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Quantitative thresholds based decision support approach for the home health care scheduling and routing problem

  • Jamal Abdul NasirEmail author
  • Chuangyin Dang
Article
  • 23 Downloads

Abstract

In the domain of Home Health Care (HHC), precise decisions regarding patient’s selection, staffing level, and scheduling of health care staff have a significant impact on the efficiency and effectiveness of the HHC system. However, decentralized planning, the absence of well defined decision rules, delayed decisions and lack of interactive tools typically lead towards low satisfaction level among all the stakeholders of the HHC system. In order to address these issues, we propose an integrated three phase decision support methodology for the HHC system. More specifically, the proposed methodology exploits the structure of the HHC problem and logistic regression based approaches to identify the decision rules for patient acceptance, staff hiring, and staff utilization. In the first phase, a mathematical model is constructed for the HHC scheduling and routing problem using Mixed-Integer Linear Programming (MILP). The mathematical model is solved with the MILP solver CPLEX and a Variable Neighbourhood Search (VNS) based method is used to find the heuristic solution for the HHC problem. The model considers the planning concerns related to compatibility, time restrictions, distance, and cost. In the second phase, Bender’s method and Receiver Operating Characteristic (ROC) curves are implemented to identify the thresholds based on the CPLEX and VNS solution. While the third phase creates a fresh solution for the HHC problem with a new data set and validates the thresholds predicted in the second phase. The effectiveness of these thresholds is evaluated by utilizing performance measures of the widely-used confusion matrix. The evaluation of the thresholds shows that the ROC curves based thresholds of the first two parameters achieved 67% to 71% accuracy against the two considered solution methods. While the Bender’s method based thresholds for the same parameters attained more than 70% accuracy in cases where probability value is small (p ≤ 0.5). The promising results indicate that the proposed methodology is applicable to define the decision rules for the HHC problem and beneficial to all the concerned stakeholders in making relevant decisions.

Keywords

Decision rules Home health care Nurse scheduling Patients selection Quantitative thresholds 

Notes

Acknowledgements

This research work was partially supported by CityU 11301014 of Hong Kong SAR Government.

