隨著老年人口的持續增加，台灣已逐步進入高齡化社會。根據內政部統計，至2024年第一季，全台灣65歲以上人口已達到415.8萬人，占總人口數的17.8%。為應對這一挑戰，政府積極推動長照2.0政策，並與地方長照中心合作，在社區內設立據點，不僅為長照中心內的居民 (residential care facilities, RCFs)提供服務，同時也外派照顧服務人員進行居家照護服務 (home health care, HHC)。此外，針對需要醫療照護的患者，長照中心與醫院合作，根據具體的照護需求，派遣醫生與照顧服務人員共同提供服務。然而，照護人員始終處於短缺狀態，未能滿足長照需求，也因此導致長照護理人員時常需要加班，無法達到生活與工作的平衡，服務品質更無法顧及。
本研究因應以上挑戰，提出通過多中心間長照護理人員的相互支援，緩解人力不足的問題。同時，為提升服務品質，研究加入被照護居民與照顧者的適配程度、照顧者之間的協作適配程度、照護服務的連續性、班表健康度以及每位居民對長照服務時間段的偏好等因素，並在派發任務時，結合國內勞工法規和照護人員對班別的偏好進行人員排班，確保班表的合規性與長照護理人員對工作的滿意度。最後綜合上述條件，建立混合整數規劃模型，並使用深度強化學習輔以數學模型求解大規模實例，提供一套有效的排程與人力資源配置模式，期望在提升長照服務效率的同時，兼顧照護服務人員的工作品質。

With a continuously aging population, Taiwan is entering an aged society. According to Ministry of the Interior statistics, by Q1 2024, there were 4.158 million people aged 65 or older (17.8% of the population). To address this, the government has promoted the Long-Term Care (LTC) 2.0 policy, working with local centers to provide both residential care facility (RCF) and home health care (HHC) services, and collaborating with hospitals for medical care. However, persistent caregiver shortages lead to overtime and poor work–life balance, affecting service quality.
This study proposes multi-center caregiver collaboration to alleviate staffing shortages. To enhance service quality, factors such as resident–caregiver matching, caregiver collaboration, care continuity, schedule health, and resident time preferences are integrated into the scheduling process. Task assignment also considers labor laws and staff shift preferences to ensure compliance and satisfaction. A mixed-integer programming model is developed, with deep reinforcement learning assisting large-scale optimization, providing an effective approach to scheduling and resource allocation for LTC, aiming to improve both service efficiency and caregiver work quality.

Abdalkareem, Z. A., Amir, A., Al-Betar, M. A., Ekhan, P., & Hammouri, A. I. (2021). Healthcare scheduling in optimization context: a review. Health and Technology, 11(3), 445-469. https://doi.org/10.1007/s12553-021-00547-5
Ahmed, A., & Ali, H. (2020). Modeling patient preference in an operating room scheduling problem. Operations Research for Health Care, 25, 100257. https://doi.org/10.1016/j.orhc.2020.100257
Akjiratikarl, C., Yenradee, P., & Drake, P. R. (2007). PSO-based algorithm for home care worker scheduling in the UK. Computers & Industrial Engineering, 53(4), 559-583. https://doi.org/10.1016/j.cie.2007.06.002
Ang, S. Y., Razali, S. N. A. M., & Kek, S. L. (2019). Optimized preference of security staff scheduling using integer linear programming approach. Compusoft, 8(4), 3103-3111.
