Article
Finding Targets in Non-Radial FDH Models: A Hybrid
Technique Based on STEM and Extended Ratio Based Approach
Mehdi Abbasi
1,
*, Mohammad Reza Mozaffari
2
, Peter F. Wanke
3
and Mohamad Amin Kaviani
4
Citation: Abbasi, M.; Mozaffari,
M.R.; Wanke, P.F.; Kaviani, M.A.
Finding Targets in Non-Radial FDH
Models: A Hybrid Technique Based
on STEM and Extended Ratio Based
Approach. Appl. Sci. 2021, 11, 10626.
https://doi.org/10.3390/
app112210626
Academic Editors: João Carlos de
Oliveira Matias and Radu Godina
Received: 18 September 2021
Accepted: 8 November 2021
Published: 11 November 2021
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Attribution (CC BY) license (https://
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4.0/).
1
Department of Industrial Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran
2
Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran; mozaffari854@yahoo.com
3
Business Analytics and Economics Research Unit, COPPEAD Graduate Business School, Federal University
of Rio de Janeiro, Rua Paschoal Lemme, 355, Rio de Janeiro 21941-901, Brazil; peter@coppead.ufrj.br
4
Department of Management and Technology, Université du Québec à Montréal,
Montreal, QC H0H H9X, Canada; Kaviani.mohammadamin@courrier.uqam.ca or
aminkaviani1366@yahoo.com
* Correspondence: abbasi.iau@gmail.com or abbasi_m@iaushiraz.ac.ir
Abstract:
Performance evaluation using interactive methods and extended ratio-based approaches
can be very important for some organizations. Free disposal hull models can be created if there is
no concern for convexity, and using non-radial DEA models can simultaneously create more logical
and practical situations for finding DMU targets. In this paper, a new hybrid technique based on the
additive slack based method and enhanced Russel measure in variable return to scale technology
has been proposed. The proposed technique can find decision making unit targets in non-radial free
disposal hull models using the step method. Furthermore, the extended ratio-based approach in the
proposed technique has been applied to find DMU targets of related non-radial free disposal hull
models without solving any mathematical programming models. Finally, targets of Fars province
pharmaceutical distributing companies were found by applying the proposed hybrid technique.
Keywords:
data envelopment analysis (DEA); additive slack based method; non-radial free disposal
hull (FDH); step method (STEM); ratio-based approach (RBA)
1. Introduction
The accurate estimation of production possibility set (PPS) boundaries is crucial
for performance analysis and efficient estimation. Different papers propose alternative
approaches to handle the issue of estimating PPSs and their respective boundaries. Non-
parametric data envelopment analysis (DEA) is possibly one of the most used linear
programming (LP) approaches to build up piecewise PPS boundaries. DEA is a useful
tool to evaluate decision making units (DMUs). Efficiency criterion can be considered as
a number between 0 and 1 for evaluating a DMU in DEA. If the efficiency criterion for
a DMU is 1, the mentioned DMU is efficient, else, it is inefficient. Evaluating DMUs in
input-oriented, output-oriented, and combined-oriented radial and non-radial models were
developed from a proposal by Farrell (1957) [
1
], and were then followed by the development
of the CCR model by Charnes et al. (1978) [
2
]. The CCR model was then developed into
the BCC model by Banker et al. (1984) [
3
]. Additive models were then suggested to
separate efficient and non-efficient DMUs [
4
]. Tone (2001) proposed a slack based model
which evaluates DMUs considering the relationship between CCR models [
5
]. The Russel
Graph Model (RGM) and the relationship between SBM and additive DEA models are very
important subjects that have been studied [
6
]. These models determine the benchmark
for efficient DMUs, in addition to calculating efficiency and non-efficiency criterion of
DMUs. Over three decades, extensive and useful studies on DEA have been undertaken to
calculate DMU efficiencies [
7
,
8
] and to find DMU benchmarks [
9
,
10
]. Chen and Zhu (2020)
completed efficient and non-efficient definitions on the basis of slack variables using the
Appl. Sci. 2021, 11, 10626. https://doi.org/10.3390/app112210626 https://www.mdpi.com/journal/applsci
