Balance in resource allocation problems: a changing reference approach

Fairness is one of the primary concerns in resource allocation problems, especially in settings which are associated with public welfare. Using a total benefit-maximizing approach may not be applicable while distributing resources among entities, and hence we propose a novel structure for integrating balance into the allocation process. In the proposed approach, imbalance is defined and measured as the deviation from a reference distribution determined by the decision-maker. What is considered balanced by the decision-maker might change with respect to the level of total output distributed. To provide an allocation policy that is in line with this changing structure of balance, we allow the decision-maker to change her reference distribution depending on the total amount of output (benefit). We illustrate our approach using a project portfolio selection problem. We formulate mixed integer mathematical programming models for the problem with maximizing total benefit and minimizing imbalance objectives. The bi-objective models are solved with both the epsilon-constraint method and an interactive algorithm.