A two stage data envelopment analysis model with undesirable output (original) (raw)
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Data Envelopment Analysis (DEA) is one of the well-known methods for calculating efficiency, determining efficient boundaries and evaluating efficiency that is used in specific input and output conditions. Traditional models of DEA do not try to reduce undesirable outputs and increase undesirable inputs. Therefore, in this study, in addition to determining the efficiency of Decision-Making Units (DMU) with the presence of some undesirable input and output components, its effect has also been investigated on the efficiency limit. To do this, we first defined the appropriate production possibility set according to the problem assumptions, and then we presented a new method to determine the unfavorable performance of some input and output components in decision-making units. And we determined the impact of unfavorable inputs and outputs on the efficient boundary. We also showed the model result by providing examples for both unfavorable input and output states and solving them and dete...
Four types of dependence relationship in two consecutive stage data envelopment analysis model
THE 4TH INNOVATION AND ANALYTICS CONFERENCE & EXHIBITION (IACE 2019), 2019
Data Envelopment Analysis (DEA) model usually does not consider the interaction between the decision making units (DMU). The interaction can be represented in the form of two consecutive stages in which the outputs from the precedent stage will be the inputs for the latter stage. The two consecutive stage DEA model can be represented as Non-separable DEA (NS-DEA) which integrates both desirable and undesirable output. The undesirable output unlike desirable output, indicates a higher efficiency if the output is lower or not productive. The different orientation between desirable and undesirable output may affect the efficiency score especially if it was formed in two consecutive stages. Thus, this research attempts to address four different types of dependence relationship which can occur in the formation of two consecutive stage DEA models and to investigate the impact towards the overall efficiency of the DMUs. The finding shows that the determination of positive or negative correlation between the two stages which combines both desirable and undesirable output, are more likely to be influenced by the orientation of the first precedent stage.
The general practice in performance and production efficiency measurement has been to ignore additional products of most transformation processes that can be classified as "undesirable outputs" -which are a subset of the output set. Without the inclusion of these factors, the efficiency evaluation becomes a purely technical measure of the system alone, and does not account for the interaction of the system with the surrounding environment and the impact of policy decisions on the system. In addition, there are also technological dependencies arising due to the relationships between the desirable and the undesirable outputs. One of the analytical tools normally used in efficiency evaluation is Data Envelopment Analysis, DEA.
Modeling undesirable factors in data envelopment analysis
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Data envelopment analysis is a mathematical programming technique for identifying efficient frontiers for peer decision making units with multiple inputs and multiple outputs. These performance factors (inputs and outputs) are classified into two groups: desirable and undesirable. Obviously, undesirable factors in production process should be reduced to improve the performance. In the current paper, we present a data envelopment analysis (DEA) model in which can be used to improve the relative performance via increasing undesirable inputs and decreasing undesirable outputs.
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International Journal of Mathematics in Operational Research, 2015
The main goal of this paper is to develop a new data envelopment analysis (DEA) model to use optimal weights of each decision making unit (DMU) to improve its relative efficiency aligned with other DMUs. In spite of the vast amount of studies in this area and related tools and techniques, current literature deploys the optimal weights of DMUs to calculate the DMUs' relative efficiency and benchmarking for each DMU is less investigated. In order to fill this gap, this paper proposes a model for obtaining benchmark(s) for each DMU. Furthermore, a numerical example is used to illustrate the capability of the proposed model.
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The changing economic conditions have challenged many organizations to search for more effective performance measurement methods. Data envelopment analysis (DEA) is a widely used mathematical programming approach for comparing the inputs and outputs of a set of homogeneous decision making units (DMUs) by evaluating their relative efficiency. Performance measurement in the conventional DEA is based on the assumptions that inputs should be minimized and outputs should be maximized. However, there are circumstances in real-world problems where some output variables should be minimized. We consider the concepts of technical efficiency (the ratio of the desirable outputs to inputs) and ecological efficiency (the ratio of the desirable outputs to undesirable outputs) in DEA. We then introduce a new measure called process environmental quality efficiency (the ratio of the inputs to the undesirable outputs) and use game theory to integrate these three different efficiency scores into one overall efficiency score. The cooperative and non-cooperative game theory concepts are used to integrate different efficiency ratios into a linear model. We also present a case study to exhibit the efficacy of the procedures and to demonstrate the applicability of the proposed models.
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A Complete Efficiency Ranking of Decision Making Units in Data Envelopment Analysis
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The efficiency measures provided by DEA can be used for ranking Decision Making Units (DMUs), however, this ranking procedure does not yield relative rankings for those units with 100% efficiency. Andersen and Petersen have proposed a modified efficiency measure for efficient units which can be used for ranking, but this ranking breaks down in some cases, and can be unstable when one of the DMUs has a relatively small value for some of its inputs. This paper proposes an alternative efficiency measure, based on a different optimization problem that removes the difficulties.
Archives of Computational Methods in Engineering
DEA, incepted in 80s, has emerged as a popular decision-making technique, for determining the efficiency of similar units. Due to its simplicity and applicability, DEA has gained the attention of scientists and researchers working in diverse areas, which has contributed towards a rich literature both in terms of theoretical development as well as different applications. This paper tries to bring together the near 40 years of existence of DEA in a concise format by discussing the popular DEA models, their advantages and shortcomings, and different applications of DEA. It also provides a brief bibliometric analysis to highlight the development of DEA over the years in terms of publication trends, highly cited papers, journal citation, etc.