Efficiency ranking with common set of weights based on data envelopment analysis and satisfaction degree

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.

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.

A characteristic of data envelopment analysis (DEA) is to allow individual decision-making units (DMUs) to select the factor weights that are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. In order to rank all the DMUs on the same scale, this paper proposes a compromise solution approach for generating common weights under the DEA framework. The efficiency scores calculated from the standard DEA model are regarded as the ideal solution for the DMUs to achieve. A common set of weights which produces the vector of efficiency scores for the DMUs closest to the ideal solution is sought. Based on the generalized measure of distance, a family of efficiency scores called ‘compromise solutions’ can be derived. The compromise solutions have the properties of unique solution and Pareto optimality not enjoyed by the solutions derived from the existing methods of common weights. An example of forest management illustrates that the compromise solution approach is able to generate a common set of weights, which not only differentiates efficient DMUs but also detects abnormal efficiency scores on a common base.

Data envelopment analysis (DEA) is a method for measuring efficiency of peer decision-making units (DMUs). Conventional DEA evaluates the performance of each DMU using a set of most favourable weights. As a result, traditional DEA models can be considered methods for the analysis of the best relative efficiency or analysis of the optimistic efficiency. DEA efficient DMUs obtained from conventional DEA models create an efficient production frontier. Traditional DEA can be used to identify units with good performance in the most desirable scenarios. There is a similar approach that evaluates the performance indicators of each DMU using a set of most unfavourable weights. Accordingly, such models can be considered models for analysing the worst relative efficiency or pessimistic efficiency. This approach uses the inefficient production frontier for determining the worst relative efficiency that can be assigned to each DMU. DMUs lying on the inefficient production frontier are referred to as DEA inefficient while those neither on the efficient frontier nor on the inefficient frontier are declared DEA inefficient. It can be argued that both relative efficiencies should be considered simultaneously and any approach with only one of them would be biased. This paper proposed the integration of both efficiencies as an interval so that the overall performance score would belong to this interval. It was shown that efficiency interval provided more information than either of the two efficiencies, which was illustrated using two numerical examples.

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 common non-parametric frontier analysis method. The multiplier framework of DEA allows flexibility in the selection of endogenous input and output weights of decision making units (DMUs) as to cautiously measure their efficiency. The calculation of DEA scores requires the solution of one linear program per DMU and generates an individual set of endogenous weights (multipliers) for each performance dimension. Given the large number of DMUs in real applications, the computational and conceptual complexities are considerable with weights that are potentially zero-valued or incommensurable across units. In this paper, we propose a two-phase algorithm to address these two problems. In the first step, we define an ideal DMU (IDMU) which is a hypothetical DMU consuming the least inputs to secure the most outputs. In the second step, we use the IDMU in a LP model with a small number of constraints to determine a common set of weights (CSW). In the final step of the process, we calculate the efficiency of the DMUs with the obtained CSW. The proposed model is applied to a numerical example and to a case study using panel data from 286 Danish district heating plants to illustrate the applicability of the proposed method.

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

A key issue within the emissions trading system is how tradable emissions permits (TEPs) are initially allocated among a set of entities. This study proposes an approach based on the proportional allocation concept to allocate TEPs among a set of decision making units (DMUs). We firstly deduce a TEP allocation set based on the rule that the TEPs allocated to DMUs should be proportional to their environmental contribution. We then obtain the allocation intervals of DMUs from the set, expressing the allocation as the convex combination between the upper and the lower bound. Finally, we define the satisfaction degree as the coefficient of the convex combination, and propose an algorithm based on the max‐min fairness of satisfaction degrees to obtain a unique TEP allocation plan. To illustrate our approach, we provide the example of how TEPs are allocated among 30 provincial administrative regions in China. Our findings indicate that our allocation method can be helpful for achieving a saving in energy consumption and reducing emissions. In addition, from the data envelopment analysis perspective, the TEP allocation set can ensure that both each individual DMU and the organization as a whole become efficient under a common set of variable weights.

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.