Arulkumaran, K., Deisenroth, M. P., Brundage, M., & Bharath, A. A. (2017). Deep reinforcement learning: A brief survey. IEEE Signal Processing Magazine, 34(6), 26-38. https://doi.org/10.1109/MSP.2017.2743240
Barbosa, C. D., Balp, M.-M., Kulich, K., Germain, N., & Rofail, D. (2012). A literature review to explore the link between treatment satisfaction and adherence, compliance, and persistence. Patient Preference and Adherence, 6, 39-48. https://doi.org/10.2147/PPA.S24752
Batista, A., Senapati, A., Davoodi, M., & Calabrese, J. M. (2024). Personnel staffing and scheduling during disease outbreaks: A contact network-based analysis. Computers & Industrial Engineering, 193, 110112. https://doi.org/10.1016/j.cie.2024.110112
Begur, S. V., Miller, D. M., & Weaver, J. R. (1997). An integrated spatial DSS for scheduling and routing home-health-care nurses. Interfaces, 27(4), 35-48. https://doi.org/10.1287/inte.27.4.35
Bice, T. W., & Boxerman, S. B. (1977). A quantitative measure of continuity of care. Medical Care, 15(4), 347-349. https://doi.org/10.1097/00005650-197704000-00010
Braekers, K., Hartl, R. F., Parragh, S. N., & Tricoire, F. (2016). A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience. European Journal of Operational Research, 248(2), 428-443. https://doi.org/10.1016/j.ejor.2015.07.028
Cathrine, T. (2019). Attrition analysis and retention strategies among staff nurses – a survey study. Indian Journal of Community Health, 31(2), 257 - 261. https://doi.org/10.47203/IJCH.2019.v31i02.018
Chabouh, S., El-Amraoui, A., Hammami, S., & Bouchriha, H. (2023). A systematic review of the home health care planning literature: Emerging trends and future research directions. Decision Analytics Journal, 7, 100215. https://doi.org/10.1016/j.dajour.2023.100215
Chahed, S., Marcon, E., Sahin, E., Feillet, D., & Dallery, Y. (2009). Exploring new operational research opportunities within the home care context: the chemotherapy at home. Health Care Management Science, 12(2), 179-191. https://doi.org/10.1007/s10729-009-9099-6
Chaieb, M., Jemai, J., & Mellouli, K. (2020). A decomposition - construction approach for solving the home health care scheduling problem. Health Care Management Science, 23(2), 264-286. https://doi.org/10.1007/s10729-019-09479-z
Chen, W., & Li, J. (2024). Teleconsultation dynamic scheduling with a deep reinforcement learning approach. Artificial Intelligence in Medicine, 149, 102806. https://doi.org/10.1016/j.artmed.2024.102806
Clapper, Y., Bekker, R., Berkhout, J., & Moeke, D. (2024). Balancing continuity of care and home care schedule costs using blueprint routes. Operations Research for Health Care, 42, 100441. https://doi.org/10.1016/j.orhc.2024.100441
de Aguiar, A. R. P., Ramos, T. R. P., & Gomes, M. I. (2023). Home care routing and scheduling problem with teams’ synchronization. Socio-Economic Planning Sciences, 86, 101503. https://doi.org/10.1016/j.seps.2022.101503
Di Mascolo, M., Martinez, C., & Espinouse, M.-L. (2021). Routing and scheduling in Home Health Care: A literature survey and bibliometric analysis. Computers & Industrial Engineering, 158, 107255. https://doi.org/10.1016/j.cie.2021.107255
Drezet, L. E., & Billaut, J. C. (2008). A project scheduling problem with labour constraints and time-dependent activities requirements. International Journal of Production Economics, 112(1), 217-225. https://doi.org/10.1016/j.ijpe.2006.08.021
Erhard, M., Schoenfelder, J., Fügener, A., & Brunner, J. O. (2018). State of the art in physician scheduling. European Journal of Operational Research, 265(1), 1-18. https://doi.org/10.1016/j.ejor.2017.06.037
