Open AccessA Linear Programming Relaxation DEA Model for Selecting a Single Efficient Unit with Variable RTS Technology
Author(s) -
Reza Akhlaghi,
Mohsen Rostamy-Malkhalifeh,
Alireza Amirteimoori,
Sohrab Kordrostami
Publication year - 2021
Publication title -
croatian operational research review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.176
H-Index - 5
eISSN - 1848-9931
pISSN - 1848-0225
DOI - 10.17535/crorr.2021.0011
Subject(s) - linear programming , data envelopment analysis , mathematical optimization , variable (mathematics) , computer science , relaxation (psychology) , set (abstract data type) , linear model , scale (ratio) , selection (genetic algorithm) , unit (ring theory) , mathematics , artificial intelligence , machine learning , psychology , mathematical analysis , social psychology , physics , mathematics education , quantum mechanics , programming language
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.