Determining Maximal Reference Set in Data Envelopment Analysis

TL;DR

This paper introduces a new MILP-based method to identify the maximal reference set in data envelopment analysis, ensuring all reference DMUs are captured efficiently and universally across models.

Contribution

It proposes a general, unified MILP approach for determining the maximal reference set in DEA, compatible with various models and formulations.

Findings

The approach effectively identifies all reference DMUs in DEA.

It is adaptable to different DEA models and formulations.

The method improves computational efficiency through LP-based procedures.

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.