Table 2.2. Case of rescheduling with disruptions
| Number of disturbances | Number of reassigned visits per caregiver | Computation time (s) |
| 1 | 1 2 3 | 4.66-5.09 4.66-5.09 4.66-5.09 |
| 2 | 1 2 3 | 4.66-5.09 4.66-5.09 4.66-5.09 |
| 2 | 1 2 3 | 4.66-5.09 4.66-5.09 4.70-5.36 |
We also tested the rescheduling algorithm by adding disruptions represented by staff absences. The rescheduling phase can occur after the first route is calculated. Table 2.2 presents the results obtained when we have one to four disruptions. These visits are reassigned to other caregivers, and we find that each caregiver has one to three visits added to their initial schedule. Rescheduling is achieved in seconds. It is very efficient for the coordinator who needs a reactive system.
2.5. Conclusions and perspectives
In this chapter, we have focused on the HHC scheduling and rescheduling problems. We took into account the constraints related to the preferences, availabilities and dependency levels of patients as well as the qualifications and working hours of caregivers.
We have developed a genetic algorithm that calculates a schedule and also takes into account disruptions in real time. Re-planning makes it possible to reassign the unachieved activities in the case of an absence in a very short time (a few seconds). We were able to show the robustness and efficiency of our approach, which allows the scheduler manager to obtain all the schedule in few seconds, whether for the purposes of planning or rescheduling.
From the perspective of research, in future studies we will be able to integrate uncertainties related to the care duration as well as to take into account the rescheduling of other criteria, such as the absence of a patient at home or the development of their care condition.
2.6. References
Ben Hassen, H., Tounsi, J., Ben Bachouch, R. (2019). An artificial immune algorithm for HHC planning based on multi-agent system. Procedia Computer Science, 164, 251–256.
Braislford, S. and Vissers, J. (2011). OR in healthcare: A European perspective. European Journal of Operational Research, 212(2), 223–234.
Cappanera, P. (2013). Home care optimization: Impact of pattern generation policies on scheduling and routing decisions. Electronic Notes in Discrete Mathematics, 41, 53–60.
Cappanera, P., Scutella, M.G., Nervi, F., Galli, L. (2018). Demand uncertainty in robust home care optimization. Omega, 80, 95–110.
Cardoso, T., Oliveira, M.D., Barbosa-Povoa, A., 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, 321–334.
Cissé, M., Yalçindag, S., Kergosien, Y., Sahin, 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, 13–14(C), 1–22.
David, G. and Kim, K.L. (2018). The effect of workforce assignment on performance: Evidence from home health care. Journal of Health Economics, 59, 26–45.
Decerle, J., Grunder, O., El Hassani, A.H., Barakat, O. (2018). A memetic algorithm for a home health care routing and scheduling problem. Operations Research for Health Care, 16, 59–71.
Decerle, J., Grunder, O., El Hassani, A.H., Barakat, O. (2019). A memetic algoritm for multi-objective optimization of the home health care problem. Swarm and Evolutionary Computation, 44, 712–727.
Di Mascolo, M., Espinouse, M.L., El Hajri, Z., (2017). Planning in home health care structures: A literature review. IFAC PapersOnLine, 50(1), 4656–4659.
Di Mascolo, M., Espinouse, M.L., Ait Haddadene, S.R. (2018). Taking patients’ wishes into account for daily planning in the home health care context. IFAC PapersOnLine, 51(11), 1010–1015.
Emiliano, W., Telhada, J., Do Sameiro Carvalho, M. (2017). Home health care logistics planning: A review and framework. Procedia Manufacturing, 13, 848–955.
Erdem, M. and Koç, C. (2019). Analysis of electric vehicles in home health care routing problem. Journal of Cleaner Production, 234, 1471–1483.
Falkenauer, E. (1992). The grouping genetic algorithms – Widening the scope of the GAs. Belgian Journal of Operations Research, Statistics and Computer Science, 6, 79–102.
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.
Fikar, C. and Hirsch, P. (2017). Home health care routing and scheduling: A review. Computers and Operations Research, 77, 86–95.
Filho, E.V.G. and Tiberti, A.J. (2006). A group genetic algorithm for the machine cell formation problem. International Journal of Production Economics, 102, 1–21.
Grenouilleau, F., Legrain, A., Lahrichi, N., Rousseau, L.M. (2019). A set partitioning heuristic for the home health care routing problem. European Journal of Operational Research, 275, 295–303.
Grenouilleau, F., Lahrichi, N., Rousseau, L.M. (2020). New decomposition methods for home care scheduling with predefined visits. Computers and Operations Research, 115, 104–855.
Hewitt, M., Nowak, M., Nataraj, N. (2016). Planning strategies for home health care delivery. Asia-Pacific Journal of Operational Research, 33(5), 1650041.
Holland, J.H. (1975). Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. University of Michigan Press, Ann Arbor, USA.
Issaoui, B., Zidi, I., Marcon, E., Ghedira, K. (2015). New multi-objective approach for the home care service problem based on scheduling algorithms and variable neighborhood descent. Electronic Notes in Discrete Mathematics, 47, 181–188.
Koeleman, P.M., Bhulai, S., Meersbergen, M. (2012). Optimal patient and personnel scheduling plocies for care-at-home service facilities. European Journal of Operational Research, 219(3), 557–563.
Lanzarone, E. and Matta, A. (2014). Robust nurse-to-patient assignment in home care services to minimize overtimes under continuity of care. Operational Research for Health Care, 3(2), 48–58.
Marcon, E., Chaabane, S., Sallez, Y., Bonte, T., Trentesaux, D. (2017). A multi-agent system based on reactive decision rules for solving the caregiver routing problem in HHC. Simulation Modelling Practice Theory, 74, 134–151.
Martinez, C., Espinousse, M-L., Di Mascolo, M. (2019). Re-planning in home healthcare: A review decomposition approach to minimize idle time for workers while ensuring continuity of care. IFAC PapersOnLine, 52(13), 654–659.