Ranking of different common set of weights models using a voting model and its application in determining efficient DMUs

Survey on rank preservation and rank reversal in data envelopment analysis

Data envelopment analysis (DEA) is a non-parametric technique for measuring the efficiency of decision making units (DMU) with exact input and output terms. So far, a number of DEA models with interval data have been developed. The radial DEA model such as CCR or BCC model with interval data are well known as basic DEA models with interval data. However, these radial DEA models have some defects. In this study, we develop a new approach based upon the slacks-based measurement (SBM) of super-efficiency model for dealing with interval data in DEA. The SBM super-efficiency DEA model can not only discriminate the performance of efficient DMUs from inefficient ones, but can distinguish between the efficient DMUs. In addition, this model can overcome the drawback that the super-efficiency model can be infeasible under variable returns to scale (VRS) assumption. An illustrative example is provided to verify the idea of this paper and show its potential application and validity.

Data envelopment analysis (DEA) with considering the best condition for each decision making unit (DMU) assesses the relative efficiency for it and divides a homogenous group of DMUs into two categories: efficient and inefficient, but traditional DEA models can not rank efficient DMUs. Although some models were introduced for ranking efficient DMUs, Franklin Lio & Hsuan peng (2008), proposed a common weights analysis (CWA) approach for ranking them. These DMUs are ranked according to the efficiency score weighted by the common set of weights and shadow prices. This study shows there are some cases that shadow prices of efficient DMUs are equal, hence this method is not applicable for ranking them. Next, we propose a new method for ranking units with equal shadow prices.

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.

In Data envelopment analysis (DEA), the best performers are called DEA efficient and the efficiency score of a DEA efficient unit is denoted by unity. Ranking DEA efficient units is an interesting subject. This paper proposed a super-efficiency DEA model based on slack-based measure to evaluate engineering camouflage projects. A slack-based measure of DEA model was introduced, and then it was extended to super-efficiency issue. The method differs from the traditional radial measure, it takes account of the slacks of decision making units (DMU). The efficient DMUs can also be ranked completely. A numerical example illustrates the availability in the evaluating process of engineering camouflage projects.

This study attempts to exploit information from environmental variables together with data envelopment analysis (DEA) efficiency scores for efficiency predictions of groups with more limited information. Based on DEA efficiency scores, decision-making units (DMUs) are sorted into two sets containing efficient and inefficient units, respectively. Then they are reshuffled into homogeneous groups with respect to environmental factors. We assume that the efficiency of DMUs in such a homogeneous group would be correlated. However, efficiency of different groups would vary. A beta binomial logistic model is proposed to fit such phenomena and is applied to predict the performance of a new group of commercialization projects for given environmental characteristics.

In this paper, we have formulated Data Envelopment Analysis (DEA) models to reduce the inputs in an inefficient Decision Making Unit (DMU) when the specific inputs are under the constant sum constraint. We have also extended the models to reallocate the excess input without any reduction in efficiency of other DMUs. These DEA models and methods developed in this work will help decision makers in developing an optimal strategy to transfer excess input to other DMUs. Theoretical results have been illustrated with the help of a case study.

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.

Abstract. The traditional data envelopment analysis (DEA) model ignores the cooperative relationship among decision-making units (DMUs), so it is difficult to evaluate the DMUs efficiency reasonably. In this study, we use a cross-efficiency and bootstrap truncated regression (BTR) model to analyze the determining factors of digital mobile e-learning. The empirical results of this research indicate the following results: (1) Importing digital mobile e-learning can really enhance the efficiency of school management. (2) The school size, tablet PC numbers, total equipment expenses associated with tablet PC and school location are important determinants for affecting the efficiency of school management. Owing to the government is full implementation of the new learns model, that is, to be where the students able to experience the authentic joy of new learning model and attract students join. The result of the study suggested that in order to increase the school’s cross-efficiency model efficiency. The first assist the school in upgrading the Wi-Fi technology and network equipment. In general, the school adds to the Wi-Fi technology and network equipment. That would enlarge the school network and as to attract more school will adopt the new learning. It is where the students able to experience the authentic joy of new learning model and attract students join. Thus, the schools will increase school size. However, it should be noted that total equipment expenses associated with tablet PC have the negative influence on school management efficiency due to the increasing costs for furnishing the related internet and network equipment or device to facilitate for teaching and learning among teachers and students by digital mobile e-learning. The results of this research can also be the reference for educational authorities when formulating policies and regulations for promoting digital mobile e-learning in high school in Taiwan. Keywords. Operating efficiency, Digital mobile e-Learning, Data envelopment analysis (DEA), Truncated bootstrapped regression (TBR), Cross efficiency model. JEL. I21, I25, I28.