Ernst, A. T., Jiang, H., Krishnamoorthy, M., & Sier, D. (2004). Staff scheduling and rostering: A review of applications, methods and models. European Journal of Operational Research, 153(1), 3-27. https://doi.org/10.1016/S0377-2217(03)00095-X
Euchi, J., Masmoudi, M., & Siarry, P. (2022). Home health care routing and scheduling problems: a literature review. 4OR, 20(3), 351-389. https://doi.org/10.1007/s10288-022-00516-2
Fathollahi-Fard, A. M., Govindan, K., Hajiaghaei-Keshteli, M., & Ahmadi, A. (2019). A green home health care supply chain: New modified simulated annealing algorithms. Journal of Cleaner Production, 240, 118200. https://doi.org/10.1016/j.jclepro.2019.118200
Fernandez, A., Gregory, G., Hindle, A., & Lee, A. C. (1974). A Model for Community Nursing in a Rural County. Journal of the Operational Research Society, 25(2), 231-239. https://doi.org/10.1057/jors.1974.40
Fikar, C., & Hirsch, P. (2017). Home health care routing and scheduling: A review. Computers & Operations Research, 77, 86-95. https://doi.org/10.1016/j.cor.2016.07.019
Frifita, S., & Masmoudi, M. (2020). VNS methods for home care routing and scheduling problem with temporal dependencies, and multiple structures and specialties. International Transactions in Operational Research, 27(1), 291-313. https://doi.org/10.1111/itor.12604
Grenouilleau, F., Legrain, A., Lahrichi, N., & Rousseau, L.-M. (2019). A set partitioning heuristic for the home health care routing and scheduling problem. European Journal of Operational Research, 275(1), 295-303. https://doi.org/10.1016/j.ejor.2018.11.025
Hiermann, G., Prandtstetter, M., Rendl, A., Puchinger, J., & Raidl, G. R. (2015). Metaheuristics for solving a multimodal home-healthcare scheduling problem. Central European Journal of Operations Research, 23(1), 89-113. https://doi.org/10.1007/s10100-013-0305-8
Koeleman, P. M., Bhulai, S., & van Meersbergen, M. (2012). Optimal patient and personnel scheduling policies for care-at-home service facilities. European Journal of Operational Research, 219(3), 557-563. https://doi.org/10.1016/j.ejor.2011.10.046
Kraul, S., & Brunner, J. O. (2023). Stable annual scheduling of medical residents using prioritized multiple training schedules to combat operational uncertainty. European Journal of Operational Research, 309(3), 1263-1278. https://doi.org/10.1016/j.ejor.2023.02.007
Lei, L., Tan, Y., Zheng, K., Liu, S., Zhang, K., & Shen, X. (2020). Deep reinforcement learning for autonomous internet of things: model, applications and challenges. IEEE Communications Surveys & Tutorials, 22(3), 1722-1760. https://doi.org/10.1109/COMST.2020.2988367
Lester, W. (2024). Work-life balance. Nephrology Nursing Journal, 51(3), 231-236. https://doi.org/10.37526/1526-744X.2024.51.3.231
Lieder, A., Moeke, D., Koole, G., & Stolletz, R. (2015). Task scheduling in long-term care facilities: A client-centered approach. Operations Research for Health Care, 6, 11-17. https://doi.org/10.1016/j.orhc.2015.06.001
Liu, W., Dridi, M., Fei, H., & El Hassani, A. H. (2021). Hybrid metaheuristics for solving a home health care routing and scheduling problem with time windows, synchronized visits and lunch breaks. Expert Systems with Applications, 183, 115307. https://doi.org/10.1016/j.eswa.2021.115307
Liu, W., Dridib, M., Fathollahi-Fard, A. M., & El Hassani, A. H. (2024). A customized adaptive large neighborhood search algorithm for solving a multi-objective home health care problem in a pandemic environment. Swarm and Evolutionary Computation, 86, 101507. https://doi.org/10.1016/j.swevo.2024.101507
