Abstract
The home health care (HHC) covers a wide range of health care services carried out in patients’ home in case of illness, injury or aging. Each caregiver should as far as possible adhere to the schedule set by the decision maker. However, unforeseen events would sometimes occur and delay the delivery of care services, which will qualify the service as poor or even risky. Deterministic models ignore this uncertainty, which can arise at any time and will therefore lead to non-compliance with the predefined schedule. Furthermore, patients need several care activities per day, and some of them require to be simultaneous by their nature such as dressing, getting out of bed and bathing. In this work, a stochastic programming model with recourse (SPR model) is proposed to deal with the home health care routing and scheduling problem (HHCRSP) where uncertainties in terms of traveling and caring times that may occur as well as synchronization of services are considered. The objective is to minimize the transportation cost and the expected value of recourse, which is estimated using Monte Carlo simulation. The recourse is defined as a penalty cost for patients’ delayed services and a remuneration for caregivers’ extra working time. The deterministic model is solved by CPLEX, the genetic algorithm (GA) and the general variable neighborhood search (GVNS) based heuristics. The SPR model is solved by Monte Carlo simulation embedded into the GA. Computational results highlight the efficiency of GVNS and GA based heuristics and the complexity of the SPR model in terms of CPU running times.
Similar content being viewed by others
Data Availability
Datasets related to this article can be found at http://dx.doi.org/10.17632/cwvgxbvw4f.1, an open-source online data repository hosted at Mendeley Data.
References
Baker J. E. (1985). Adaptive selection methods for genetic algorithms. In Proceedings of an International Conference on Genetic Algorithms and their applications, pp. 101–111. Hillsdale, New Jersey
Bazirha, M., Kadrani, A., & Benmansour, R. (2019). Daily scheduling and routing of home health care with multiple availability periods of patients. In International Conference on Variable Neighborhood Search, pp. 178–193. Springer
Bazirha, M., Kadrani, A., & Benmansour, R. (2020). Scheduling optimization of the home health care problem with stochastic travel and care times. In 2020 5th International Conference on Logistics Operations Management (GOL), pp. 1–8. IEEE
Ben-Tal, A., El Ghaoui, L., & Nemirovski, A. (2009). Robust optimization (Vol. 28). Princeton: Princeton University Press.
Bernard, D. G. (1955). Linear programming under uncertainty. Management Science, 1, 97–206.
Bertsimas, D., Brown, D. B., & Caramanis, C. (2011). Theory and applications of robust optimization. SIAM Review, 53(3), 464–501.
Bräysy, O., & Gendreau, M. (2005). Vehicle routing problem with time windows, part i: Route construction and local search algorithms. Transportation Science, 39(1), 104–118.
Burke, E. K., De Causmaecker, P., Berghe, G. V., & Van Landeghem, H. (2004). The state of the art of nurse rostering. Journal of Scheduling, 7(6), 441–499.
Charnes, A., & Cooper, W. W. (1959). Chance-constrained programming. Management Science, 6(1), 73–79.
Chepuri, K., & Homem-De-Mello, T. (2005). Solving the vehicle routing problem with stochastic demands using the cross-entropy method. Annals of Operations Research, 134(1), 153–181.
Cissé, M., Yalçındağ, S., Kergosien, Y., Şahin, E., Lenté, C., & Matta, A. (2017). Or problems related to home health care: A review of relevant routing and scheduling problems. Operations Research for Health Care, 13, 1–22.
Davis, L. (1991). Handbook of genetic algorithms
Errico, F., Desaulniers, G., Gendreau, M., Rei, W., & Rousseau, L. M. (2016). A priori optimization with recourse for the vehicle routing problem with hard time windows and stochastic service times. European Journal of Operational Research, 249(1), 55–66.
Gendreau, M., Laporte, G., & Séguin, R. (1996). Stochastic vehicle routing. European Journal of Operational Research, 88(1), 3–12.
Glover, F. (1986). Future paths for integer programming and links to artificial intelligence. Computers & Operations Research, 13(5), 533–549.
Goldberg, D.E., & Deb, K (1991). A comparative analysis of selection schemes used in genetic algorithms. In Foundations of genetic algorithms, vol. 1, pp. 69–93. Elsevier
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.
