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

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.

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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 Journal

  2. 2.

    Begur SV, Miller DM, Weaver JR (1997) An integrated spatial DSS for scheduling and routing home-health-care nurses. Interfaces 27(4):3–48

    Google 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 USA

  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):2866–2890

    Article  Google 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):962–976

    Article  Google 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):598–610

    Article  Google 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):15–30

    Article  Google 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)

  9. 9.

    Shao YF, Bard JF, Jarrah aI (2012) The therapist routing and scheduling problem. IIE Trans 44(10):868–893

    Article  Google 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 219:574–587

    Article  Google Scholar 

  11. 11.

    Demirbilek M, Branke J, Strauss A (2018) Dynamically accepting and scheduling patients for home healthcare. Health Care Management Science

  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 Care

  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 449–454

  14. 14.

    Lanzarone E, Matta A (2011) A cost assignment policy for home care patients. Flex Serv Manuf J 24(4):465–495

    Article  Google 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):748–762

    Article  Google 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):1141–1147

    Article  Google 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):587–598

    Article  Google 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.e35

    Article  Google 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 7:53–60

    Article  Google 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 14:22–35

    Article  Google Scholar 

  21. 21.

    Ellenbecker CH (2004) A theoretical model of job retention for home health care nurses. J Adv Nurs 47(3):303–310

    Article  Google Scholar 

  22. 22.

    Wright PD, Mahar S (2013) Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction. Omega 41(6):1042–1052

    Article  Google Scholar 

  23. 23.

    Ulm K (1991) A statistical method for assessing a threshold in epidemiological studies. Stat Med 10:341–349

    Article  Google Scholar 

  24. 24.

    Bender R (1999) Quantitative risk assessment in epidemiological studies investigating threshold effects. Biom J 41(3):305–319

    Article  Google 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):123–128

    Article  Google Scholar 

  26. 26.

    Kitchenham B (2010) What’s up with software metrics? - A preliminary mapping study. J Syst Softw 83(1):37–51

    Article  Google 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):216–225

    Article  Google 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):1188–1197

    Article  Google 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):244–257

    Article  Google 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 220–225

  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):484–490

    Article  Google Scholar 

  32. 32.

    Hertz A, Lahrichi N (2008) A patient assignment algorithm for home care services. J Oper Res Soc 60(4):481–495

    Article  Google Scholar 

  33. 33.

    Hiermann G, Prandtstetter M, Rendl A, Puchinger J, Raidl GR (2013) Metaheuristics for solving a multimodal home-healthcare scheduling problem. CEJOR, 89–113

  34. 34.

    Bredström D, Rönnqvist M (2008) Combined vehicle routing and scheduling with temporal precedence and synchronization constraints. Eur J Oper Res 191(1):19–31

    Article  Google Scholar 

  35. 35.

    Dohn A, Rasmussen MS, Larsen J (2011) The vehicle routing problem with time windows and temporal dependencies. Networks 58(4):273–289

    Article  Google 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):3034–3048

    Article  Google 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):304–335

    Article  Google Scholar 

  38. 38.

    Trautsamwieser A, Gronalt M, Hirsch P (2011) Securing home health care in times of natural disasters. OR Spectr 33(3):787–813

    Article  Google 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 85–92

  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 41:471–478

    Article  Google 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):179–191

    Article  Google 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 72:160–176

    Article  Google 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 117:30–41

    Article  Google 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 Science

  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 24–37

  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 61:106–121

    Article  Google 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):1125–1131

    Article  Google Scholar 

  48. 48.

    Solomon MM (1987) Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper Res 35(2):254–265

    Article  Google Scholar 

  49. 49.

    Hansen P, Mladenović N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130:449–467

    Article  Google 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 337–360

  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 145–184

  52. 52.

    Singh S, Kahlon KS (2014) Object oriented software metrics threshold values at quantitative acceptable risk level. CSIT 2(3):191–205

    Article  Google Scholar 

  53. 53.

    Green DM, Swets JA (1966) Signal detection theory and psychophysics. Wiley

  54. 54.

    Zweig MH., Campbell G (1993) Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clin Chem 39(4):561–577

    Article  Google Scholar 

  55. 55.

    Hosmer DW, Lemeshow S (2000) Wiley series in probability and statistics: applied logistic regression. Wiley

  56. 56.

    Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143:29–36

    Article  Google Scholar 

  57. 57.

    Fawcett T (2006) An introduction to roc analysis. Pattern Recogn Lett 27(8):861–874

    Article  Google Scholar 

  58. 58.

    Lewis DD (1991) Evaluating text categorization. In: Proceedings of speech and natural language workshop. Morgan Kaufmann, pp 312–318

  59. 59.

    Yang Y (1999) An evaluation of statistical approaches to text categorization. Inf Retr 1(1):69–90

    Article  Google Scholar 

  60. 60.

    Sokolova M, Lapalme G (2009) A systematic analysis of performance measures for classification tasks. Inform Process Manag 45(4):427–437

    Article  Google 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):1159–1174

    Article  Google Scholar 

  62. 62.

    Churchill GA, Doerge RW (1994) Empirical threshold values for quantitative trait mapping. GENETICS 138:963–971

    Google Scholar 

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Acknowledgements

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

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Correspondence to Jamal Abdul Nasir.

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Nasir, J.A., Dang, C. Quantitative thresholds based decision support approach for the home health care scheduling and routing problem. Health Care Manag Sci 23, 215–238 (2020). https://doi.org/10.1007/s10729-019-09469-1

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Keywords

  • Decision rules
  • Home health care
  • Nurse scheduling
  • Patients selection
  • Quantitative thresholds