Maenhout, B., & Vanhoucke, M. (2013). An integrated nurse staffing and scheduling analysis for longer-term nursing staff allocation problems. Omega, 41(2), 485-499. https://doi.org/10.1016/j.omega.2012.01.002
Malagodi, L., Lanzarone, E., & Matta, A. (2021). Home care vehicle routing problem with chargeable overtime and strict and soft preference matching. Health Care Management Science, 24(1), 140-159. https://doi.org/10.1007/s10729-020-09532-2
Martinez, C., Espinouse, M. L., & Mascolo, M. D. (2019). Re-planning in home healthcare: A decomposition approach to minimize idle time for workers while ensuring continuity of care. IFAC-PapersOnLine, 52(13), 654-659. https://doi.org/10.1016/j.ifacol.2019.11.104
Méndez-Fernández, I., Lorenzo-Freire, S., García-Jurado, I., Costa, J., & Carpente, L. (2020). A heuristic approach to the task planning problem in a home care business. Health Care Management Science, 23(4), 556-570. https://doi.org/10.1007/s10729-020-09509-1
Moosavi, A., Ozturk, O., & Patrick, J. (2022). Staff scheduling for residential care under pandemic conditions: The case of COVID-19. Omega, 112, 102671. https://doi.org/10.1016/j.omega.2022.102671
Nagayoshi, M., & Tamaki, H. (2022). An approach of exchanging work shifts using reinforcement learning on a constructive nurse scheduling system. Journal of Robotics, Networking and Artificial Life, 9(2), 154-158. https://doi.org/10.57417/jrnal.9.2_154
Ooms, A., Heaton-Shrestha, C., Connor, S., McCawley, S., McShannon, J., Music, G., & Trainor, K. (2022). Enhancing the well-being of front-line healthcare professionals in high pressure clinical environments: A mixed-methods evaluative research project. International Journal of Nursing Studies, 132, 104257. https://doi.org/10.1016/j.ijnurstu.2022.104257
Park, J., Kim, B.-I., Eom, M., & Choi, B. K. (2021). Operating room scheduling considering surgeons’ preferences and cooperative operations. Computers & Industrial Engineering, 157, 107306. https://doi.org/10.1016/j.cie.2021.107306
Quintanilla, S., Ballestín, F., & Pérez, Á. (2020). Mathematical models to improve the current practice in a home healthcare unit. OR Spectrum, 42(1), 43-74. https://doi.org/10.1007/s00291-019-00565-w
Rekabi, S., Moradi, B., Salamian, F., Fadavi, N., Zokaee, M., & Aghsami, A. (2024). A home healthcare routing-scheduling optimization model considering time-balancing and outsourcing. Supply Chain Analytics, 7, 100077. https://doi.org/10.1016/j.sca.2024.100077
Restrepo, M. I., Rousseau, L.-M., & Vallée, J. (2020). Home healthcare integrated staffing and scheduling. Omega, 95, 102057. https://doi.org/10.1016/j.omega.2019.03.015
Restrepo, M. I., Semet, F., & Pocreau, T. (2019). Integrated shift scheduling and load assignment optimization for attended home delivery. Transportation Science, 53(4), 1150-1174. https://doi.org/10.1287/trsc.2018.0857
Riazi, S., Wigström, O., Bengtsson, K., & Lennartson, B. (2019). A column generation-based gossip algorithm for home healthcare routing and scheduling problems. IEEE Transactions on Automation Science and Engineering, 16(1), 127-137. https://doi.org/10.1109/TASE.2018.2874392
Ritchie, C. S., & Leff, B. (2018). Population health and tailored medical care in the home: the roles of home-based primary care and home-based palliative care. Journal of Pain and Symptom Management, 55(3), 1041-1046. https://doi.org/10.1016/j.jpainsymman.2017.10.003
Ruotsalainen, J. H., Verbeek, J. H., Mariné, A., & Serra, C. (2014). Preventing occupational stress in healthcare workers. Cochrane Database of Systematic Reviews(12). https://doi.org/10.1002/14651858.CD002892.pub4
