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A branch-and-price algorithm for the home health care scheduling and routing problem with stochastic service times and skill requirements

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  • Biao Yuan
  • Ran Liu
  • Zhibin Jiang

Abstract

Home health care (HHC) is defined as providing medical and paramedical services for patients at their own domicile. In the HHC industry, it is crucial for health care organisations to assign caregivers to patients and devise reasonable visiting routes to save total operational cost and improve the service quality. However, some special constraints make the problem hard to solve. For example, patients’ service times are usually stochastic due to their varying health conditions; caregivers are organised in a hierarchical structure according to their skills to satisfy patients’ demands. In this paper, we address a HHC scheduling and routing problem with stochastic service times and skill requirements. A stochastic programming model with recourse is proposed to formulate the problem in which the expected penalty for late arrival at customers is considered. To solve the problem, it is equivalently transformed into a master problem and a pricing sub-problem. A column generation algorithm is developed to solve the relaxation of the master problem and obtain its lower bound. A label algorithm and several effective accelerating techniques are devised to solve the pricing sub-problem. To obtain feasible solutions, the column generation procedure is embedded within the branch and bound framework. The effectiveness of the proposed algorithm is validated through numerical experiments.

Suggested Citation

  • Biao Yuan & Ran Liu & Zhibin Jiang, 2015. "A branch-and-price algorithm for the home health care scheduling and routing problem with stochastic service times and skill requirements," International Journal of Production Research, Taylor & Francis Journals, vol. 53(24), pages 7450-7464, December.
    • Handle: RePEc:taf:tprsxx:v:53:y:2015:i:24:p:7450-7464
    DOI: 10.1080/00207543.2015.1082041
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    1. Shima Azizi & Özge Aygül & Brenton Faber & Sharon Johnson & Renata Konrad & Andrew C. Trapp, 2023. "Select, route and schedule: optimizing community paramedicine service delivery with mandatory visits and patient prioritization," Health Care Management Science, Springer, vol. 26(4), pages 719-746, December.
    2. Pouria Khodabandeh & Vahid Kayvanfar & Majid Rafiee & Frank Werner, 2021. "A Bi-Objective Home Health Care Routing and Scheduling Model with Considering Nurse Downgrading Costs," IJERPH, MDPI, vol. 18(3), pages 1-24, January.
    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. 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).
    5. Ran Liu & Biao Yuan & Zhibin Jiang, 2019. "A branch-and-price algorithm for the home-caregiver scheduling and routing problem with stochastic travel and service times," Flexible Services and Manufacturing Journal, Springer, vol. 31(4), pages 989-1011, December.
    6. Hossein Hashemi Doulabi & Gilles Pesant & Louis-Martin Rousseau, 2020. "Vehicle Routing Problems with Synchronized Visits and Stochastic Travel and Service Times: Applications in Healthcare," Transportation Science, INFORMS, vol. 54(4), pages 1053-1072, July.
    7. Minh Phuoc Doan & Julien Fondrevelle & Valérie Botta-Genoulaz & Jose Francisco Ferreira Ribeiro, 2022. "Impact of flexible work contracts and multi-skilled agents on a multi-objective workforce planning problem," Post-Print hal-03119408, HAL.
    8. 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.
    9. Zhan, Yang & Wang, Zizhuo & Wan, Guohua, 2021. "Home service routing and appointment scheduling with stochastic service times," European Journal of Operational Research, Elsevier, vol. 288(1), pages 98-110.
    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. Gang Du & Luyao Zheng & Xiaoling Ouyang, 2019. "Real-time scheduling optimization considering the unexpected events in home health care," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 196-220, January.
    12. Mohammed Bazirha & Abdeslam Kadrani & Rachid Benmansour, 2023. "Stochastic home health care routing and scheduling problem with multiple synchronized services," Annals of Operations Research, Springer, vol. 320(2), pages 573-601, January.
    13. Biao Yuan & Zhibin Jiang, 2017. "Disruption Management for the Real-Time Home Caregiver Scheduling and Routing Problem," Sustainability, MDPI, vol. 9(12), pages 1-15, November.
    14. Reihaneh, Mohammad & Ansari, Sina & Farhadi, Farbod, 2023. "Patient appointment scheduling at hemodialysis centers: An exact branch and price approach," European Journal of Operational Research, Elsevier, vol. 309(1), pages 35-52.
    15. Shi, Yong & Boudouh, Toufik & Grunder, Olivier, 2019. "A robust optimization for a home health care routing and scheduling problem with consideration of uncertain travel and service times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 52-95.
    16. Nikzad, Erfaneh & Bashiri, Mahdi & Abbasi, Babak, 2021. "A matheuristic algorithm for stochastic home health care planning," European Journal of Operational Research, Elsevier, vol. 288(3), pages 753-774.
    17. Mahyar Mirabnejad & Hadi Mohammadi & Mehrdad Mirzabaghi & Amir Aghsami & Fariborz Jolai & Maziar Yazdani, 2022. "Home Health Care Problem with Synchronization Visits and Considering Samples Transferring Time: A Case Study in Tehran, Iran," IJERPH, MDPI, vol. 19(22), pages 1-25, November.
    18. Liping Zhou & Na Geng & Zhibin Jiang & Shan Jiang, 2022. "Integrated Multiresource Capacity Planning and Multitype Patient Scheduling," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 129-149, January.
    19. Tsang, Man Yiu & Shehadeh, Karmel S., 2023. "Stochastic optimization models for a home service routing and appointment scheduling problem with random travel and service times," European Journal of Operational Research, Elsevier, vol. 307(1), pages 48-63.
    20. Ahmadi-Javid, Amir & Jalali, Zahra & Klassen, Kenneth J, 2017. "Outpatient appointment systems in healthcare: A review of optimization studies," European Journal of Operational Research, Elsevier, vol. 258(1), pages 3-34.
    21. 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.

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