Analysis and Modeling of Home Health Care Planning for Operations Improvement


Student thesis: Doctoral Thesis

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Awarding Institution
Award date11 Oct 2017



The costs associated with the health care facilities are increasing in many developed countries due to the requirement for long term and continuous health care support for an aging population. Changes in our society with respect to smaller family size, reduced number of marriages, persistent employment and a growing number of elderly residents are posing threats to the conventional style of family care, thereby increasing the number of care-dependent individuals. In response to these special health care demands, new alternatives to the traditional hospitalization concept have been developed, including Home Health Care (HHC). However, the growing HHC industry is new and facing serious challenges regarding decisions related to patient's acceptance, staffing level and scheduling of health care staff. Moreover, the issues related to patient satisfaction, cost reduction and maintaining experienced health care staff significantly impact on the efficiency and effectiveness of the HHC system. This thesis considers HHC planning problems from different perspectives, presenting solutions to the identified problems using operations research and metaheuristics. Important planning aspects of these HHC problems are identified which require critical decisions and the focus of this thesis is to tackle planning problems in a such manner as to provide the necessary support to make decisions on a quantitative basis. This thesis aims to improve the operations of HHC organizations through identification of complex planning issues and subsequent development of mathematical models and algorithms. Furthermore, the results analysis and meaningful insights suggest the directions for improvement.

Chapter 1 introduces the HHC system and related issues. This chapter aims to identify different characteristics and issues related to the HHC problems, explaining the different features, complexities and restrictions associated with the HHC system. The characteristics of the HHC problems with respect to strategic, tactical and operational level decisions are discussed. Then, the various problems in the HHC domain which can be solved using operation research methods are presented. This investigation aims to determine the nature of the HHC problems, identifying research gaps for future work.

Chapter 2 presents a HHC planning problem which integrates the resource dimensioning issues with the assignment aspects and patients group-based care services. The objective of this chapter is to determine the most suitable strategic and tactical resources in combination with linking the elderly and isolated patients in social and community circles through the settings of the HHC problem. An integer linear programming model is developed and solved through CPLEX to give an optimal selection of locations for HHC offices, health care workers and patient cluster centres, as well as the assignment specifics among all of them. The model is solved under four different scenarios to observe the effects on cost and other decisions. The detailed analysis of scenario-based results provides insights about the model behaviour, revealing cost reduction under different conditions.

Chapter 3 details the decision support methodology for the HHC problem under quantitative thresholds based methods. 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) and solved with CPLEX. 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 solution. The effectiveness of these thresholds is evaluated by utilizing performance measures of the widely-used confusion matrix. While the third phase replicates the whole study by replacing the CPLEX with a Variable Neighbourhood Search (VNS) based heuristic method to validate the thresholds and proposed methodology. 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.

In Chapter 4, the HHC problem model is extended to the perspective of long term economic sustainability as well as operational efficiency. A more flexible MILP model is formulated by incorporating the dynamic arrival and departure of patients along with the selection of new patients and nursing staff. An integrated model is proposed that jointly addresses: (i) patient selection; (ii) nurse hiring; (iii) nurse to patient assignment; and (iv) scheduling and routing decisions in a daily HHC planning problem. A more flexible MILP model is formulated, which extends the HHC problem from conventional scheduling and routing issues to demand and capacity management aspects. It enables a HHC firm to solve the daily scheduling and routing problem considering existing patients and nursing staff in combination with simultaneous selection of new patients and nurses, optimizing the existing routes by including new patients and nurses. The model considers planning issues related to compatibility, time restrictions, contract durations, idle time and workload balance. Two heuristic methods are proposed to solve the model by exploiting the VNS approach. Results obtained from the heuristic methods are compared with CPLEX. Numerical experiments performed on different data sets, show the efficiency and effectiveness of the solution methods to handle the considered problem.

Chapter 5 presents a medium term HHC assignment problem which permits individual patients to access multiple visits per day for multiple services during the planning horizon of one week. The studied problem also addresses service quality and employee satisfaction through penalized objective function for violations of preference based assignment criteria and work load balance. Patients can specify preferred days, and time windows while preferred area for service and work load balance factors are considered to enhance the job satisfaction for nurses. A mathematical model is developed to represent the problem and solved through CPLEX. The model takes into account planning constraints related to compatibility, assignment restrictions, maximum workload, and allowed visits per patient for each day against each service. In order to solve the large sized problems, a local search based Hybrid Genetic Algorithm (HGA) is proposed. HGA and VNS are used to solve the studied problem and results are compared against the available optimal results of CPLEX. The analysis of the results confirms the usefulness and efficiency of the proposed solution method.

Finally, the study conclusion and suggestions for further work are presented.