Skip to main content

Advertisement

SpringerLink
Log in

A comprehensive multi-objective mixed integer nonlinear programming model for an integrated elderly care service districting problem

  • S.I.: RealCaseOR
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

The integrated care service districting (ICSD) problem is an important logistics decision that the elderly care structures (ECS) face when designing service networks to deliver integrated care to the elderly. The ICSD problem, which aims to prepare enhanced care worker recruitment and training plans for all well-designed service districts, is formulated as a multi-objectives mixed integer nonlinear programming (MOMINLP) model. Several criteria are considered, such as balanced workload of care workers among districts, compactness, indivisibility of elderly locations, and the unknown number of districts to be designed. The model considers three objectives simultaneously, including minimizing the total cost of hiring care workers necessary in all service districts, balancing the workload among districts, and achieving as much compactness of district as possible. Results for analysis were obtained by nondominated sorting genetic algorithm II, a well-known multi-objective evolutionary algorithm for continuous multi-objective optimization, which was modified for our MOMINLP model and tested with actual case. Effects of key parameters, including district- and service-related parameters, on these three objectives were analyzed based on different concerns from decision-makers. Furthermore, different correlations among the deviation of service workload and policies for work encouragement were analyzed for ECS. It informs decision-makers about the performance of key factors of the ICSD problem and improves service quality with proper decisions on related parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

ICSD:

Integrated care service districting

ECS:

Elderly care structure

MOMINLP:

Multi-objective mixed integer nonlinear programming

MOEA:

Multi-objective evolutionary algorithm

NSGA-II:

Nondominated sorting genetic algorithm II

TSP:

Traveling salesman problem

SBX:

Simulated binary crossover

VRP:

Vehicle routing problem

PN :

Size of population in NSGA-II

GN :

Number of generations of NSGA-II

References

  • Agrawal, R. B., Deb, K., & Agrawal, R. B. (1995). Simulated binary crossover for continuous search space. Complex Systems,9(2), 115–148.

    Google Scholar 

  • Ansari, S., McLay, L. A., & Mayorga, M. E. (2015). A maximum expected covering problem for district design. Transportation Science,51(1), 376–390.

    Google Scholar 

  • Ariyasingha, I. D. I. D., & Fernando, T. G. I. (2015). Performance analysis of the multi-objective ant colony optimization algorithms for the traveling salesman problem. Swarm and Evolutionary Computation,23, 11–26.

    Google Scholar 

  • Asafuddoula, M., Ray, T., & Sarker, R., et al. (2012). An adaptive constraint handling approach embedded MOEA/D. Paper presented at the 2012 IEEE congress on evolutionary computation.

  • Bard, J. F., & Jarrah, A. I. (2009). Large-scale constrained clustering for rationalizing pickup and delivery operations. Transportation Research Part B: Methodological,43(5), 542–561.

    Google Scholar 

  • Benzarti, E. (2012). Home health care operations management: Applying the districting approach to home health care. (Doctoral dissertation), Ecole Centrale Paris.

  • Benzarti, E., Sahin, E., & Dallery, Y. (2013). Operations management applied to home care services: Analysis of the districting problem. Decision Support Systems,55, 587–598.

    Google Scholar 

  • Blais, M., Lapierre, S. D., & Laporte, G. (2003). Solving a home-care districting problem in an urban setting. Journal of the Operational Research Society,54(11), 1141–1147.

    Google Scholar 

  • Boldy, D., & Howell, N. (1980). The geographical allocation of community care resources—A case study. Journal of the Operational Research Society,31(2), 123–129.

    Google Scholar 

  • Bouajaja, S., & Dridi, N. (2017). A survey on human resource allocation problem and its applications. Operational Research,17(2), 339–369.

    Google Scholar 

  • Brownlee, A. E. I., & Wright, J. A. (2015). Constrained, mixed-integer and multi-objective optimisation of building designs by NSGA-II with fitness approximation. Applied Soft Computing,33, 114–126.