References

  1. 1.
    Rest K-D, Hirsch P (2015) Daily scheduling of home health care services using time-dependent public transport. Flexible Services and Manufacturing JournalGoogle Scholar
  2. 2.
    Begur SV, Miller DM, Weaver JR (1997) An integrated spatial DSS for scheduling and routing home-health-care nurses. Interfaces 27(4):3–48Google Scholar
  3. 3.
    Cheng E, Rich LJ (1998) A home health care routing and scheduling problem. Technical Report TR98-04, Department of CAAM, Rice University, Houston USAGoogle Scholar
  4. 4.
    Bertels S, Fahle T (2006) A hybrid setup for a hybrid scenario: combining heuristics for the home health care problem. Comput Oper Res 33(10):2866–2890Google Scholar
  5. 5.
    Eveborn P, Flisberg P, Ronnqvist M (2006) Laps care an operational system for staff planning of home care. Eur J Oper Res 171(3):962–976Google Scholar
  6. 6.
    Rasmussen MS, Justesen T, Dohn A, Larsen J (2012) The home care crew scheduling problem: preference-based visit clustering and temporal dependencies. Eur J Oper Res 219(3):598–610Google Scholar
  7. 7.
    Mankowska DS, Meisel F, Bierwirth C (2014) The home health care routing and scheduling problem with interdependent services. Health Care Manag Sci 17(1):15–30Google Scholar
  8. 8.
    Nasir JA, Dang C (2018) Solving a more flexible home health care scheduling and routing problem with joint patient and nursing staff selection. Sustainability, 10(1)Google Scholar
  9. 9.
    Shao YF, Bard JF, Jarrah aI (2012) The therapist routing and scheduling problem. IIE Trans 44(10):868–893Google Scholar
  10. 10.
    Nickel S, Schröder M, Steeg J (2012) Mid-term and short-term planning support for home health care services. Eur J Oper Res 219:574–587Google Scholar
  11. 11.
    Demirbilek M, Branke J, Strauss A (2018) Dynamically accepting and scheduling patients for home healthcare. Health Care Management ScienceGoogle Scholar
  12. 12.
    Rodriguez-Verjan C, Augusto V, Xie X (2017) Home health-care network design: location and configuration of home health-care centers. Operations Research for Health CareGoogle Scholar
  13. 13.
    Borsani V, Matta A, Beschi G, Sommaruga F (2006) A home care scheduling model for human resources. In: 2006 International conference on service systems and service management, vol 1, pp 449–454Google Scholar
  14. 14.
    Lanzarone E, Matta A (2011) A cost assignment policy for home care patients. Flex Serv Manuf J 24(4):465–495Google Scholar
  15. 15.
    Carello G, Lanzarone E (2014) A cardinality-constrained robust model for the assignment problem in Home Care services. Eur J Oper Res 236(2):748–762Google Scholar
  16. 16.
    Blais M, Lapierre SD, Laporte G (2003) Solving a home-care districting problem in an urban setting. J Oper Res Soc 54(11):1141–1147Google Scholar
  17. 17.
    Benzarti E, Sahin E, Dallery Y (2013) Operations management applied to home care services: analysis of the districting problem. Decis Support Syst 55(2):587–598Google Scholar
  18. 18.
    Xiao R, Miller JA, Zafirau WJ, Gorodeski EZ, Young JB (2018) Impact of home health care on health care resource utilization following hospital discharge: a cohort study. Am J Med 131(4):395–407.e35Google Scholar
  19. 19.
    Han SJ, Kim HK, Storfjell J, Mi JK (2013) Clinical outcomes and quality of life of home health care patients. Asian Nurs Res 7:53–60Google Scholar
  20. 20.
    Garavaglia G, Lettieri E, Agasisti T, Lopez S (2011) Efficiency and quality of care in nursing homes: an italian case study. Health Care Manag Sci 14:22–35Google Scholar
  21. 21.
    Ellenbecker CH (2004) A theoretical model of job retention for home health care nurses. J Adv Nurs 47(3):303–310Google Scholar
  22. 22.
    Wright PD, Mahar S (2013) Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction. Omega 41(6):1042–1052Google Scholar
  23. 23.
    Ulm K (1991) A statistical method for assessing a threshold in epidemiological studies. Stat Med 10:341–349Google Scholar
  24. 24.
    Bender R (1999) Quantitative risk assessment in epidemiological studies investigating threshold effects. Biom J 41(3):305–319Google Scholar
  25. 25.
    Ozanne B, Nelson J, Cousineau J, Lambert M, Phan V, Mitchell G, Alvarez F, Ducruet T, Jouvet P (2012) Threshold for toxicity from hyperammonemia in critically ill children. J Hepatol 56(1):123–128Google Scholar
  26. 26.
    Kitchenham B (2010) What’s up with software metrics? - A preliminary mapping study. J Syst Softw 83(1):37–51Google Scholar
  27. 27.
    Shatnawi R (2010) A quantitative investigation of the acceptable risk levels of object-oriented metrics in open-source systems. IEEE Trans Softw Eng 36(2):216–225Google Scholar
  28. 28.
    Mendling J, Gonzalez LS, García F, Rosa ML (2012) Thresholds for error probability measures of business process models. J Syst Softw 85(5):1188–1197Google Scholar
  29. 29.
    Ferreira KM, Bigonha MS, Bigonha RS, Mendes LFO, Almeida HC (2012) Identifying thresholds for object-oriented software metrics. J Syst Softw 85(2):244–257Google Scholar
  30. 30.
    Nasir JA, Dang C (2016) Identifying quantitative thresholds for the home health care problem. In: 2016 IEEE symposium on computers and communication (ISCC), pp 220–225Google Scholar
  31. 31.
    Braysy O, Dullaert W, Nakari P (2009) The potential of optimization in communal routing problems: case studies from finland. J Transp Geogr 17(6):484–490Google Scholar
