A Simulation study of fairness-profit trade-off in project selection based on HHI and Knapsack models

Each company continually has to choose the projects in which to invest, among the numerous proposals submitted by company departments. Just a few projects among those put forward for funding can be actually accepted, due to the unavoidable discrepancy between available money and required investments. Though overall profit maximization could appear as the natural allocation goal, it is to be considered that such an allocation may eventually produce a rather unbalanced distribution of the overall budget, where some departments get most of it and others get a very small slice or no money at all. In this paper, we examine how the search for fairness in budget allocation impacts the overall profit, to assess whether a greater degree of satisfaction among departments can be achieved while pursuing profit maximization at the same time. We adopt a constrained knapsack model and the Herfindahl-Hirschman Index (HHI) as a measure of fairness, and perform a MonteCarlo simulation to measure the extent of profit sacrifice in the quest for fairness. We find that just a small sacrifice in profit is often needed to achieve a balanced distribution of the overall budget.