Optimizing an Adolescent Hybrid Telemedical Mental Health Service Through Staff Scheduling Using Mathematical...

According to the World Health Organization, globally, one in seven 10- to 19-year-olds experiences a mental disorder, accounting for 13% of the global burden of disease in this age group. Half of all mental illnesses begin by the age of 14 years and some teenagers with severe presentations must be admitted to the hospital and assessed by highly skilled mental health care practitioners. Digital telehealth solutions can be useful for the assessment of young individuals remotely. Ultimately, this technology can save travel costs for the health service rather than assessing adolescents in person at the corresponding hospital. Especially in rural regions, where travel times can be high, this innovative approach can make a difference to patients by providing quicker assessments.

The aim of this study is to share insights on how we developed a decision support tool to assign staff to days and locations where adolescent mental health patients are assessed face to face. Where possible, patients are seen through video consultation. The model not only seeks to reduce travel times and consequently carbon emissions but also can be used to find a minimum number of staff to run the service.

To model the problem, we used integer linear programming, a technique that is used in mathematical modeling. The model features 2 objectives: first, we aim to find a minimum coverage of staff to provide the service and second, to reduce travel time. The constraints that are formulated algebraically are used to ensure the feasibility of the schedule. The model is implemented using an open-source solver backend.

In our case study, we focus on real-world demand coming from different hospital sites in the UK National Health Service (NHS). We incorporate our model into a decision support tool and solve a realistic test instance. Our results reveal that the tool is not only capable of solving this problem efficiently but also shows the benefits of using mathematical modeling in health services.

Our approach can be used by NHS managers to better match capacity and location-dependent demands within an increasing need for hybrid telemedical services, and the aims to reduce traveling and the carbon footprint within health care organizations.