Unequal But Fair: Incorporating Distributive Justice In Operational Allocation Models

Fairness is a natural concern when model-based decisions affect human beings. In personnel-management decisions, employees' perceptions of fairness depend both upon the decision processes as well as the resulting outcomes. Acting as a key part of decision processes, operational models often emphasize equality, or sameness, of outcomes among individuals. Fair outcomes, as a manifestation of distributive justice, involve balancing two competing aspects: equality and equity. Equity, in opposition to equality, is concerned with an individual's outcomes being commensurate with their inputs. While both aspects of distributive justice can be an expectation of members of an organization, they present an inherent trade-off; more of one requires less of the other. In order to balance the trade-off between equity and equality, we propose a bi-objective, non-linear optimization model, which is then extended to a mixed-integer formulation in a service-oriented case study. Specifically, the case study model allocates physicians' contracted clinical time across multiple emergency department locations. Deviations from physicians' equity-weighted preferences for where they work are minimized and a Pareto frontier of objectively fair solutions is derived. As a result, the time physicians were allocated to locations they did not prefer was substantially reduced. In addition, pre- and post-implementation surveys revealed statistically significant improvements in employee reported perceptions of fairness, transparency, and overall satisfaction with the work-time-allocation process. The evidence supports the conclusion that decision models designed to result in unequal outcomes can still be perceived as fair by the employees they affect.