Profit-fairness trade-off in project selection

Allocating the overall budget to projects is a major decision for an organization. Taking that decision by looking at the overall profit only may result in an unfair treatment of departments, with some departments overloaded and others underemployed (and dissatisfied). We consider an alternative approach, where the budget allocation is accomplished by aiming at fairness as well as profit. We adopt a knapsack-type Integer Linear Programming formulation to optimize both quality indicators of budget allocation, employing a fairly wide selection of fairness measures. The resulting optimization routines are applied to a representative selection of instances generated through Monte Carlo simulation. We show that high levels of fairness can be achieved for realistic scenarios with only a moderate loss of profit. Large companies appear to be able to achieve a better trade-off between fairness and profit. Striving for fairness also leads to funding more projects, thus increasing the usage level of the organization's human and material resources.