Planning the Delivery of Home-Based Long-Term Care: A Mathematical Programming-Based Tool to Support Routes’ Planning

  • Daniel Espadinha
  • Teresa Cardoso-GriloEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 278)


The adequate planning of home-based long-term care (HBLTC) is essential in the current European setting where long-term care (LTC) demand is increasing rapidly, and where home-based care represents a potential cost-saving alternative from traditional inpatient care. Particularly, this planning should involve proper route planning to ensure visits of health professionals to patients’ homes. Nevertheless, literature in the specific area of HBLTC planning is still scarce. Accordingly, this paper proposes a tool based on a mathematical programming model—the \(LTC^{routes}\)—for supporting the daily planning of routes to visit LTC patients’ homes in National Health Service-based countries. The model allows exploring the impact of considering different objectives relevant in this sector, including the minimization of costs and the maximization of service level. Patients’ preferences, traffic conditions and budget constraints are also considered in the proposed model. To illustrate the applicability of the model, a case study based on the National Network of LTC in Portugal is analyzed.


Health care planning Long-term care Home-based care Route planning Mathematical programming 


  1. 1.
    Akjiratikarl, C., Yenradee, P., Drake, P.R.: PSO-based algorithm for home care worker scheduling in the UK. Comput. Ind. Eng. 53(4), 559–583 (2007)CrossRefGoogle Scholar
  2. 2.
    Baker, M.: Making Sense of the NHS White Papers, 2nd edn. Radcliffe Medical Press, Oxon (2000)Google Scholar
  3. 3.
    Bachouch, R.B., Guinet, A., Hajri-Gabouj, S.: A decision-making tool for home health care nurses’ planning. Supply Chain Forum Int. J. 12(1), 14–20 (2011)CrossRefGoogle Scholar
  4. 4.
    Bertels, S., Fahle, T.: A hybrid setup for a hybrid scenario: combining heuristics for the home health care problem. Comput. Oper. Res. 33(10), 2866–2890 (2006)CrossRefGoogle Scholar
  5. 5.
    Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer, New York (1997)zbMATHGoogle Scholar
  6. 6.
    Braekers, K., Hartl, R.F., Parragh, S.N., Tricoire, F.: A bi-objective home care scheduling problem: analyzing the trade-off between costs and client inconvenience. Eur. J. Oper. Res. 248(2), 428–443 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cardoso, T., Oliveira, M., Barbosa-Póvoa, A., Nickel, S.: Modeling the demand for long-term care services under uncertain information. Health Care Manag. Sci. 15(4), 385–412 (2012)CrossRefGoogle Scholar
  8. 8.
    Cohon, J.L.: Multiobjective Programming and Planning. Academic Press Inc., London (1978)zbMATHGoogle Scholar
  9. 9.
    Fikar, C., Hirsch, P.: Home health care routing and scheduling: a review. Comput. Oper. Res. 77, 86–95 (2017)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Gutirrez, E.V., Vidal, C.J.: Home health care logistics management: Framework and research perspectives. Int. J. Ind. Eng. Manag. 4(3), 173–182 (2013)Google Scholar
  11. 11.
    Knapp, M., Somani, A.: Health financing: long term care, organization and financing. In: Carrin, G., Buse, K., Heggenhougen, K., Quah, S.R. (eds.) Health Systems Policy, Finance, and Organization, pp. 250–9. AcademicPress, San Diego (2009)Google Scholar
  12. 12.
    Lanzarone, E., Matta, A.: Robust nurse-to-patient assignment in home care services to minimize overtimes under continuity of care. Oper. Res. Health Care 3(2), 48–58 (2014)CrossRefGoogle Scholar
  13. 13.
    Maya Duque, P.A., Castro, M., Srensen, K., Goos, P.: Home care service planning. The case of Landelijke Thuiszorg. Eur. J. Oper. Res. 243(1), 292–301 (2015)CrossRefGoogle Scholar
  14. 14.
    Milburn, A.B.: Operations research applications in home healthcare. In: Hall, R. (eds) Handbook of Healthcare System Scheduling. International Series in Operations Research & Management Science, vol. 168. Springer, Boston (2012)Google Scholar
  15. 15.
    Miller, C.E., Tucker, A.W., Zemlin, R.A.: Integer programming formulation of traveling salesman problems. J. Assoc. Comput. Mach. 7, 326–329 (1960)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Ministry of Health: Decreto-lei n 101/2006: Cria a Rede Nacional de Cuidados Continuados Integrados [Create the National Network of Long-Term Care], Dirio da Repblica: I Srie-A, no 109 de 6 de Junho (2006)Google Scholar
  17. 17.
    Ministry of Health: Lei n 48/90: Lei de bases da saúde [Fundamental principles of health], Diário da República: I Série-A, n 195 de 24 de Agosto (1990)Google Scholar
  18. 18.
    Rodriguez, C., Garaix, T., Xie, X., Augusto, V.: Staff dimensioning in homecare services with uncertain demands. Int. J. Prod. 53(24), 7396–410 (2015)CrossRefGoogle Scholar
  19. 19.
    Simões, J., Augusto, G.F., Fronteira, I., Hernández-Quevedo, C.: Portugal: health system review. Health Syst. Transition 19(2), 1–184 (2017)Google Scholar
  20. 20.
    Trautsamwieser, A., Hirsch, P.: Optimization of daily scheduling for home health care services. J. Appl. Oper. Res. 3(3), 124–136 (2011)Google Scholar
  21. 21.
    Vidal, C.J., Gutirrez, E., Gutierrez, V.: Home health care logistics management problems: a critical review of models and methods. Revista Facultad Ingeniería Univ. Antioq. 68, 160–175 (2013)Google Scholar
  22. 22.
    World Health Organization: Home-based long-term care: report of a WHO study group. World Health Organization, Geneva (2000)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Instituto Universitário de Lisboa (ISCTE-IUL)LisboaPortugal
  2. 2.Centre for Management Studies of Instituto Superior Técnico (CEG-IST), Instituto Universitário de Lisboa (ISCTE-IUL)LisboaPortugal

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