Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach

Kaoru Tone

doi:doi:10.11648/j.ajomis.20210604.11

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Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach

Kaoru Tone

Published in American Journal of Operations Management and Information Systems (Volume 6, Issue 4)

Received: 6 October 2021 Accepted: 21 October 2021 Published: 30 October 2021

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Abstract

In Data Envelopment Analysis (DEA) the situation of inputs vs. outputs is positioned as cause and effect. Effects include desirable (ordinary) outputs and undesirable outputs, e.g. pollutants. This situation is well studied and many applications have been published. In this paper, we introduce a new type of inputs, called Good (Desirable) Inputs. As explained in Introduction, we find several examples of such inputs, e.g. Electric car, Women in office and Test takers of vaccine. We handle this by means of SBM (Slacks-based Measure). Usually, efficiency values of DEA models are in the range (0, 1], while in this model a negative efficiency value may be assigned to inefficient DMUs (decision making units). This is caused by shortages of Good Input values. As an example, we refer to “Women’s Rights Movements” in a country where women’s right is not fully guaranteed. Suppose local governments where men and women are serving as officers. They are inputs to office, while Women are Desirable input and Men are Ordinary input. As outputs, we assume Service as Ordinary output and Claim as Undesirable output. Several extensions of this model are introduced. (a) Variable returns to scale, (b) Weight restrictions, (c) Super-efficiency issue and (d) SBM_Max model.

Published in	American Journal of Operations Management and Information Systems (Volume 6, Issue 4)
DOI	10.11648/j.ajomis.20210604.11
Page(s)	67-74
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

DEA, SBM, Desirable Inputs

References

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[2]	Chen, C.-Y., & Lin, J.-R. (2021) Environmental Efficiency and Urban Ecology. Theoretical Economics Letters, 11, 422-446. https://doi.org/10.4236/tel.2021.113028
[3]	Dongling Bai & Qianli Dong & Syed Abdul Rehman Khan & Yan Chen & Dongfang Wang & Lei Yang. (2021) Spatial analysis of logistics ecological efficiency and its influencing factors in China: based on super-SBM-undesirable and spatial Dubin models. Environmental Science and Pollution Research. https://doi.org/10.1007/s11356-021-16323-x
[4]	Lili Ding & Mingliang Wu & Zheng Jiao & Yongyou Nie (2021) The positive role of trade openness in industrial green total factor productivity—provincial evidence from China. Environmental Science and Pollution Research. https://doi.org/10.1007/s11356-021-16164-8
[5]	Liu, B.; Sun, Z.; Li, H. Can (2021) Carbon Trading Policies Promote Regional Green Innovation Efficiency? Empirical Data from Pilot Regions in China. Sustainability 2021, 13, 2891. https://doi.org/ 10.3390/su13052891
[6]	Tone K. (2001) A slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research. 2001, 130, 498-509.
[7]	Tone K. (2002) A slacks-based measure of super-efficiency in data envelopment analysis, European Journal of Operational Research. 143, 32-41.
[8]	Tone K. (2003) Dealing with undesirable outputs in DEA: A slacks-based measure (SBM) approach, GRIPS Research Report Series I-2003-0005.
[9]	Tone K. (2016) Data Envelopment Analysis as a Kaizen Tool: SBM Variations Revisited, Bulletin of Mathematical Sciences and Applications, 2016, 16, 49-61. doi: 10.18052/www.scipress.com/BMSA.16.49.
[10]	Tone K. (2010) Variations on the theme of slacks-based measure of efficiency in DEA, European Journal of Operational Research. 200 (2010) 901-907.
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[12]	Tone K. & Tsutsui M. (2010) Dynamic DEA: A slacks-based measure approach. Omega. 38, 145-156.
[13]	Tone K. & Tsutsui M. (2014) Dynamic DEA with network structure: A slacks-based measure approach. Omega, 42, 124-131.
[14]	Wu H., Xue Y., Hao Y., Ren S. (2021) How does internet development affect energy-saving and emission reduction? Evidence from China. Energy Economics, https://doi.org/10.1016/j.eneco.2021.105577

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Kaoru Tone. (2021). Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach. American Journal of Operations Management and Information Systems, 6(4), 67-74. https://doi.org/10.11648/j.ajomis.20210604.11

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ACS Style

Kaoru Tone. Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach. Am. J. Oper. Manag. Inf. Syst. 2021, 6(4), 67-74. doi: 10.11648/j.ajomis.20210604.11

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AMA Style

Kaoru Tone. Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach. Am J Oper Manag Inf Syst. 2021;6(4):67-74. doi: 10.11648/j.ajomis.20210604.11

