Maximin Fairness-profit Tradeoff in Project Budget Allocation

Companies typically select those projects that maximize their profit as the primary criterion, within the limited budget at their disposal. This criterion may lead to some company departments getting an exceedingly large share of the overall budget and induce a negative perception of unfairness among the less favourite ones. We investigate how profit optimization can be sought after while achieving the desired level of fairness at the same time. Adopting a maximin approach to fairness and using an Integer Linear Programming solver, we show that a linear trade-off is possible, since fairness and profit exhibit a nearly perfect linear anticorrelation. Fairness can be improved by even a relatively small reduction of profit, especially in large companies (i.e., managing a large number of projects).