    Google Scholar 

  • Chaves, A. A., & Nogueira Lorena, L. A. (2011). Hybrid evolutionary algorithm for the capacitated centered clustering problem. Expert Systems with Applications,38(5), 5013–5018.

    Google Scholar 

  • Cho, J. H., Wang, Y., Chen, I. R., et al. (2017). A survey on modeling and optimizing multi-objective systems. IEEE Communications Surveys & Tutorials,19(3), 1867–1901.

    Google Scholar 

  • Deb, K. (2000). An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering,186(2), 311–338.

    Google Scholar 

  • Deb, K. (2012). Advances in evolutionary multi-objective optimization. Paper presented at the search based software engineering, Berlin.

  • Deb, K., Pratap, A., Agarwal, S., et al. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation,6(2), 182–197.

    Google Scholar 

  • Deep, K., Singh, K. P., Kansal, M. L., et al. (2009). A real coded genetic algorithm for solving integer and mixed integer optimization problems. Applied Mathematics and Computation,212(2), 505–518.

    Google Scholar 

  • Dulebenets, M. A. (2018). A comprehensive multi-objective optimization model for the vessel scheduling problem in liner shipping. International Journal of Production Economics,196, 293–318.

    Google Scholar 

  • Gov, H. K. (2018). Health care voucher. Retrieved from http://www.hcv.gov.hk/eng/pub_background.htm.

  • Gurobi. (2018). Gurobi works for multi-objective optimization. Retrieved from http://www.gurobi.com/documentation/7.5/refman/working_with_multiple_obje.html.

  • Gutiérrez-Gutiérrez, E. V., & Vidal, C. J. (2015). A home health care districting problem in a rapid-growing city. Ingeniería y Universidad,19, 87–113.

    Google Scholar 

  • Haugland, D., Ho, S. C., & Laporte, G. (2007). Designing delivery districts for the vehicle routing problem with stochastic demands. European Journal of Operational Research,180(3), 997–1010.

    Google Scholar 

  • Hess, S. W., & Samuels, S. A. (1971). Experiences with a sales districting model: Criteria and implementation. Management Science,18(4), 41–54.

    Google Scholar 

  • Jain, H., & Deb, K. (2014). An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, Part II: Handling constraints and extending to an adaptive approach. IEEE Transactions on Evolutionary Computation,18(4), 602–622.

    Google Scholar 

  • Jarrah, A. I., & Bard, J. F. (2011). Pickup and delivery network segmentation using contiguous geographic clustering. Journal of the Operational Research Society,62(10), 1827–1843.

    Google Scholar 

  • Jarrah, A. I., & Bard, J. F. (2012). Large-scale pickup and delivery work area design. Computers & Operations Research,39(12), 3102–3118.

    Google Scholar 

  • Kalcsics, J. (2015). Districting problem. In G. Laporte, S. Nickel, & F. da Gama (Eds.), Location science (pp. 595–622). Cham: Springer.

    Google Scholar 

  • Kang, D., Jung, J., & Bae, D. H. (2011). Constraint-based human resource allocation in software projects. Software: Practice and Experience,41(5), 551–577.

    Google Scholar 

  • Konur, D., & Geunes, J. (2016). Integrated districting, fleet composition, and inventory planning for a multi-retailer distribution system. Annals of Operations Research. https://doi.org/10.1007/s10479-016-2338-6.

    Article  Google Scholar 

  • Krause, N., Scherzer, T., & Rugulies, R. (2005). Physical workload, work intensification, and prevalence of pain in low wage workers: Results from a participatory research project with hotel room cleaners in Las Vegas. American Journal of Industrial Medicine,48(5), 326–337.

    Google Scholar 

  • Lahrichi, N., Lapierre, S., Hertz, A., et al. (2006). Analysis of a territorial approach to the delivery of nursing home care services based on historical data. Journal of Medical Systems,30(4), 283–291.

