Balance in resource allocation problems: a changing reference approach

Abstract

Fairness has become one of the primary concerns in resource allocation problems, especially in settings which are associated with public welfare. Using a pure e ciency maximizing approach may not be applicable while distributing resources among entities, hence we propose a novel structure for integrating balance into the allocation process. In the proposed approach, balance is de ned and measured as the deviation from a reference distribution determined by the decision maker. We acknowledge that 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 (bene t). We illustrate our approach using a project portfolio selection problem. We formulate a mixed integer mathematical programming model for the problem with maximizing e ciency and minimizing imbalance objectives. The bi-objective model is initially solved with the epsilon constraint method. However for larger problem instances this approach fails to nd solutions within reasonable time limits. Hence we implement metaheuristic algorithms and report on their performance. As an alternative solution method, an interactive algorithm is presented and used to nd the most preferred solution of the decision maker. The proposed resource allocation model provides important insights to decision makers regarding the tradeo between e ciency and fairness, and provides a useful tool to incorporate speci c balance concerns into the problem.