A Two-Step Centralized Model via Data Envelopment Analysis for Allocating Aggregate Carbon Emissions Abatements

The interest in Data Envelopment Analysis (DEA) as a method for analyzing the productivity of homogeneous Decision Making Units (DMUs) has significantly increased in recent years. One of the main goals of DEA is to measure for each DMU its production efficiency relative to the other DMUs under analysis. Apart from a relative efficiency score, DEA also provides reference DMUs for inefficient DMUs. An inefficient DMU has, in general, more than one reference DMU, and an efficient DMU may be a reference unit for a large number of inefficient DMUs. These reference and efficiency relations describe a net which connects efficient and inefficient DMUs. We visualize this net by applying Sammon’s mapping. Such a visualization provides a very compact representation of the respective reference and efficiency relations and it helps to identify for an inefficient DMU efficient DMUs respectively DMUs with a high efficiency score which have a similar structure and can therefore be used as models. Furthermore, it can also be applied to visualize potential outliers in a very efficient way.

This study aimed to measure the efficiency scores of 75 dairy buffalo farms in the province of Nueva Ecija, Central Luzon, Philippines, using an input-oriented, variable-return-to-scale Data Envelopment Analysis (DEA) model. The farmer-informants or decision-making units (DMUs) were categorized as smallholders, family modules, and semi-commercial in operations. Personal interviews using structured questionnaires were done to gather various information on the socio-economic and management practices of the DMUs. Output in the form of volume and value of milk produced and inputs such as quantities and costs of biologics, feeds, forage, and labor were also collected and evaluated among individual DMUs. The efficiency scores were computed using PIM-DEA software, which identified fully efficient DMUs lying on the frontier line (scores of 1.0) and those enveloped by it (inefficient DMUs with scores of less than 1.0). The overall mean Technical Efficiency (TE), Allocative Efficiency (AE), and Economic Efficiency (EE) scores among the DMUs were 0.80, 0.81, and 0.65, respectively. Most of the inefficient DMUs were in the smallholder category. In sum, smallholder DMUs classified under low and moderate TE clusters should reduce their inputs by 53.31% and 40.01%, respectively, to become fully efficient. Likewise, higher lambda values among efficient peer DMUs indicate the best practice frontiers that the inefficient peer DMUs can benchmark with. Extension and advisory services can help promote the best management practices of the frontiers to improve the TE, AE, and EE of the inefficient DMUs.

Data envelopment analysis (DEA) is a considerable mathematical programming technique for measuring the relative efficiencies of a set of decision making units (DMUs) with multiple inputs and multiple outputs. Conventional DEA assists decision makers in distinguishing between efficient and inefficient DMUs in a homogeneous group. However, it does not give more information about the efficient DMUs. In this paper, a new method is proposed to differentiae the performance of efficient units. In the proposed method a new DEA model is constructed by introducing some virtual units called relative similar units associated with efficient units into the possibility production set. We present two practical examples to demonstrate the applicability of the proposed method and to exhibit the efficacy of the procedures.

Data Envelopment Analysis (DEA) is a non-parametric method for evaluating the efficiency of Decision Making Units (DMUs) with multiple inputs and outputs. In the traditional DEA models, the DMU is allowed to use its most favorable multiplier weights to maximize its efficiency. There is usually more than one efficient DMU which cannot be further discriminated. Evaluating DMUs with different multiplier weights would also be somewhat irrational in practice. The common weights DEA model is an effective method for solving these problems. In this paper, we propose a methodology combining the common weights DEA with Shannon’s entropy. In our methodology, we propose a modified weight restricted DEA model for calculating non-zero optimal weights. Then these non-zero optimal weights would be aggregated to be the common weights using Shannon’s entropy. Compared with the traditional models, our proposed method is more powerful in discriminating DMUs, especially when the inputs and outputs are numerous. Our proposed method also keeps in accordance with the basic DEA method considering the evaluation of the most efficient and inefficient DMUs. Numerical examples are provided to examine the validity and effectiveness of our proposed methodology.

A data envelopment analysis model with interval data and undesirable output for combined cycle power plant performance assessment

Data envelopment analysis (DEA) is a mathematical programming approach for calculating the relative efficiency of a group of decision making units (DMUs). After efficiency measurement process some DMUs may have the same measure of efficiency, specifically some DMUs may be found efficient. The question is which DMU performs better within a group of DMUs with the same measure of efficiency. The current article aims to answer this question based the DMU's aid not only to the associated group but also its aid to the whole production system. This yields to two ranking indices. The first index is for ranking inefficient DMUs with the same measure of efficiency and the second index is for ranking efficient DMUs. A comparison between the proposed approaches and well-known ranking index in the literature is provided and proposed approaches are explained by many numerical examples and a real life data illustration.

Survey on rank preservation and rank reversal in data envelopment analysis

Data envelopment analysis (DEA) is used to evaluate the performance of decision making units (DMUs) with multiple inputs and outputs in a homogeneous group. In this way, the acquired relative efficiency score for each decision making unit lies between zero and one where a number of them may have an equal efficiency score of one. DEA successfully divides them into two categories of efficient DMUs and inefficient DMUs. A ranking for inefficient DMUs is given but DEA does not provide further information about the efficient DMUs. One of the popular methods for evaluating and ranking DMUs is the common set of weights (CSW) method. We generate a CSW model with considering nondiscretionary inputs that are beyond the control of DMUs and using ideal point method. The main idea of this approach is to minimize the distance between the evaluated decision making unit and the ideal decision making unit (ideal point). Using an empirical example we put our proposed model to test by applying it to the data of some 20 bank branches and rank their efficient units.