    Google Scholar 

  • Lepak, D. P., & Snell, S. A. (1999). The human resource architecture: Toward a theory of human capital allocation and development. Academy of Management Review,24(1), 31–48.

    Google Scholar 

  • Lin, M., Chin, K.-S., Fu, C., et al. (2017). An effective greedy method for the Meals-On-Wheels service districting problem. Computers & Industrial Engineering,106, 1–19.

    Google Scholar 

  • Lin, M., Chin, K. S., Wang, X., & Tsui, K. L. (2016). The therapist assignment problem in home healthcare structures. Expert Systems with Applications, 62, 44–62.

    Google Scholar 

  • Lin, C.-M., & Gen, M. (2008). Multi-criteria human resource allocation for solving multistage combinatorial optimization problems using multiobjective hybrid genetic algorithm. Expert Systems with Applications,34(4), 2480–2490.

    Google Scholar 

  • Maya Duque, P. A., Castro, M., Sörensen, K., et al. (2015). Home care service planning. The case of Landelijke Thuiszorg. European Journal of Operational Research,243(1), 292–301.

    Google Scholar 

  • Meng, K., Lou, P., Peng, X., et al. (2017). Multi-objective optimization decision-making of quality dependent product recovery for sustainability. International Journal of Production Economics,188, 72–85.

    Google Scholar 

  • Minella, G., Ruiz, R., & Ciavotta, M. (2008). A review and evaluation of multiobjective algorithms for the flowshop scheduling problem. INFORMS Journal on Computing,20(3), 451–471.

    Google Scholar 

  • Moreno, S., Pereira, J., & Yushimito, W. (2017). A hybrid K-means and integer programming method for commercial territory design: A case study in meat distribution. Annals of Operations Research. https://doi.org/10.1007/s10479-017-2742-6.

    Article  Google Scholar 

  • Negreiros, M., & Palhano, A. (2006). The capacitated centred clustering problem. Computers & Operations Research,33(6), 1639–1663.

    Google Scholar 

  • Otero, L. D., Centeno, G., Ruiz-Torres, A. J., et al. (2009). A systematic approach for resource allocation in software projects. Computers & Industrial Engineering,56(4), 1333–1339.

    Google Scholar 

  • Pezzella, F., Bonanno, R., & Nicoletti, B. (1981). A system approach to the optimal health-care districting. European Journal of Operational Research,8(2), 139–146.

    Google Scholar 

  • Pureza, V., Morabito, R., & Reimann, M. (2012). Vehicle routing with multiple deliverymen: Modeling and heuristic approaches for the VRPTW. European Journal of Operational Research,218, 636–647.

    Google Scholar 

  • Ray, T., Tai, K., & Seow, K. C. (2001). Multiobjective design optimization by an evolutionary algorithm. Engineering Optimization,33(4), 399–424.

    Google Scholar 

  • Ríos-Mercado, R. Z., & Fernández, E. (2009). A reactive GRASP for a commercial territory design problem with multiple balancing requirements. Computers & Operations Research,36(3), 755–776.

    Google Scholar 

  • Salazar-Aguilar, M. A., Ríos-Mercado, R. Z., González-Velarde, J. L., et al. (2012). Multiobjective scatter search for a commercial territory design problem. Annals of Operations Research,199(1), 343–360.

    Google Scholar 

  • Savsani, V., & Tawhid, M. A. (2017). Non-dominated sorting moth flame optimization (NS-MFO) for multi-objective problems. Engineering Applications of Artificial Intelligence,63, 20–32.

    Google Scholar 

  • Shanker, R. J., Turner, R. E., & Zoltners, A. A. (1975). Sales territory design: An integrated approach. Management Science,22(3), 309–320.

    Google Scholar 

  • Steiner Neto, P. J., Datta, D., Arns Steiner, M. T., et al. (2017). A multi-objective genetic algorithm based approach for location of grain silos in Paraná State of Brazil. Computers & Industrial Engineering,111, 381–390.