Holland, J. H. (1992). Genetic algorithms. Scientific American, 267(1), 66–73.
Juan, A. A., Faulin, J., Jorba, J., Caceres, J., & Marquès, J. M. (2013). Using parallel & distributed computing for real-time solving of vehicle routing problems with stochastic demands. Annals of Operations Research, 207(1), 43–65.
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680.
Laporte, G., Louveaux, F., & Mercure, H. (1992). The vehicle routing problem with stochastic travel times. Transportation Science, 26(3), 161–170.
Li, X., Tian, P., & Leung, S. C. (2010). Vehicle routing problems with time windows and stochastic travel and service times: Models and algorithm. International Journal of Production Economics, 125(1), 137–145.
Liu, R., Yuan, B., & Jiang, Z. (2017). Mathematical model and exact algorithm for the home care worker scheduling and routing problem with lunch break requirements. International Journal of Production Research, 55(2), 558–575.
Luo, Z., Qin, H., Zhang, D., & Lim, A. (2016). Adaptive large neighborhood search heuristics for the vehicle routing problem with stochastic demands and weight-related cost. Transportation Research Part E: Logistics and Transportation Review, 85, 69–89.
Mankowska, D. S., Meisel, F., & Bierwirth, C. (2014). The home health care routing and scheduling problem with interdependent services. Health Care Management Science, 17(1), 15–30.
Marinaki, M., & Marinakis, Y. (2016). A glowworm swarm optimization algorithm for the vehicle routing problem with stochastic demands. Expert Systems with Applications, 46, 145–163.
Mendoza, J. E., Rousseau, L. M., & Villegas, J. G. (2016). A hybrid metaheuristic for the vehicle routing problem with stochastic demand and duration constraints. Journal of Heuristics, 22(4), 539–566.
Mladenović, N., & Hansen, P. (1997). Variable neighborhood search. Computers & Operations Research, 24(11), 1097–1100.
Rasmussen, M. S., Justesen, T., Dohn, A., & Larsen, J. (2012). The home care crew scheduling problem: Preference-based visit clustering and temporal dependencies. European Journal of Operational Research, 219(3), 598–610.
Redjem, R., & Marcon, E. (2016). Operations management in the home care services: a heuristic for the caregivers routing problem. Flexible Services and Manufacturing Journal, 28(1–2), 280–303.
Rest, K. D., & Hirsch, P. (2016). Daily scheduling of home health care services using time-dependent public transport. Flexible Services and Manufacturing Journal, 28(3), 495–525.
Sarasola, B., Doerner, K. F., Schmid, V., & Alba, E. (2016). Variable neighborhood search for the stochastic and dynamic vehicle routing problem. Annals of Operations Research, 236(2), 425–461.
Shi, Y., Boudouh, T., & Grunder, O. (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, 128, 52–95.
Shi, Y., Boudouh, T., Grunder, O., & 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.
Taillard, E. (1990). Some efficient heuristic methods for the flow shop sequencing problem. European Journal of Operational research, 47(1), 65–74.
Tarricone, R., & Tsouros, A.D (2008). Home care in Europe: the solid facts. WHO Regional Office Europe
Taş, D., Dellaert, N., van Woensel, T., & De Kok, T. (2014). The time-dependent vehicle routing problem with soft time windows and stochastic travel times. Transportation Research Part C: Emerging Technologies, 48, 66–83.
Taş, D., Gendreau, M., Dellaert, N., Van Woensel, T., & De Kok, A. (2014). Vehicle routing with soft time windows and stochastic travel times: A column generation and branch-and-price solution approach. European Journal of Operational Research, 236(3), 789–799.
Trautsamwieser, A., & Hirsch, P. (2011). Optimization of daily scheduling for home health care services. Journal of Applied Operational Research, 3(3), 124–136.
Von Neumann, J., & Ulam, S. (1951). Monte carlo method. National Bureau of Standards Applied Mathematics Series, 12(1951), 36.
WHO, A., & Course, L. (2017). World report on ageing and health 2015
Yuan, B., Liu, R., & 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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bazirha, M., Kadrani, A. & Benmansour, R. Stochastic home health care routing and scheduling problem with multiple synchronized services. Ann Oper Res 320, 573–601 (2023). https://doi.org/10.1007/s10479-021-04222-w
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-021-04222-w