A formal model and a mathematical programming based analysis framework for tactical-level planning of home care systems

Home care is a viable alternative to delivering health care services, especially for the elderly. Due to various operational characteristics, home care organizations are significantly different from the traditional institutionalized health care delivery systems, such as hospitals. In this study, we first propose a formal object model in which we define the entities involved in a home care system and their relations. Later we demonstrate that, the proposed formal model can be used to develop mathematical programming models that include generic system-level constraints and represent tactical-level aggregate planning problems in perspectives of various stakeholders, such as regulators, patients, health care institutions, funding bodies and system resources. We develop an agent-based simulation algorithm to provide a general understanding on how the actors interact and the system evolves based on actors' simplistic decision making. We also propose an iterative optimization algorithm that involves mathematical programming based decision making for actor groups in a systematic manner so as to come up with an agreed-upon solution that reflects the collective wellbeing of all system actors. The total of formal model, generic and system level constraints, actors' perspectives as well as two different modeling approaches constitutes an analysis framework which can be employed in analyzing the evolutionary progress of the overall system. Our numerical study shows that the proposed analysis framework and the algorithms representing two different and complementing approaches are valuable tools in investigating the evolution of a health care system including home care as an alternative means of service.