  Fairness is a major concern in contemporary decision problems. In these
situations, the objective is to maximize fairness while preserving the efficacy
of the underlying decision-making problem. This paper examines repeated
decisions on problems involving multiple stakeholders and a central decision
maker. Repetition of the decision-making provides additional opportunities to
promote fairness while increasing the complexity from symmetry to finding
solutions. This paper presents a general mathematical programming framework for
the proposed fairness-over-time (FOT) decision-making problem. The framework
includes a natural abstraction of how a stakeholder's acquired utilities can be
aggregated over time. In contrast with a natural, descriptive formulation, we
demonstrate that if the aggregation function possesses certain basic
properties, a strong reformulation can be written to remove symmetry from the
problem, making it amenable to branch-and-cut solvers. Finally, we propose a
particular relaxation of this reformulation that can assist in the construction
of high-quality approximate solutions to the original problem and can be solved
using simultaneous row and column generation techniques.
