This work addresses a multi agent allocation problem in which multiple departments compete for shares of a company budget. Each department has its own portfolio of projects with given expected profits and costs and selects an optimal subset of its projects consuming its assigned budget share. Besides considering the total profit of the company a central decision maker should also take fairness issues into account. Thus, we introduce an equity criterion based on maximin fairness. The resulting trade-off between total profit and fairness indicators is studied in this contribution. To this purpose a bicriteria ILP model is presented where one of the objectives is the maximization of the overall profit and the other is the maximization of the minimum budget allocated to one of the departments. We perform an experimental analysis showing a nearly perfect linear anticorrelation between profit and fairness index values.
Naldi, M., Nicosia, G., Pacifici, A., Pferschy, U. (2016). Maximin Fairness in Project Budget Allocation. ELECTRONIC NOTES IN DISCRETE MATHEMATICS, 55, 65-68 [10.1016/j.endm.2016.10.017].