Dynamic DEA: A slacks-based measure approach☆

Abstract

In data envelopment analysis, there are several methods for measuring efficiency change over time, e.g. the window analysis and the Malmquist index. However, they usually neglect carry-over activities between consecutive two terms. These carry-overs play an important role in measuring the efficiency of decision making units in each term as well as over the whole terms based on the long-term viewpoint. Dynamic DEA model proposed by Färe and Grosskopf is the first innovative contribution for such purpose. In this paper we develop their model in the slacks-based measure (SBM) framework, called Dynamic SBM (DSBM). The SBM model is non-radial and can deal with inputs/outputs individually, contrary to the radial approaches that assume proportional changes in inputs/outputs. Furthermore, according to the characteristics of carry-overs, we classify them into four categories, i.e. desirable, undesirable, free and fixed. Desirable carry-overs correspond, for example, to profit carried forward and net earned surplus carried to the next term, while undesirable carry-overs include, for example, loss carried forward, bad debt and dead stock. Free and fixed carry-overs indicate, respectively, discretionary and non-discretionary ones. We develop Dynamic SBM models that can evaluate the overall efficiency of decision making units for the whole terms as well as the term efficiencies.

Input-Output Analysis for Sustainability by Using DEA Method: A Comparison Study between European and Asian Countries

“…Tone and Tsutsui [51] developed the modified SBM DEA model by incorporating desirable outputs, and there are two approaches: (1) the bad output model, which separates outputs into good (desirable) and bad (undesirable) without assuming the correlation between them; (2) the non-separable model, which posits the inseparability of good (desirable) outputs and bad (undesirable) outputs. In other words, a reduction in undesirable outputs will inevitably require a cut in desirable outputs.…”

“…It is hence possible to derive the efficiency of the different groups and the meta-frontier, and then the meta-technology ratios (MTRs). This model combines the modifications proposed by Tone and Tsutsui [51], and O'Donnell et al [52], as follows:…”

Progressive Time-Weighted Dynamic Energy Efficiency, Energy Decoupling Rate, and Decarbonization: An Empirical Study on G7 and BRICS

“…Moreover, this study changes the previous DEA model for each data period as being independent in the latest DEA idea, whereby each independent data period is connected by an input factor in the dynamic DEA model. Tone and Tsutsui [17] note that the dynamic DEA model with carry-over factors between two consecutive terms can consider the time change effect and the long-term optimization. In the empirical analysis, this paper targets energy efficiency in emerging countries since their economic growth rates are stronger and their gas emissions cause the global warming, which relates to climate change as a concern of developed countries.…”

Hybrid Dynamic Network Data Envelopment Analysis

“…Tone and Tsutsui [13] developed the network structure by applying it in the dynamic network DEA using a slack-based measure.…”

“…Soleimani-damaneh [12] also utilized the envelopment models for estimating returns to scale in dynamic DEA. To cope with long time point of view, Tone and Tsutsui [13] put forward a dynamic DEA model that adds carry-over activities into the model to measure period specific efficiency based on the long time optimization during the whole period. Then, Tone and Tsutsui extended the model by a combination of network DEA and dynamic DEA [14].…”