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.
Similar content being viewed by others
References
Rest K-D, Hirsch P (2015) Daily scheduling of home health care services using time-dependent public transport. Flexible Services and Manufacturing Journal
Begur SV, Miller DM, Weaver JR (1997) An integrated spatial DSS for scheduling and routing home-health-care nurses. Interfaces 27(4):3–48
Cheng E, Rich LJ (1998) A home health care routing and scheduling problem. Technical Report TR98-04, Department of CAAM, Rice University, Houston USA
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
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
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
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
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)
Shao YF, Bard JF, Jarrah aI (2012) The therapist routing and scheduling problem. IIE Trans 44(10):868–893
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
Demirbilek M, Branke J, Strauss A (2018) Dynamically accepting and scheduling patients for home healthcare. Health Care Management Science
Rodriguez-Verjan C, Augusto V, **e X (2017) Home health-care network design: location and configuration of home health-care centers. Operations Research for Health Care
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
Lanzarone E, Matta A (2011) A cost assignment policy for home care patients. Flex Serv Manuf J 24(4):465–495
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
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
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
**ao 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
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
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
Ellenbecker CH (2004) A theoretical model of job retention for home health care nurses. J Adv Nurs 47(3):303–310
Wright PD, Mahar S (2013) Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction. Omega 41(6):1042–1052
Ulm K (1991) A statistical method for assessing a threshold in epidemiological studies. Stat Med 10:341–349
Bender R (1999) Quantitative risk assessment in epidemiological studies investigating threshold effects. Biom J 41(3):305–319
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
Kitchenham B (2010) What’s up with software metrics? - A preliminary map** study. J Syst Softw 83(1):37–51
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
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
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
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
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
Hertz A, Lahrichi N (2008) A patient assignment algorithm for home care services. J Oper Res Soc 60(4):481–495
Hiermann G, Prandtstetter M, Rendl A, Puchinger J, Raidl GR (2013) Metaheuristics for solving a multimodal home-healthcare scheduling problem. CEJOR, 89–113
Bredström D, Rönnqvist M (2008) Combined vehicle routing and scheduling with temporal precedence and synchronization constraints. Eur J Oper Res 191(1):19–31
Dohn A, Rasmussen MS, Larsen J (2011) The vehicle routing problem with time windows and temporal dependencies. Networks 58(4):273–289
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
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
Trautsamwieser A, Gronalt M, Hirsch P (2011) Securing home health care in times of natural disasters. OR Spectr 33(3):787–813
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
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
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
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
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
Bekker R, Moeke D, Schmidt B (2018) Kee** pace with the ebbs and flows in daily nursing home operations. Health Care Management Science
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
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
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
Solomon MM (1987) Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper Res 35(2):254–265
Hansen P, Mladenović N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130:449–467
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
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
Singh S, Kahlon KS (2014) Object oriented software metrics threshold values at quantitative acceptable risk level. CSIT 2(3):191–205
Green DM, Swets JA (1966) Signal detection theory and psychophysics. Wiley
Zweig MH., Campbell G (1993) Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clin Chem 39(4):561–577
Hosmer DW, Lemeshow S (2000) Wiley series in probability and statistics: applied logistic regression. Wiley
Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143:29–36
Fawcett T (2006) An introduction to roc analysis. Pattern Recogn Lett 27(8):861–874
Lewis DD (1991) Evaluating text categorization. In: Proceedings of speech and natural language workshop. Morgan Kaufmann, pp 312–318
Yang Y (1999) An evaluation of statistical approaches to text categorization. Inf Retr 1(1):69–90
Sokolova M, Lapalme G (2009) A systematic analysis of performance measures for classification tasks. Inform Process Manag 45(4):427–437
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
Churchill GA, Doerge RW (1994) Empirical threshold values for quantitative trait map**. GENETICS 138:963–971
Acknowledgements
This research work was partially supported by CityU 11301014 of Hong Kong SAR Government.
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
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10729-019-09469-1