    Google Scholar 

  • Subtil, R. F., Carrano, E. G., & Souza, M. J. F., et al. (2010). Using an enhanced integer NSGA-II for solving the multiobjective generalized assignment problem. Paper presented at the IEEE congress on evolutionary computation.

  • United Nations, D. O. E. A. S. A., Population Division. (2017). World population prospects: the 2017 revision. Retrieved from https://esa.un.org/unpd/wpp/Publications/Files/WPP2017_KeyFindings.pdf.

  • Vanneschi, L., Henriques, R., & Castelli, M. (2017). Multi-objective genetic algorithm with variable neighbourhood search for the electoral redistricting problem. Swarm and Evolutionary Computation,36, 37–51.

    Google Scholar 

  • Wang, R., Xiong, J., Ishibuchi, H., et al. (2017). On the effect of reference point in MOEA/D for multi-objective optimization. Applied Soft Computing,58, 25–34.

    Google Scholar 

  • Xinhuanet. (2018). China health care industry development report 2016—talent. Retrieved from http://www.xinhuanet.com/gongyi/yanglao/2017-01/24/c_129457792.htm.

  • Yoshimura, M., Fujimi, Y., Izui, K., et al. (2006). Decision-making support system for human resource allocation in product development projects. International Journal of Production Research,44(5), 831–848.

    Google Scholar 

  • Yu, S., Zheng, S., Gao, S., et al. (2017). A multi-objective decision model for investment in energy savings and emission reductions in coal mining. European Journal of Operational Research,260(1), 335–347.

    Google Scholar 

  • Zhang, X., Zheng, X., Cheng, R., et al. (2018). A competitive mechanism based multi-objective particle swarm optimizer with fast convergence. Information Sciences,427, 63–76.

    Google Scholar 

  • Zhou, S., Li, X., Du, N., et al. (2018). A multi-objective differential evolution algorithm for parallel batch processing machine scheduling considering electricity consumption cost. Computers & Operations Research,96, 55–68.

    Google Scholar 

  • Zoltners, A. A., & Sinha, P. (2005). The 2004 ISMS practice prize winner—Sales territory design: thirty years of modeling and implementation. Marketing Science,24(3), 313–331.

    Google Scholar 

Download references

Acknowledgements

We thank the guest editors and two anonymous referees for their helpful comments, which have greatly improved the exposition of this paper. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 71471118, 71871145, 71801158), the Major Project of National Natural Science Foundation of China (Grant No. 71790615), the Key Project of National Natural Science Foundation of China (Grant No. 71431006), the Humanities and Social Science Foundation of Ministry of Education of China (Grant Nos. 14YJC630096, 18YJC630088), Start-Up Funds of Shenzhen University (Grant No. 2018058), the Hong Kong RGC (Grant No. T32-102/14N).

Author information

Authors and Affiliations

  1. Department of Management Science, College of Management, Shenzhen University, Shenzhen, 518060, Guangdong, People’s Republic of China

    Meiyan Lin & Lijun Ma

  2. Department of Systems Engineering and Engineering Management and Centre of Systems Informatics Engineering, City University of Hong Kong, Kowloon, Hong Kong, People’s Republic of China

    Kwai Sang Chin & Kwok Leung Tsui

  3. Institute of Big Data, Intelligent Management and Decision, Shenzhen University, Shenzhen, 518060, Guangdong, People’s Republic of China

    Meiyan Lin & Lijun Ma

Authors
  1. Meiyan Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kwai Sang Chin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lijun Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kwok Leung Tsui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lijun Ma.

Appendix

Appendix

See Tables 2, 3 and Fig. 11.

Table 2 Sample records of admission and discharge
Full size table
Table 3 The daily schedule of a care worker
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, M., Chin, K.S., Ma, L. et al. A comprehensive multi-objective mixed integer nonlinear programming model for an integrated elderly care service districting problem. Ann Oper Res 291, 499–529 (2020). https://doi.org/10.1007/s10479-018-3078-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-018-3078-6

Keywords

Search

Navigation