Original scientific paper
https://doi.org/10.17535/crorr.2021.0011
A Linear Programming Relaxation DEA Model for Selecting a Single Efficient Unit with Variable RTS Technology
Reza Akhlaghi
; Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
Mohsen Rostamy-Malkhalifeh
; Department of Mathematics, Tehran Science and Research Branch, Islamic Azad University, Tehran, Iran
Alireza Amirteimoori
; Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
Sohrab Kordrostami
; Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
Abstract
The selection-based problem is a type of decision-making issue which involves opting for a single option among a set of available alternatives. In order to address the selection-based problem in data envelopment analysis (DEA), various integrated mixed binary linear programming (MBLP) models have been developed. Recently, an MBLP model has been proposed to select a unit in DEA with variable returns-to-scale technology. This paper suggests utilizing the linear programming relaxation model rather than the MBLP model. The MBLP model is proved here to be equivalent to its linear programming relaxation problem. To the best of the authors’ knowledge, this is the first linear programming model suggested for selecting a single efficient unit in DEA under the VRS (Variable Returns to Scale) assumption. Two theorems and a numerical example are provided to validate the proposed LP model from both theoretical and practical perspectives.
Keywords
data envelopment analysis (DEA); selection-based problem; single efficient unit; mixed binary linear programming (MBLP); relaxation problem
Hrčak ID:
267801
URI
Publication date:
23.12.2021.
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