  32. 32.
    Hertz A, Lahrichi N (2008) A patient assignment algorithm for home care services. J Oper Res Soc 60(4):481–495Google Scholar
  33. 33.
    Hiermann G, Prandtstetter M, Rendl A, Puchinger J, Raidl GR (2013) Metaheuristics for solving a multimodal home-healthcare scheduling problem. CEJOR, 89–113Google Scholar
  34. 34.
    Bredström D, Rönnqvist M (2008) Combined vehicle routing and scheduling with temporal precedence and synchronization constraints. Eur J Oper Res 191(1):19–31Google Scholar
  35. 35.
    Dohn A, Rasmussen MS, Larsen J (2011) The vehicle routing problem with time windows and temporal dependencies. Networks 58(4):273–289Google Scholar
  36. 36.
    Doerner KF, Gronalt M, Hartl RF, Kiechle G, Reimann M (2008) Exact and heuristic algorithms for the vehicle routing problem with multiple interdependent time windows. Comput Oper Res 35(9):3034–3048Google Scholar
  37. 37.
    Yalçındaǧ S, Matta A, Şahin E, George Shanthikumar J (2016) The patient assignment problem in home health care: using a data-driven method to estimate the travel times of care givers. Flex Serv Manuf J 28 (1-2):304–335Google Scholar
  38. 38.
    Trautsamwieser A, Gronalt M, Hirsch P (2011) Securing home health care in times of natural disasters. OR Spectr 33(3):787–813Google Scholar
  39. 39.
    Kergosien Y, Lenté C, Billaut J-C (2009) Home health care problem: an extended multiple traveling salesman problem. In: Proceedings of the 4th multidisciplinary international scheduling conference: theory and applications (MISTA 2009), pp 85–92Google Scholar
  40. 40.
    Allaoua H, Borne S, Létocart L, Calvo RW (2013) A matheuristic approach for solving a home health care problem. Electron Notes Discret Math 41:471–478Google Scholar
  41. 41.
    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 Manag Sci 12(2):179–191Google Scholar
  42. 42.
    Shi Y, Boudouh T, Grunder O (2017) A hybrid genetic algorithm for a home health care routing problem with time window and fuzzy demand. Expert Syst Appl 72:160–176Google Scholar
  43. 43.
    Nasir JA, Hussain S, Dang C (2018) An integrated planning approach towards home health care, telehealth and patients group based care. J Netw Comput Appl 117:30–41Google Scholar
  44. 44.
    Bekker R, Moeke D, Schmidt B (2018) Keeping pace with the ebbs and flows in daily nursing home operations. Health Care Management ScienceGoogle Scholar
  45. 45.
    Benlarbi S, El Emam K, Goel N, Rai S (2000) Thresholds for object-oriented measures. In: Proceedings of the 11th international symposium on software reliability engineering, pp 24–37Google Scholar
  46. 46.
    Arar ÖF, Ayan K (2016) Deriving thresholds of software metrics to predict faults on open source software replicated case studies. Expert Syst Appl 61:106–121Google Scholar
  47. 47.
    Grouven U, Küchenhoff H, Schräder P, Bender R (2008) Flexible regression models are useful tools to calculate and assess threshold values in the context of minimum provider volumes. J Clin Epidemiol 61(11):1125–1131Google Scholar
  48. 48.
    Solomon MM (1987) Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper Res 35(2):254–265Google Scholar
  49. 49.
    Hansen P, Mladenović N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130:449–467Google Scholar
  50. 50.
    Kindervater G, Savelsbergh M (1997) Vehicle routing: handling edges exchanges. In: Aarts EHL, Lenstra JK (eds) Local search in combinatorial optimization. Wiley, London, pp 337–360Google Scholar
  51. 51.
    Hansen P, Mladenović N (2003) Variable neighborhood search. In: Glover HF, Kochenberger G (eds) Handbook of metaheuristics, vol 57. Springer, New York, pp 145–184Google Scholar
  52. 52.
    Singh S, Kahlon KS (2014) Object oriented software metrics threshold values at quantitative acceptable risk level. CSIT 2(3):191–205Google Scholar
  53. 53.
    Green DM, Swets JA (1966) Signal detection theory and psychophysics. WileyGoogle Scholar
  54. 54.
    Zweig MH., Campbell G (1993) Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clin Chem 39(4):561–577Google Scholar
  55. 55.
    Hosmer DW, Lemeshow S (2000) Wiley series in probability and statistics: applied logistic regression. WileyGoogle Scholar
  56. 56.
    Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143:29–36Google Scholar
  57. 57.
    Fawcett T (2006) An introduction to roc analysis. Pattern Recogn Lett 27(8):861–874Google Scholar
  58. 58.
    Lewis DD (1991) Evaluating text categorization. In: Proceedings of speech and natural language workshop. Morgan Kaufmann, pp 312–318Google Scholar
  59. 59.
    Yang Y (1999) An evaluation of statistical approaches to text categorization. Inf Retr 1(1):69–90Google Scholar
  60. 60.
    Sokolova M, Lapalme G (2009) A systematic analysis of performance measures for classification tasks. Inform Process Manag 45(4):427–437Google Scholar
  61. 61.
    Sánchez-González L, García F, Ruiz F, Mendling J (2012) Quality indicators for business process models from a gateway complexity perspective. Inf Softw Technol 54(11):1159–1174Google Scholar
  62. 62.
    Churchill GA, Doerge RW (1994) Empirical threshold values for quantitative trait mapping. GENETICS 138:963–971Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Systems Engineering and Engineering ManagementCity University of Hong KongKowloon TongHong Kong

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