Performance assessment of decision making units in different levels using a hierarchical clustering DEA method

Author Name: B. Dalvand, *F. Hosseinzadeh Lotfi, G. R. Jahanshahloo
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Data envelopment analysis (DEA) is a performance assessment technique which mathematically provide a covering frontier referred to as the efficiency frontier. In DEA theory the units are supposed to be homogenous and comparable, whereas, this assumption is not always hold in practical issues when there is high-level units. In this paper, to have a fair assessment and augment the competition between the Decision Making Units (DMUs) we provide an algorithm based on hierarchical clustering and evaluate DMUs in difference levels. Finally, we apply suggested procedure to evaluate the performance of Iranian commercial banks.


Data envelopment analysis, Hierarchical agglomerative clustering, Data mining


Data Envelopment Analysis (DEA) as a non-parametric efficiency measurement method was first described in Charnes et. al. (1978) and then extended by Banker et. al (1984), for performance assessment of a set of peer Decision Making Units (DMUs) each of which uses multiple inputs to produce multiple outputs. In some cases there is no global standard for evaluating the performance of the under evaluated firms, if any, may be far from the realities of society under evaluation. In fact, some existing absolute standards adopted by advanced countries may be defined taking into account their own society.While, measuring a society in a developing country according to these standards may led to very poor or even disappointing efficiency score. Accordingly, one of the strengths of DEA is calculating the relative efficiency of DMUs. DEA technique, occasionally called frontier analysis, establishes a covering frontier called efficiency frontier considering a Production Possibility Set (PPS). The DMUs located on the frontier as the standards of performance are defined efficient in a sense of DEA that DMUs not on the efficient frontier could try to achieve. Classical DEA models assign an efficiency score to inefficient units according to their distances to the efficient frontier. Actually, the main aim of calculating the relative efficiency is to create a competitive environment between the members of the society underevaluation.While in practical issues we may face a case which the selected PPS contains extraordinary units that because of having access to favorable technical, economic, political and technical conditions, are known efficient with a much higher efficiency level than the others. So, it is difficult or even impossible for some inefficient units to achieve such high-level units. On the other hand, considering the new PPS after eliminating these high-level units led to obtaining optimistic score efficiency for remaining units. It seems that a fair strategy in such cases is that inefficient DMUs improve their performance hierarchically. It means, addition to taking into account the best of society, an inefficient DMU be evaluated compared with units which located on lower levels and are more compatible with it. To handle this situations, Cooper et. al (2002 ) suggested a hierarchical category so that all DMUs are divided into several categories based on desired criteria and then each DMU is evaluated comparing with DMUs in the same and higher category levels. Alirezaee and Mir-Hassani (2006) presented an algorithm and partition all DMUs into some finite disjoint sets corresponding to different frontiers. The main contribution of current paper is to augment the competition between the units by partitioning all DMUs into different levels in terms of size. To do so, we implement hierarchical agglomerative clustering as one of the commonly clustering technique in data mining and evaluate each unit comparing with members of the clusters that it belongs to. The outline of the paper is organized as follows. In Section 2, we present an introduction to data envelopment analysis. Section 3 suggests a new method based on hierarchical agglomerative clustering for measuring the efficiency of DMUs in different levels. In section 4, we illustrate the proposed approach with an application to Iranian commercial banks. The paper ends with some conclusions and future research directions in Section 5.




The classic Data Envelopment Analysis (DEA) models developed with the assumption that we deal with a set of peer Decision Making Units (DMUs), whereas, we may face  heterogeneity  among DMUs in the presence of high-level in the actual world. So, in this contribution, we implemented the hierarchical agglomerative clustering and examined the efficiency of all units in different cluster to have a fair evaluation and reduce the effect of heterogeneity on the score efficiency. Our research can be extended in several ways. First, the analysis in this paper is based on technical efficiency score of DMUs related to different levels. While in situations where prices are known at each DMU, another kind of relative efficiency in DEA literature such as the cost, revenue and profit efficiency can be taken in to account for more curate analysis. Second, there are many families of data clustering algorithm, each of which classifies data based on a specific criteria, e.g. partitioning techniques of clustering like k-means and k-medoids and density-based clustering algorithms like DBSCAN and SNN. However, the analysis of obtained results through implementing different method to choose the best cluster may be an interesting future research undertaking. Third, we believe that future researches are necessary to develop an appropriate clustering and evaluation method in the presence of imprecise or negative data. Also, in case of classification problems with DMUs whose activity continues across a multiple periods, the manager will deals with multi-period production system and it is required to investigate the effective factors on efficiencies and technology changes

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