Volume 56, Number 2, March-April 2022
|Page(s)||649 - 687|
|Published online||14 April 2022|
Malmquist-Luenberger productivity indexes for dynamic network DEA with undesirable outputs and negative data
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India
* Corresponding author: firstname.lastname@example.org
Accepted: 7 February 2022
The data envelopment analysis (DEA) technique is well known for computing the Malmquist-Luenberger productivity index (MLPI) in measuring productivity change in the decision-making units (DMUs) over two consecutive periods. In this research, we detect infeasibility of the directional distance function (DDF) based DEA model of MLPI under the variable returns to scale technology when data takes on negative values. We address this problem by developing a novel DDF-based DEA model that computes an improved MLPI. We extend the DDF approach to the dynamic network structure and introduce the dynamic MLPI for analyzing the performance of DMUs over time. We also develop the dynamic sequential MLPI to detect shifts in the efficient frontiers due to random shocks or technological advancements over time. The dynamic network structure in the two indexes comprises multiple divisions in DMUs connected vertically by intermediate productivity links and horizontally over time by carryovers. The proposed models are feasible and bounded with undesirable features and negative and non-negative data values. Real data of 39 Indian commercial public and private banks from 2008 to 2019 used to illustrate the two indexes.
Mathematics Subject Classification: 90B10 / 90C05 / 90C08 / 90C39 / 90C90 / 91B06
Key words: Data envelopment analysis / directional distance function / dynamic network structure / productivity change / dynamic Malmquist-Luenberger productivity indexes
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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