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A new multi-component DEA approach using common set of weights methodology and imprecise data: an application to public sector banks in India with undesirable and shared resources

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Jolly Puri at Indian Institute of Technology Roorkee
Jolly Puri
Shiv Prasad Yadav at Indian Institute of Technology Roorkee
Shiv Prasad Yadav
Harish Garg at Thapar Institute of Engineering & Technology, Patiala
Harish Garg
  • Thapar Institute of Engineering & Technology, Patiala
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Abstract and Figures

Owing to the importance of internal structure of decision making units (DMUs) and data uncertainties in real situations, the present paper focuses on multi-component data envelopment analysis (MC-DEA) approach with imprecise data. The undesirable outputs and shared resources are also incorporated in the production process of multi-component DMUs to validate real problems. The interval efficiencies of DMUs and their components in MC-DEA are often challenging with imprecise data. In many practical situations, different set of weights may be resulted into valid efficiency intervals for DMUs but invalid interval efficiencies for their components. Therefore, the present study proposes a new common set of weights methodology, based on interval arithmetic and unified production frontier, to determine unique weights for measuring these interval efficiencies. It is a two-level mathematical programming approach that preserves linearity of DEA and exhibits stronger discrimination power among the DMUs as compared to some existing approaches. Theoretically, the aggregate efficiency interval of each DMU lies between the components’ interval efficiencies. Further, the proposed approach is also applied to banks in India for proving its acceptability in practical applications. The performance of each bank is investigated in terms of two components: general business and bancassurance business for the years 2011–2013. The present study emphasized expanding pattern of bancassurance business in current market scenario with more percentage increase as contrasted to general business.
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Ann Oper Res (2017) 259:351–388
DOI 10.1007/s10479-017-2540-1
A new multi-component DEA approach using common
set of weights methodology and imprecise data: an
application to public sector banks in India with
undesirable and shared resources
Jolly Puri1·Shiv Prasad Yadav2·Harish Garg1
Published online: 31 May 2017
© Springer Science+Business Media New York 2017
Abstract Owing to the importance of internal structure of decision making units (DMUs)
and data uncertainties in real situations, the present paper focuses on multi-component data
envelopment analysis (MC-DEA) approach with imprecise data. The undesirable outputs
and shared resources are also incorporated in the production process of multi-component
DMUs to validate real problems. The interval efficiencies of DMUs and their components in
MC-DEA are often challenging with imprecise data. In many practical situations, different
set of weights may be resulted into valid efficiency intervals for DMUs but invalid interval
efficiencies for their components. Therefore, the present study proposes a new common set of
weights methodology, based on interval arithmetic and unified production frontier, to deter-
mine unique weights for measuring these interval efficiencies. It is a two-level mathematical
programming approach that preserves linearity of DEA and exhibits stronger discrimination
power among the DMUs as compared to some existing approaches. Theoretically, the aggre-
gate efficiency interval of each DMU lies between the components’ interval efficiencies.
Further, the proposed approach is also applied to banks in India for proving its acceptability
in practical applications. The performance of each bank is investigated in terms of two com-
ponents: general business and bancassurance business for the years 2011–2013. The present
study emphasized expanding pattern of bancassurance business in current market scenario
with more percentage increase as contrasted to general business.
Keywords Multi-component DEA ·Undesirable outputs ·Shared resources ·Imprecise
data ·Interval efficiency ·Bank performance
BJolly Puri
puri.jolly@gmail.com
Shiv Prasad Yadav
spyorfma@gmail.com
Harish Garg
harishg58iitr@gmail.com
1School of Mathematics, Thapar University, Patiala 147004, India
2Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India
123
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... Izadikhah et al. [12] and Puri, Yadav, and Garg. [13] considered DEA models with shared resources and measured interval efficiencies. Stefaniec et al. [14] and Zhou and Hu [15] introduced a network with shared resources that incorporates undesirable output. ...
... The objective function of the model (10) is to maximize the weighted sum of stage-efficiency scores. With regards to the weights defined in (12), equivalent to the objective function of the model (10) is the relation (13). For each stage, weight is defined as a ratio of the sum of weighted inputs of each stage to the sum of weighted inputs of all stages. ...
... Then, considering relations (11) and (12), the objective function of the model (10) will be defined as the sum of weighted stage efficiency scores (13). ...
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