STOKASTİK TALEPLİ VE ÇOK PERİYOTLU EVDE SAĞLIK HİZMETLERİNİN PLANLANMASI PROBLEMİ

Abstract

Evde Sağlık Hizmetleri (ESH), yaşlanan nüfus ve kronik hastalıkların yükselmesiyle birlikte giderek daha fazla önem kazanmaktadır. Ancak, bu hizmetlerin etkin ve verimli bir şekilde planlanması ve yönetilmesi, stokastik hasta talepleri, değişken yol koşulları ve kaynakların kapasitesi gibi birçok kısıtla karşı karşıyadır. Özellikle, hasta taleplerinin stokastik doğası, planlamada önemli bir belirsizlik faktörü oluşturmakta ve planların çoğu zaman yeniden düzenlenmesini gerektirmektedir. Ayrıca, ESH'nin çok periyotlu bir yapısı vardır, yani her hasta için farklı zaman dilimlerinde farklı türden hizmetler gerekebilmektedir. Bu çalışmanın ana amacı, stokastik hasta talepleri ve çok periyotlu planlama ihtiyaçlarını dikkate alarak, ESH hizmetlerinin sunumunu daha etkin ve verimli bir şekilde yapabilecek bir matematiksel model önermektir. Önerilen model, kaynakların daha etkin bir şekilde ayrılmasına, servis kalitesinin artırılmasına ve acil durumlarla daha etkin bir şekilde başa çıkılmasına da katkı sağlayacaktır. Bu, hem hastalara daha iyi hizmet sunumu hem de sağlık sistemi için daha düşük maliyetler anlamına gelmektedir.

Keywords

• Evde sağlık hizmetleri
• Araç rotalama problemi
• Stokastik talep
• Stokastik programlama

The Multi-Period Home Health Care Planning Problem with Stochastic Demand

Abstract

Home Health Services (HHS) are gaining increasing importance with the aging population and the rise in chronic illnesses. However, the effective and efficient planning and management of these services face numerous constraints, such as stochastic patient demands, variable road conditions, and resource capacities. In particular, the stochastic nature of patient demands creates a significant uncertainty factor in planning, often requiring the reorganization of plans. Furthermore, HHS has a multi-periodic structure; that is, different types of services may be needed for each patient at different time slots. The main aim of this study is to propose a mathematical model that takes into account stochastic patient demands and multiperiodic planning needs to make the provision of HHS more effective and efficient. The proposed model will contribute to the more effective allocation of resources, the improvement of service quality, and better handling of emergency situations. This translates to both better service provision for patients and lower costs for the healthcare system.

Keywords

• Home care services
• Vehicle routing problem
• Stochastic demand
• Stochastic programming

References

1. 1. Bazirha, M., Kadrani, A. ve Benmansour, R. (2023) Stochastic home health care routing and scheduling problem with multiple synchronized services, Annals of Operations Research, 320(2), 573-601. doi:10.1007/s10479-021-04222-w
2. 2. Cardoso, T., Oliveira, MD., Barbosa-Povoa, A. ve Nickel, S. (2015) An integrated approach for planning a long-term care network with uncertainty, strategic policy and equity considerations, European Journal of Operational Research, 247(1), 321-334. doi:10.1016/j.ejor.2015.05.074
3. 3. Carello, G. ve Lanzarone, E. (2021) An implementor-adversary approach for uncertain and time-correlated service times in the nurse-to-patient assignment problem, Computers&Operations Research. doi:10.1016/j.cor.2021.105378
4. 4. Chen, C., Rubinstein, ZB., Smith, SF. ve Lau, HC. (2017) Tackling large-scale home health care delivery problem with uncertainty, Twenty-Seventh International Conference on Automated Planning and Scheduling, Pittsburgh, 358-366. https://www.ri.cmu.edu/publications/tackling-large-scale-home-health-care-delivery-problem-with-uncertainty/
5. 5. Chen, H., Luo, X., Zhang, Z. ve Zhou, O. (2021) Stochastic bi-level programming model for home healthcare scheduling problems considering the degree of satisfaction, Journal Of Systems Science And Systems Engineering, 30(5), 572–599. doi:10.1007/s11518-021-5507-3
6. 6. Du, G. ve Zhang, J. (2022) Cross-regional manpower scheduling and routing problem with stochastic service times in home health care, Computers & Industrial Engineering, 173, 108668. doi:10.1016/j.cie.2022.108668
7. 7. Euchi, J., Masmoudi, M. ve Siarry, P. (2022) Home health care routing and scheduling problems: a literature review, 4or-A Quarterly Journal Of Operations Research, 20, 351–389. doi:10.1007/s10288- 022-00516-2
8. 8. Fu, Y., Ding, F., Mu, Z., Sun, C. ve Gao, K. (2022) Integrating scheduling and routing decisions into home health care operation with skill requirements and uncertainities, Journal of Simulation. doi:10.1080/17477778.2022.2108735

