A Comparison of Fairness Metrics for Health Care Problems

Fairness and balancing-related metrics can be modelled in several ways, and no single definition of fairness is universally accepted. From the application point of view, fairness is a rather common objective in problems where a decision maker needs to allocate resources/workloads to agents. This is also a rather common requirement in the health care field. For example, fair assignment constraints can be found in personnel rostering, and in workload or resource assignment problems. In particular, our analysis is motivated by the Blood Donor Appointment Scheduling (BDAS) problem, in which it is required to assign a number of donors of the different blood types over the days to achieve an as-constant-as-possible production of each blood type, hence enforcing balancing. Solving these problems may not be trivial, because quantities may not be divisible by the number of agents, additional constraints must be considered (e.g., limited capacities), or there are perturbations such as stochastic demands. In this work, we compare several approaches to model fair assignments and discuss their relevance to common health care service management problems. We show that different ways of modelling balancing constraints in the same problem produce different results, and we test them on benchmark instances inspired by the BDAS problem to derive insights on their performance.