Efficiency measurement is crucial to management for performance evaluation of several decision-making units (DMUs) in order to find the most efficient unit. Data envelopment analysis (DEA) is a practical and popular method that has been used widely for efficiency measurement in many applications. Thus, in the literature of DEA, several mixed integer DEA models are developed to efficiency measure and find the best efficient unit. In some situations, some factors named dual-role factors may be simultaneously considered as both inputs and outputs. However, a little attention has been paid in the literature of DEA to these types of factors. The current paper develops a new mixed integer linear DEA model to identify the best efficient DMU in the presence of dual-role factors. The basic DEA models consider different roles for each dual-role factor, and also solve at least one model for each DMU to determine the best unit. However, the developed approach in this paper considers a unique role for each dual-role factor, and also determines the best unit through by solving just one mixed integer DEA model. Two numerical examples are used to illustrate the profits and applicability of the developed approach.

Assessing the efficiency of a supply chain (SC) is of great importance for managers and policy makers. For this aim, we propose a network data envelopment analysis (NDEA) model to reflect the internal structure of networks in efficiency evaluation. For many of the real-world performance evaluation problems, data of inputs and outputs are available, and their ratio conveys important messages to managers. However, conventional data envelopment analysis (DEA) models are no longer able to deal with ratio data. This paper aims to extend the NDEA models with the ratio data (NDEA-R) to evaluate the performance of SCs. Therefore, given the internal structure of a supply chain, relationships among different divisions of an SC are determined under two assumptions of free-links and fixed-links. Applicability of the proposed models is illustrated by evaluating supply chain of 19 hospitals in Iran over 6 months. By performing sensitivity analysis, we find out that the overall efficiency score of decision-making units (DMUs) under the fixed link assumption is greater than or equal to the overall efficiency of DMUs under free link assumption. Our proposed model overcomes the underestimation of efficiency and pseudo-inefficiency scores.

Efficiency evaluation based on data envelopment analysis in the big data context

Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In Data Envelopment Analysis (DEA), it is highly important to identify the defining hyperplanes and especially the strong defining hyperplanes of the empirical PPS. Although DEA models can determine the efficiency of a Decision Making Unit (DMU), but they cannot present efficient frontiers of PPS. In this paper, we propose a new method to determine all strong efficient (Pareto-efficient) DMUs and strong defining hyperplanes of the PPS with constant returns to scale including the Pareto-efficient DMUs. Furthermore, we apply the newly proposed method to find the normal vectors or gradient of the strong defining hyperplanes of the PPS including strong efficient DMUs which are under evaluation. Consequently, the equations of these hyperplanes are determined. To illustrate the applicability of the proposed method, some numerical examples are finally provided. Our method can be easily implemented using existing packages for operation research, such as GAMS.

This paper improves the integrated data envelopment analysis (DEA) model proposed by Asosheh et al. [1], for evaluating and ranking information technology (IT) projects in presence of both cardinal and ordinal data. They used balanced scorecard (BSC) for defining IT projects evaluation criteria and introduced a new DEA model to obtain most efficient IT project by considering imprecise data. This paper shows that their model randomly selects one efficient decision making unit (DMU) or IT project as the most efficient and the selection depends on the program or method is used for solving the problem. We develop their idea and propose a modified model to determine the most efficient DMU. In addition, this paper proposes a new algorithm for finding and ranking other efficient DMUs. The capability and usefulness of the proposed model is indicated by a numerical example.

A generalized model for data envelopment analysis with interval data