9. 9. Grieco, L., Utley, M. ve Crowe, S. (2021) Operational research applied to decisions in home health care: A systematic literature review, Journal of the Operational Research Society, 72(9), 1960-1991. doi:10.1080/01605682.2020.1750311
10. 10. Liu, R., Yuan, B. ve Jiang, Z. (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, 31, 989-1011. doi:10.1007/s10696-018-9328-8
11. 11. Mascolo, D., Martinez, M.,C. ve Espinouse, M.,L. (2021) Routing and scheduling in Home Health Care: A literature survey and bibliometric analysis, Computers& Industrial Engineering, 158, 107255. doi:10.1016/j.cie.2021.107255
12. 12. Nikzad, E., Bashiri, M. ve Abbasi, B. (2021) A matheuristic algorithm for stochastic home health care planning, European Journal of Operational Research, 288(3), 753-774. doi:10.1016/j.ejor.2020.06.040
13. 13. Nikzad, E., Bashiri, M. ve Abbasi, B. (2023) Home healthcare staff dimensioning problem for temporary caregivers: A matheuristic solution approach, Computers & Operations Research, 152. doi:10.1016/j.cor.2022.106126
14. 14. Rodriguez, C., Garaix, T., Xie, X. ve Augusto, V. (2015) Staff dimensioning in homecare services with uncertain demands, International Journal of Production Research, 53(24), 7396-7410. doi:10.1080/00207543.2015.1081427
15. 15. Shi, Y., Boudouh, T. ve Grunder, O. (2017) A home health care routing problem with stochastic travel and service time, IFAC-PapersOnLine, 50(1), 13987-13992. doi:10.1016/j.ifacol.2017.08.2419
16. 16. Shi, Y., Boudouh, T., Grunder, O. ve Wang, D. (2018) Modeling and solving simultaneous delivery and pick-up problem with stochastic travel and service times in home health care, Expert systems with applications, 102, 218-233. doi:10.1016/j.eswa.2018.02.025
17. 17. Shi, Y., Boudouh, T. Ve Grunder, O., (2019) A robust optimization for a home health care routing and scheduling with consideration of uncertain travel and service times, Transportation Research Part E, 128, 52-95. doi:10.1016/j.tre.2019.05.015
18. 18. Tsang, MY. ve Shehadeh, KS. (2023) Stochastic optimization models for a home service routing and appointment scheduling problem with random travel and service times, European Journal Of Operational Research, 307(1), 48-63. doi:10.1016/j.ejor.2022.09.020
19. 19. Yang, X., Zhang, T., Mao, N., Chen, Q., Bai, L. ve Chen, W. (2018) The stochastic home health care routing problem in dense communities with multi-appointment, In 2018 15th International Conference on Service Systems and Service Management, IEE, Hangzhou-China, 1-6. https://c85689232ea394a8dc08a512c1f46793a2397178.vetisonline.com/stamp/stamp.jsp?tp=&arnumber=8464971
20. 20. Yuan, B., Liu, R. ve Jiang, Z. (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, 53(24), 7450-7464. doi:10.1080/00207543.2015.1082041
21. 21. Yuan, B., Liu, R. ve Jiang, Z. (2018) Daily scheduling of caregivers with stochastic times, International Journal of Production Research, 56(9), 3245-3261. doi:10.1080/00207543.2018.1445879
22. 22. Zhan, Y., Wang, Z. ve Wan, G. (2021) Home service routing and appointment scheduling with stochastic service times, European Journal of Operational Research, 288, 98-110. doi:10.1016/j.ejor.2020.05.037