Heart patients shows several symptoms and it is rigid to point them. Data envelopment analysis (DEA) delivers a comparative efficiency degree for each decision-making units (DMUs) with several inputs and outputs. Evaluating of hospitals is one of the major applications in DEA. In current study, CCR input oriented (CCR IO ) model is applied. A new-two stage DEA model and a cross-efficiency are considered for efficiency evaluation and ranking of DMUs at the same periods. The data covers a six-year span from 2011 to 2016 for 12 local heart hospitals. The system was implemented in Banxia Frontier Analyst software and average efficiency scores, efficient DMUs contribution, inefficient DMUs reference, number of efficient DMUs, number of inefficient DMUs, target and potential improvement are compared. The sixth, the tenth and the eleventh hospitals with five high efficient DMUs (100%) among six DMUs are introduced as the highest performance hospitals and second period with an average efficiency of 85.07% is presented by means of the best presentation period.

In recent years, social network analysis (SNA) has been combined with data envelopment analysis (DEA) to select benchmarks and fully rank decision-making-units (DMUs). However, such methods fail to identify the most suitable benchmarks for the group. On one hand, they may incorrectly identify an efficient DMU as a suitable benchmark for the group. On the other hand, they fail to recognise any inefficient DMU as a benchmark for the group. To address such limitations occurred in the conventional DEA-based SNA approaches, this study proposes a modified DEA–SNA method. The new approach selects preferred benchmarks from the perspective of the entire DMU group considering both efficient DMUs and inefficient DMUs as candidates. The proposed method can identify efficient DMUs that obtain little endorsement from inefficient DMUs and inefficient DMUs that could be good benchmarks because they are endorsed by many DMUs with worse performance. The benchmarking information helps decision-makers identify suitable benchmarks, especially for those units whose efficiency scores are too low to learn from the industry leaders. Two examples are used to illustrate the practicability and superiority of our proposed method.

Data envelopment analysis (DEA) is a tool for measuring the relative efficiency of decision-making units (DMUs) that perform similar tasks. One of the uses of the DEA is the establishment of benchmarks for inefficient DMUs. These benchmarks play the role of target for inefficient DMUs. However, traditional DEA (TDEA) models fail to rank the efficient DMUs, and as a result, they cannot determine a benchmark for the inefficient DMUs. To overcome this shortcoming, this paper proposes virtual network DEA (NDEA) approach. The proposed method not only ranks the whole inefficient and efficient DMUs but also establishes a virtual benchmark called ideal DMU. The case study demonstrates the applicability of the proposed model.

Data envelopment analysis (DEA) models compute efficiency score for decision making units (DMUs) and discriminate between efficient and inefficient DMUs. Therefore, they rank DMUs except when multiple DMUs have an efficiency score of 1. This paper proposes a new method for complete ranking of DMUs that is based on cross-efficiency evaluation method. One of the drawbacks of the cross-efficiency evaluation method is the existence of multiple cross-efficiency scores due to the presence of alternative optimal solutions of the dual multiplier model. Hence choosing weights between alternative optimal solutions as part of a procedure for ranking DMUs is problematic. Liang et al. (2008) introduced alternative secondary goals in cross-efficiency evaluation. However, this paper finds that their approach is problematic in some situations. As a result, this paper seeks to introduce a new secondary objective function in cross-efficiency evaluation for removing their difficulties. Numerical demonstration reveals the validity of the proposed method by using a real data set of a case study which consists of 20 Iranian bank branches. Key words: Data envelopment analysis (DEA), ranking, cross-efficiency.

Ranking efficient decision making units in data envelopment analysis based on reference frontier share

A complete ranking of DMUs using restrictions in DEA models

This chapter presents work on the use of an artificial intelligence technique to cluster stratified samples of container terminals derived from Data Envelopment Analysis (DEA). This technique is Kohonen’s self-organizing map (SOM; (Kohonen, 1995)). Data envelopment analysis measures the relative efficiency of comparable entities called Decision Making Units (DMUs) essentially performing the same task using similar multiple inputs to produce similar multiple outputs ((Charnes et al., 1978)). The purpose of DEA is to empirically estimate the so-called efficient frontier based on the set of available DMUs. DEA provides the user with information about the efficient and inefficient units, as well as the efficiency scores and reference sets for inefficient units. The results of the DEA analysis, especially the efficiency scores, are used in practical applications as performance indicators. There are many problems associated with applying the DEA in some applications. One problem is that the improvement projection for inefficient units in DEA analysis is concrete relative to its efficiency score. This means, in DEA, relative performance of any DMU can be contrasted only to the efficient DMUs that register unit efficiency score. There is no influence on the performance of efficient DMUs by presence or absence of inefficient DMUs. Therefore, the classical DEA does not actually provide a direct means to rank DMUs based on their relative degrees of efficiency or inefficiency ((Sharma & Yu, 2010)). The second problem is that the DEA models assume that all DMUs are homogenous and identical in their operations ((Seiford, 1994)). Since various applications have heterogeneous DMUs and there is a high request to evaluate these applications under the DEA due to its acceptance as a performance measurement in different kind of business, we have to modify the DEA to work with these applications. If the heterogeneous DMUs are assessed by DEA without any modifications, the DEA yields a biased performance scores and inaccurate analyses. For example, the resources (land, equipment, and labor) of container terminals varies across the world, which requires to be evaluated in term of its common input characterstics. An essential requirement in analyzing these container terminals is to build a fair referencing system for each container terminal to manage and provide a solid plan that improves all inefficient terminals and supports all efficient terminals. This system can not be assessed under the standard DEA due to the non-homogenous nature of these container terminals in terms of their operations, different standards of equipments, infrastructure, and variety in quay length and area size. These factors will yield unfair benchmarking evaluation 5