Using common weights and efficiency invariance principles for resource allocation and target setting

Data envelopment analysis (DEA) has proven to be a useful technique for evaluating the relative performance of comparable and homogeneous decision-making units (DMUs). In recent years, DEA-based resource allocation and target setting approaches have gained more and more attention from both practitioners and academic researchers. In this paper, we propose a new mechanism to simultaneously adopt the principles of common weights and efficiency invariance in allocating multiple resources and setting multiple targets among DMUs. To obtain the final plan, we minimise the deviation between the possible plan based on common weights and another feasible plan emphasising efficiency invariance. If the minimum deviation equals zero, one optimal plan will be determined. In general situations, however, the proposed approach will present two plans that have a non-zero deviation. One is generated using a common set of weights for all DMUs in such a way that the change of efficiencies is minimised, while the other is generated by strictly keeping efficiency scores unchanged yet having similar or even identical weights on input-output measures for each DMU to the utmost extent. The efficacy and usefulness of the proposed approach are demonstrated using a numerical example from previous literature and an empirical application to an urban bus company in China.