Identifying the global reference set in DEA: A mixed 0-1 LP formulation with an equivalent LP relaxation

TL;DR

This paper reformulates the problem of identifying the global reference set in data envelopment analysis as a mixed 0-1 LP model and demonstrates its equivalence to an existing LP model through relaxation techniques.

Contribution

It introduces a mixed 0-1 LP formulation for the global reference set problem and proves its equivalence to the previously established LP model.

Findings

The mixed 0-1 LP model is equivalent to the existing LP model.

LP relaxation transforms the mixed model into an equivalent LP.

The approach provides a new perspective on the GRS identification problem.

Abstract

The recent study by [Mehdiloozad, Mirdehghan, Sahoo, & Roshdi (2015) On the identification of the global reference set in data envelopment analysis. EJOR, 245, 779-788] proposes a linear programming (LP) model for the problem of finding the global reference set (GRS) of the evaluated decision making unit (DMU). This technical note revisits the problem and reformulates it as a mixed 0-1 LP model. By applying the LP relaxation method, it then transforms the formulated model into an equivalent LP model. Finally, it shows that the resulting LP model is equivalent to the LP model of Mehdiloozad et al. (2015).