A linear programming based approach for determining maximal closest reference set in DEA

TL;DR

This paper introduces a linear programming method to identify the maximal set of closest reference decision-making units in DEA, focusing on the nearest benchmarks for each inefficient unit.

Contribution

It presents a novel LP-based approach for determining the maximal closest reference set in DEA, addressing a gap in existing methods that focus on furthest references.

Findings

The LP model effectively identifies the maximal closest reference set.

The method is demonstrated through a numerical example.

It provides a new perspective for benchmarking in DEA.

Abstract

Identification of the reference set for each decision making unit (DMU) is a main concern in the data envelopment analysis (DEA). All of the methods developed to date have been focused on finding the furthest reference DMUs. In this paper, we introduce the new notion of maximal closest reference set (MCRS) containing the maximum number of closest reference DMUs to the assessed DMU. Then, we develop a linear programming (LP) model for determining the MCRS for each inefficient DMU. We illustrate our method through a numerical example.