and moving the procedure to find a local optimal routing, and shooting the procedure to move away from the local optimum. Proof of feasibility for the inserting procedure is provided to prevent unnecessary insertions. Phases 2 and 3 will be repeated as needed to ensure solution quality. Solving our model with the proposed heuristic algorithm increases the total distance by 90.00% but reduces the total completion time by 25.86%. To test our model and heuristic, we examined a system with 400 home-healthcare cases in Chiang Mai. The heuristic quickly solved the problem. When total completion time is minimized, some caretakers serve up to twice as many patients as their coworkers; when total distance is minimized, workload discrepancies can increase up to seven-fold.

Suggested Citation

  • Payakorn Saksuriya & Chulin Likasiri, 2023. "Vehicle Routing Problem with Time Windows to Minimize Total Completion Time in Home Healthcare Systems," Mathematics, MDPI, vol. 11(23), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4846-:d:1292736
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/23/4846/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/23/4846/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marius M. Solomon, 1987. "Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints," Operations Research, INFORMS, vol. 35(2), pages 254-265, April.
    2. Braekers, Kris & Hartl, Richard F. & Parragh, Sophie N. & Tricoire, Fabien, 2016. "A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience," European Journal of Operational Research, Elsevier, vol. 248(2), pages 428-443.
    3. Mohamed Cissé & Semih Yalçindag & Yannick Kergosien & Evren Sahin & Christophe Lenté & Andrea Matta, 2017. "OR problems related to Home Health Care: A review of relevant routing and scheduling problems," Post-Print hal-01736714, HAL.
    4. Low, Chinyao & Chang, Chien-Min & Li, Rong-Kwei & Huang, Chia-Ling, 2014. "Coordination of production scheduling and delivery problems with heterogeneous fleet," International Journal of Production Economics, Elsevier, vol. 153(C), pages 139-148.
    5. Li, Haibing & Lim, Andrew, 2003. "Local search with annealing-like restarts to solve the VRPTW," European Journal of Operational Research, Elsevier, vol. 150(1), pages 115-127, October.
    Full references (including those not matched with items on IDEAS)

    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. Jiao Zhao & Tao Wang & Thibaud Monteiro, 2024. "A Bi-Objective Home Health Care Routing and Scheduling Problem under Uncertainty," IJERPH, MDPI, vol. 21(3), pages 1-27, March.
    2. Li, Yanfeng & Xiang, Ting & Szeto, Wai Yuen, 2021. "Home health care routing and scheduling problem with the consideration of outpatient services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    3. Pahlevani, Delaram & Abbasi, Babak & Hearne, John W. & Eberhard, Andrew, 2022. "A cluster-based algorithm for home health care planning: A case study in Australia," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 166(C).
    4. Paraskevopoulos, Dimitris C. & Laporte, Gilbert & Repoussis, Panagiotis P. & Tarantilis, Christos D., 2017. "Resource constrained routing and scheduling: Review and research prospects," European Journal of Operational Research, Elsevier, vol. 263(3), pages 737-754.
    5. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part II: Metaheuristics," Transportation Science, INFORMS, vol. 39(1), pages 119-139, February.
    6. Braysy, Olli & Hasle, Geir & Dullaert, Wout, 2004. "A multi-start local search algorithm for the vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 159(3), pages 586-605, December.
    7. Mohamed Cissé & Semih Yalçindag & Yannick Kergosien & Evren Sahin & Christophe Lenté & Andrea Matta, 2017. "OR problems related to Home Health Care: A review of relevant routing and scheduling problems," Post-Print hal-01736714, HAL.
    8. Jalel Euchi & Malek Masmoudi & Patrick Siarry, 2022. "Home health care routing and scheduling problems: a literature review," 4OR, Springer, vol. 20(3), pages 351-389, September.
    9. Zheng, Chenyang & Wang, Shuming & Li, Ningxin & Wu, Yuanhao, 2021. "Stochastic joint homecare service and capacity planning with nested decomposition approaches," European Journal of Operational Research, Elsevier, vol. 295(1), pages 203-222.
    10. Neda Tanoumand & Tonguç Ünlüyurt, 2021. "An exact algorithm for the resource constrained home health care vehicle routing problem," Annals of Operations Research, Springer, vol. 304(1), pages 397-425, September.
    11. Yanzhi Li & Andrew Lim & Brian Rodrigues, 2005. "Manpower allocation with time windows and job‐teaming constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(4), pages 302-311, June.
    12. Grenouilleau, Florian & Legrain, Antoine & Lahrichi, Nadia & Rousseau, Louis-Martin, 2019. "A set partitioning heuristic for the home health care routing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 275(1), pages 295-303.
    13. Fangzhou Yan & Huaxin Qiu & Dongya Han, 2023. "Lagrangian Heuristic for Multi-Depot Technician Planning of Product Distribution and Installation with a Lunch Break," Mathematics, MDPI, vol. 11(3), pages 1-22, January.
    14. Naderi, Bahman & Begen, Mehmet A. & Zaric, Gregory S. & Roshanaei, Vahid, 2023. "A novel and efficient exact technique for integrated staffing, assignment, routing, and scheduling of home care services under uncertainty," Omega, Elsevier, vol. 116(C).
    15. Amir M. Fathollahi-Fard & Abbas Ahmadi & Behrooz Karimi, 2021. "Multi-Objective Optimization of Home Healthcare with Working-Time Balancing and Care Continuity," Sustainability, MDPI, vol. 13(22), pages 1-33, November.
    16. Kok, A.L. & Hans, E.W. & Schutten, J.M.J., 2011. "Optimizing departure times in vehicle routes," European Journal of Operational Research, Elsevier, vol. 210(3), pages 579-587, May.
    17. A Lim & B Rodrigues & L Song, 2004. "Manpower allocation with time windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(11), pages 1178-1186, November.
    18. Yadav, Niteesh & Tanksale, Ajinkya, 2022. "An integrated routing and scheduling problem for home healthcare delivery with limited person-to-person contact," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1100-1125.
    19. Ma, Hong & Cheang, Brenda & Lim, Andrew & Zhang, Lei & Zhu, Yi, 2012. "An investigation into the vehicle routing problem with time windows and link capacity constraints," Omega, Elsevier, vol. 40(3), pages 336-347.
    20. Wang, Yu & Ropke, Stefan & Wen, Min & Bergh, Simon, 2023. "The mobile production vehicle routing problem: Using 3D printing in last mile distribution," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1407-1423.

    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:11:y:2023:i:23:p:4846-:d:1292736. 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.