Fuzzy clustering of homogeneous decision making units with common weights in data envelopment analysis

Data Envelopment Analysis (DEA) is the most popular mathematical approach to assess efficiency of decision-making units (DMUs). In complex organizations, DMUs face a heterogeneous condition regarding environmental factors which affect their efficiencies. When there are a large number of objects, non-homogeneity of DMUs significantly influences their efficiency scores that leads to unfair ranking of DMUs. The aim of this study is to deal with non-homogeneous DMUs by implementing a clustering technique for further efficiency analysis. This paper proposes a common set of weights (CSW) model with ideal point method to develop an identical weight vector for all DMUs. This study proposes a framework to measuring efficiency of complex organizations, such as banks, that have several operational styles or various objectives. The proposed framework helps managers and decision makers (1) to identify environmental components influencing the efficiency of DMUs, (2) to use a fuzzy equivalence relation approach proposed here to cluster the DMUs to homogenized groups, (3) to produce a common set of weights (CSWs) for all DMUs with the model developed here that considers fuzzy data within each cluster, and finally (4) to calculate the efficiency score and overall ranking of DMUs within each cluster

Measuring the Efficiency of Pesantren Cooperatives: Evidence in Indonesia

The Cooperative (Koperasi) as a non-Bank financial institution has the purpose of improving the welfare of its members as Koperasi Hidmat and the staffs of Latifah Mubarokiyah Koperasi Ponses Suryalaya that have been since decades ago. Over time, the ideal cooperative can show a significant development and increase the welfare of its members. This study aims to determine the efficiency of cooperative as a benchmark, because by known the performance value of a cooperation, it will known the weeknesses and advantages so that it can be improved the weaknesses and maintain the advantages.The method used is apply Data Envelopment Analysis (DEA). Inputs used from principal savings, mandatory savings, and fixed assets while the output used from savings in the cooperative, savings in other cooperative and SHU. As for result of this research indicates there are 9 perfect efficient DMUs (100 %) and inefficient DMU is 11 DMUs, consisting of 7 (IRS conditions) and 4 (DRS condition). The most inefficient cooperative is Koperasi Hidmat (2014) of 30.66% efficiency level.Kopkar IAILM is able to maintain its grade efficiency level from 2009 to 2015 when compared to other DMUs cooperatives in the observation, except in 2014. The calculation of efficiency level in this research is relative and it is not absolute, so that it is possible when the cooperative sample is added or the observation year is expanded, so it will get different result. The necessity of any cooperative or BMT based on Pondok Pesantren to make annual financial statements in order to increase accountability and transparency of fund management

Measuring The Efficiency of Pesantren Cooperatives: Evidence in Indonesia

The Cooperative (Koperasi) as a non-Bank financial institution has the purpose of improving the welfare of its members as Koperasi Hidmat  and  the staffs of Latifah Mubarokiyah Koperasi Ponses Suryalaya  that have been since decades ago. Over time, the ideal cooperative can show a significant development and increase the welfare of its members. This study aims to determine the efficiency of cooperative as a benchmark, because by known the performance value of a cooperation, it will known the weeknesses and advantages so that it can be improved the weaknesses and maintain the advantages.The method used is apply Data Envelopment Analysis (DEA). Inputs used from principal savings, mandatory savings, and fixed assets while the output used from savings in the cooperative, savings in other cooperative and SHU. As for result of this research indicates there are 9 perfect efficient DMUs (100 %) and inefficient DMU is 11 DMUs, consisting of 7 (IRS conditions) and 4  (DRS condition). The most inefficient cooperative is Koperasi Hidmat (2014) of 30.66% efficiency level.Kopkar IAILM is able to maintain its grade efficiency level from 2009 to 2015 when compared to other DMUs cooperatives in the observation, except in 2014. The calculation of efficiency level in this research is relative and it is not absolute, so that it is possible when the cooperative sample is added or the observation year is expanded, so it will get different result. The necessity of any cooperative or BMT based on Pondok Pesantren to make annual financial statements in order to increase accountability and transparency  of fund management

Fuzzy Efficiency Measures in Data Envelopment Analysis Using Lexicographic Multiobjective Approach

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.There is an extensive literature in data envelopment analysis (DEA) aimed at evaluating the relative efficiency of a set of decision-making units (DMUs). Conventional DEA models use definite and precise data while real-life problems often consist of some ambiguous and vague information, such as linguistic terms. Fuzzy sets theory can be effectively used to handle data ambiguity and vagueness in DEA problems. This paper proposes a novel fully fuzzified DEA (FFDEA) approach where, in addition to input and output data, all the variables are considered fuzzy, including the resulting efficiency scores. A lexicographic multi-objective linear programming (MOLP) approach is suggested to solve the fuzzy models proposed in this study. The contribution of this paper is fivefold: (1) both fuzzy Constant and Variable Returns to Scale models are considered to measure fuzzy efficiencies; (2) a classification scheme for DMUs, based on their fuzzy efficiencies, is defined with three categories; (3) fuzzy input and output targets are computed for improving the inefficient DMUs; (4) a super-efficiency FFDEA model is also formulated to rank the fuzzy efficient DMUs; and (5) the proposed approach is illustrated, and compared with existing methods, using a dataset from the literature

Benchmarking with network DEA in a fuzzy environment

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Benchmarking is a powerful and thriving tool to enhance the performance and profitabilities of organizations in business engineering. Though performance benchmarking has practically and theoretically developed in distinct fields such as banking, education, health and so on, supply chain benchmarking across multiple echelons that includes certain characteristics such as intermediate measure differs from other fields. In spite of incremental benchmarking activities in practice, there is the dearth of a unified and effective guideline for benchmarking in organizations. Amongst the benchmarking tools, data envelopment analysis (DEA) as a non-parametric technique has been widely used to measure the relative efficiency of firms. However, the conventional DEA models that are bearing out precise input and output data turn out to be incapable of dealing with uncertainty, particularly when the gathered data encompasses natural language expressions and human judgements. In this paper, we present an imprecise network benchmarking for the purpose of reflecting the human judgments with the fuzzy values rather than precise numbers. In doing so, we propose the fuzzy network DEA models to compute the overall system scale and technical efficiency of those organizations whose internal structure is known. A classification scheme is presented based upon their fuzzy efficiencies with the aim of classifying the organizations. We finally provide a case study of the airport and travel sector to elucidate the details of the proposed method in this study

Fuzzy Data Envelopment Analysis And Its Applications For Aggregating Preference Ranking

Over the past two decades, Data Envelopment Analysis (DEA) has appeared as an important tool in the field of efficiency measurement. DEA is used to compare Decision Making Units (DMUs) such as bank branches, hospitals, sales outlets, which consume one or more non-homogenous inputs to produce one or more nonhomogenous outputs. The DMUs consume the same inputs and produce the same outputs but generally at varying levels. One of the main characteristics of DEA is its sensitivity to data. That is, inaccurate data may divert effectively the results of efficiency analysis from its actual value. But accurate measurement in many real world problems, due to either non-availability of sophisticated measurement tools or qualitative nature of the phenomena may not be possible. This kind of information can be represented as fuzzy numbers or linguistic terms