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

• Published in: Annals of operations research Vol. 291; no. 1-2; pp. 499 - 529
• Main Authors: Lin, Meiyan, Chin, Kwai Sang, Ma, Lijun, Tsui, Kwok Leung
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2020; Springer; Springer Nature B.V
• Subjects: Adult day care centers; Algorithms; Analysis; Business and Management; Classification; Combinatorics; Decision analysis; Elder care; Evolutionary algorithms; Genetic algorithms; Industrial locations; Integrated delivery systems; Logistics; Management; Management research; Mathematical models; Mathematical optimization; Mixed integer; Model testing; Multiple objective analysis; Nonlinear programming; Objectives; Older people; Operations research; Operations Research/Decision Theory; Parameters; S.I.: RealCaseOR; Sorting algorithms; Theory of Computation; Workload; Workloads; China; Care worker allocation problem; NSGA-II; Integrated elderly care; Integrated care service districting problem; Multi-objective optimization; Mixed-integer nonlinear programming
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-018-3078-6

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.