Shahnejat-Bushehri, S., Tavakkoli-Moghaddam, R., Boronoos, M., & Ghasemkhani, A. (2021). A robust home health care routing-scheduling problem with temporal dependencies under uncertainty. Expert Systems with Applications, 182, 115209. https://doi.org/10.1016/j.eswa.2021.115209
Smalley, H. K., & Keskinocak, P. (2016). Automated medical resident rotation and shift scheduling to ensure quality resident education and patient care. Health Care Management Science, 19(1), 66-88. https://doi.org/10.1007/s10729-014-9289-8
Solomon, M. M. (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35(2), 254-265. https://doi.org/10.1287/opre.35.2.254
Soriano, J., Jalao, E. R., & Martinez, I. A. (2020). Integrated employee scheduling with known employee demand, including breaks, overtime, and employee preferences. Journal of Industrial Engineering and Management, 13(3), 451-463. https://doi.org/10.3926/jiem.3126
Ta-Dinh, Q., Pham, T.-S., Hà, M. H., & Rousseau, L.-M. (2024). A reinforcement learning approach for the online dynamic home health care scheduling problem. Health Care Management Science, 27(4), 650-664. https://doi.org/10.1007/s10729-024-09692-5
Tesauro, G., Jong, N. K., Das, R., & Bennani, M. N. (2007). On the use of hybrid reinforcement learning for autonomic resource allocation. Cluster Computing, 10(3), 287-299. https://doi.org/10.1007/s10586-007-0035-6
Van den Bergh, J., Beliën, J., De Bruecker, P., Demeulemeester, E., & De Boeck, L. (2013). Personnel scheduling: A literature review. European Journal of Operational Research, 226(3), 367-385. https://doi.org/10.1016/j.ejor.2012.11.029
Vladu, A., Ghitea, T. C., Daina, L. G., Țîrț, D. P., & Daina, M. D. (2024). Enhancing operating room efficiency: The impact of computational algorithms on surgical scheduling and team dynamics. Healthcare, 12(19).
Walker, L., & Clendon, J. (2018). Early nurse attrition in New Zealand and associated policy implications. International Nursing Review, 65(1), 33-40. https://doi.org/10.1111/inr.12411
Wang, D., Qiao, C., Liu, S., Wang, C., Yang, J., Li, Y., & Huang, P. (2020). Assessment of spatial accessibility to residential care facilities in 2020 in Guangzhou by small-scale residential community data. Sustainability, 12(8).
Wang, W., Xie, K., Guo, S., Li, W., Xiao, F., & Liang, Z. (2023). A shift-based model to solve the integrated staff rostering and task assignment problem with real-world requirements. European Journal of Operational Research, 310(1), 360-378. https://doi.org/10.1016/j.ejor.2023.02.040
Wolfe, H., & Young, J. P. (1965). Staffing the nursing unit : Part I. controlled variable staffing. Nursing Research, 14(3).
Wong, T. C., Xu, M., & Chin, K. S. (2014). A two-stage heuristic approach for nurse scheduling problem: A case study in an emergency department. Computers & Operations Research, 51, 99-110. https://doi.org/10.1016/j.cor.2014.05.018
Yadav, N., & Tanksale, A. (2023). A multi-objective approach for reducing Patient’s inconvenience in a generalized home healthcare delivery setup. Expert Systems with Applications, 219, 119657. https://doi.org/10.1016/j.eswa.2023.119657
Zhong, X. B., & Lou, V. W. Q. (2013). Person-centered care in Chinese residential care facilities: a preliminary measure. Aging & Mental Health, 17(8), 952-958. https://doi.org/10.1080/13607863.2013.790925
監察院審計部. (2022). 長照服務需求人數推估所參據資料之調查期日久遠，恐未符實況，審計部促請改善. Retrieved November 27 from https://www.audit.gov.tw/p/406-1000-7989,r12.php?Lang=zh-tw
衛福部長期照顧司. (2023a). 長照2.0相關icon. Retrieved November 27 from https://1966.gov.tw/LTC/cp-6464-72099-207.html
衛福部長期照顧司. (2023b). 長照十年計畫2.0. Retrieved October 29 from https://www.mohw.gov.tw/dl-78115-5511ccc0-cae0-4d16-b729-6d0e16228fb5.html