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@article{10.11648/j.ajomis.20210604.11,
  author = {Kaoru Tone},
  title = {Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach},
  journal = {American Journal of Operations Management and Information Systems},
  volume = {6},
  number = {4},
  pages = {67-74},
  doi = {10.11648/j.ajomis.20210604.11},
  url = {https://doi.org/10.11648/j.ajomis.20210604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajomis.20210604.11},
  abstract = {In Data Envelopment Analysis (DEA) the situation of inputs vs. outputs is positioned as cause and effect. Effects include desirable (ordinary) outputs and undesirable outputs, e.g. pollutants. This situation is well studied and many applications have been published. In this paper, we introduce a new type of inputs, called Good (Desirable) Inputs. As explained in Introduction, we find several examples of such inputs, e.g. Electric car, Women in office and Test takers of vaccine. We handle this by means of SBM (Slacks-based Measure). Usually, efficiency values of DEA models are in the range (0, 1], while in this model a negative efficiency value may be assigned to inefficient DMUs (decision making units). This is caused by shortages of Good Input values. As an example, we refer to “Women’s Rights Movements” in a country where women’s right is not fully guaranteed. Suppose local governments where men and women are serving as officers. They are inputs to office, while Women are Desirable input and Men are Ordinary input. As outputs, we assume Service as Ordinary output and Claim as Undesirable output. Several extensions of this model are introduced. (a) Variable returns to scale, (b) Weight restrictions, (c) Super-efficiency issue and (d) SBM_Max model.},
 year = {2021}
}

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TY - JOUR
T1 - Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach
AU - Kaoru Tone
Y1 - 2021/10/30
PY - 2021
N1 - https://doi.org/10.11648/j.ajomis.20210604.11
DO - 10.11648/j.ajomis.20210604.11
T2 - American Journal of Operations Management and Information Systems
JF - American Journal of Operations Management and Information Systems
JO - American Journal of Operations Management and Information Systems
SP - 67
EP - 74
PB - Science Publishing Group
SN - 2578-8310
UR - https://doi.org/10.11648/j.ajomis.20210604.11
AB - In Data Envelopment Analysis (DEA) the situation of inputs vs. outputs is positioned as cause and effect. Effects include desirable (ordinary) outputs and undesirable outputs, e.g. pollutants. This situation is well studied and many applications have been published. In this paper, we introduce a new type of inputs, called Good (Desirable) Inputs. As explained in Introduction, we find several examples of such inputs, e.g. Electric car, Women in office and Test takers of vaccine. We handle this by means of SBM (Slacks-based Measure). Usually, efficiency values of DEA models are in the range (0, 1], while in this model a negative efficiency value may be assigned to inefficient DMUs (decision making units). This is caused by shortages of Good Input values. As an example, we refer to “Women’s Rights Movements” in a country where women’s right is not fully guaranteed. Suppose local governments where men and women are serving as officers. They are inputs to office, while Women are Desirable input and Men are Ordinary input. As outputs, we assume Service as Ordinary output and Claim as Undesirable output. Several extensions of this model are introduced. (a) Variable returns to scale, (b) Weight restrictions, (c) Super-efficiency issue and (d) SBM_Max model.
VL - 6
IS - 4
ER -

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Kaoru Tone

National Graduate Institute for Policy Studies, Tokyo, Japan

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Kaoru Tone. (2021). Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach. American Journal of Operations Management and Information Systems, 6(4), 67-74. https://doi.org/10.11648/j.ajomis.20210604.11

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ACS Style

Kaoru Tone. Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach. Am. J. Oper. Manag. Inf. Syst. 2021, 6(4), 67-74. doi: 10.11648/j.ajomis.20210604.11

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AMA Style

Kaoru Tone. Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach. Am J Oper Manag Inf Syst. 2021;6(4):67-74. doi: 10.11648/j.ajomis.20210604.11

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@article{10.11648/j.ajomis.20210604.11,
  author = {Kaoru Tone},
  title = {Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach},
  journal = {American Journal of Operations Management and Information Systems},
  volume = {6},
  number = {4},
  pages = {67-74},
  doi = {10.11648/j.ajomis.20210604.11},
  url = {https://doi.org/10.11648/j.ajomis.20210604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajomis.20210604.11},
  abstract = {In Data Envelopment Analysis (DEA) the situation of inputs vs. outputs is positioned as cause and effect. Effects include desirable (ordinary) outputs and undesirable outputs, e.g. pollutants. This situation is well studied and many applications have been published. In this paper, we introduce a new type of inputs, called Good (Desirable) Inputs. As explained in Introduction, we find several examples of such inputs, e.g. Electric car, Women in office and Test takers of vaccine. We handle this by means of SBM (Slacks-based Measure). Usually, efficiency values of DEA models are in the range (0, 1], while in this model a negative efficiency value may be assigned to inefficient DMUs (decision making units). This is caused by shortages of Good Input values. As an example, we refer to “Women’s Rights Movements” in a country where women’s right is not fully guaranteed. Suppose local governments where men and women are serving as officers. They are inputs to office, while Women are Desirable input and Men are Ordinary input. As outputs, we assume Service as Ordinary output and Claim as Undesirable output. Several extensions of this model are introduced. (a) Variable returns to scale, (b) Weight restrictions, (c) Super-efficiency issue and (d) SBM_Max model.},
 year = {2021}
}

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