Determining Maximal Reference Set in Data Envelopment Analysis

Abstract: In data envelopment analysis (DEA), the occurrence of multiple reference sets is a crucial issue in identifying all the reference DMUs to a given decision making unit (DMU). To resolve this difficulty, we introduce the useful notion of maximal reference set (MRS) which contains all the reference DMUs. Based on both primal and dual formulations, we then propose a new mixed integer linear programming (MILP) based approach for determining the MRS. The proposed approach is more general than the existing ones, and has several desirable properties: (i) having a unified formulation, (ii) adaptable with different DEA models, and (iii) compatible with both primal and dual forms of the DEA models. Furthermore, our approach is made computationally effective by establishing a LP-based procedure to treat with the primal-based MILP.