Fairness over time and dynamic resource allocation

Decision making problems are typically concerned with maximizing efficiency. In contrast, we address resource allocation problems where there are multiple stakeholders and a centralized decision maker who is obliged to decide in a fair manner. Different decisions give different utility to each stakeholder. In cases where these decisions are made repeatedly, we provide efficient mathematical programming formulations to identify both the maximum fairness possible and the decisions that improve fairness over time, for reasonable metrics of fairness. We discuss the application of this framework to a number of contexts, for example in ambulance allocation, urban policing operations, and goods delivery. Where decisions in consecutive rounds are constrained, we prove structural results on identifying fair feasible allocation policies and provide a flexible exact algorithm based on column generation.