Information technology (IT) is defined as the obtainment, procedure, storage and propagation of sounding, drawing, and textual information by combining microelectronics-based computing and telecommunications. Nowadays, IT is starting to spread further from the conventional personal computer and network technologies to integrations of other fields of technology such as the use of cell phones, televisions, automobiles, etc. In other words, IT has penetrated in daily life of human beings and become one part of the whole society. The importance of IT has become momentous. Therefore, to understand the performance of efficiency and productivity of the IT firms is critical for managers as well as for personal investors. Until now, there are very few researches tried to analyze final performance of the IT firms. As a result, this research intends to use traditional Data Envelopment Analysis (DEA) CCR or BCC models to evaluate the performance of IT firms. The Decision Making Units (DMUs) on this research are chosen from IT firms in S&P 500. However, the traditional DEA models are not fair models from the aspect of improper weight derivations. Thus, this paper intends to analyze the efficiency of IT firms in S&P 500 efficiencies by using multiple objective programming (MOP) based Data Envelopment Analysis (DEA). In a MOP based DEA approach, DMUs will be evaluated based on an equal standard and the results will be evaluated more fairly. The world’s leading IT firms in S&P 500 will be evaluated based on publicly available financial reports of the fiscal year 2010. In addition, the newly developed MOP can improve the traditional DEA’s unfair weights problems and benchmark the efficiency of IT firms in S&P 500 correctly. In the empirical study, the MOP based DEA demonstrated that F5 Networks should be the communications equipment companies of IT worthwhile to be invested. In the future, performance evaluation results can be served as foundations for investment strategies definition.KeywordsInformation Technology (IT)Standard and Poor’s 500 indexPerformance EvaluationData Envelopment Analysis (DEA)Multiple Objective Programming (MOP)

ABSTRACTThe original context-dependent data envelopment analysis measures the attractiveness and progress of decision-making units (DMUs) through calculating the radial distance between the DMU under evaluation and the evaluation context. It only shows how distinct the DMU is from a single specific virtual DMU on the evaluation context, and ignores the entire evaluation context. In this paper, we incorporate the common set of weights into the original context-dependent data envelopment analysis. This improvement ensures evaluation consistency via providing an overall evaluation context.

Common sets of weights as summaries of DEA profiles of weights: With an application to the ranking of professional tennis players

In data envelopment analysis (DEA), each decision-making unit (DMU) incorporates its most favorable set of weights to calculate its efficiency. This results in a set of weights that varies for each DMU. To reduce the variation in factor weight for all DMUs, this study introduces a statistic approach to construct the lower and upper bounds of factor weights. This approach enables the weight bounds be adjusted to avoid the absence of efficient DMU or reduce the number of efficient DMUs. It can also be used to integrate expert opinions or resolve the conflict between the results obtained using DEA model and the experience of experts if expert information is available. Two examples illustrate that this method has merits in both flexibility and discrimination in performance evaluation. Moreover, the second example shows that the weights of inefficient DMUs are not suitable for ranking.

Data envelopment analysis (DEA) has been commonly used in the energy saving of enterprise plants. Nevertheless, when the traditional DEA model analyzes the effectiveness of decision-making units (DMUs), over 1/3 of the DMUs’ efficiency values are 1, so the traditional DEA model cannot distinguish the cons and pros of the DMUs. And although the DEA cross-model(DEACM) is able to differentiate the cons as well as pros of the effective DMUs, it can’t obtain the improvement direction of the ineffective DMUs. Therefore, an energy saving and management method based on an improved DEACM, which can use the higher efficiency distinction to identify the efficiency state of the DMUs, is proposed in this paper. Meanwhile, the improvement direction of the ineffective DMU can be found by the self-evaluation of the improved DEACM. Finally, the improved DEACM is utilized to save and manage the energy configuration of the PTA solvent system in the industrial process. The experimental results reveal that the practicality and effectiveness of the proposed method are verified, and in addition, the efficiency discrimination is well. Moreover, the proposed model can find the direction of the quantitative targets of energy saving to improve the energy efficiency of PTA production.

In models of data envelopment analysis (DEA), an optimal set of input and output weights is generally assumed to represent the assessed decision making unit (DMU) in the best light in comparison to all the other DMUs. The paper shows that this may not be correct if absolute weight bounds or some other weight restrictions are added to the model. A consequence may be that the model will underestimate the relative efficiency of DMUs. The incorporation of weight restrictions in a maximin DEA model is suggested. This model can be further converted to more operational forms, which are similar to the classical DEA models.