Integrated decision-making for medium-term home health care planning

Abstract

Home health care (HHC) is essential to the health care industry and may be defined as care workers visiting patients following predefined schedules in order to provide medical services in their homes. Maintaining a sustainable and effective health care system is a significant challenge due to two trends: limited resources (e.g., budget restrictions and staff shortages) and a rise in demand (e.g., population ageing and pandemic outbreaks). In response to these trends and increasing competitive pressures, HHC providers must discover new ways to decrease costs and enhance productivity by optimizing the use of resources. Efficiently organizing HHC services requires making a wide range of complex decisions on multiple levels, ranging from day-to-day operational decisions (e.g., constructing routes and visit schedules) to tactical and strategic decisions impacting a longer time horizon (e.g., rostering care workers and determining staffing levels). In addition, some complicating problem-specific characteristics need to be considered, such as matching care workers' medical skills with patients' requirements, continuity of care constraints and work-related constraints (e.g., a maximum number of shifts and weekends care workers are allowed to work). For all these reasons, it is clear that applying operations research (OR) techniques in HHC is a promising research field.

Current operations research literature on HHC is dominated by papers proposing models and solution methods for individual operational decision-making problems. An opportunity for improvement is the optimization of medium-term decision-making by integrating decisions while considering realistic problem aspects. Integrated studies are highly relevant because solving independent subproblems separately results in suboptimal decision-making.

In this talk, the specific problem setting we focus on is defined, and a matheuristic solution algorithm for the problem is proposed. In particular, the goal of this research is to develop innovative models and solution algorithms that enable making better overall medium-term (4-week) decision-making by considering the following decisions in an integrated manner: rostering (allocating care workers to days/shifts), assignment (assigning care workers to patients), scheduling (assigning care workers to patient visits with time specifications) and routing (determining the sequence of patient visits for each care worker). A number of important realistic problem characteristics (e.g., continuity of care and working time regulations) are included in the problem setting. A mixed integer linear programming model in this direction will be presented. The integrated solution algorithm developed to tackle the medium-term HHC planning problem first finds a feasible initial solution using a tailored k-means heuristic and a binary integer linear programming model. In the second phase of the solution algorithm, the initial solution is improved by a tailored large neighbourhood search heuristic while periodically solving a mathematical model.

Finally, the efficiency gains of tackling the medium-term HHC planning problem in an integrated manner instead of sequentially will be demonstrated, after which the results of some experiments conducted to derive insights for the practical organization of HHC will be discussed.