Context-dependent data envelopment analysis with common set of weights

Data envelopment analysis (DEA) identifies an empirical efficient frontier of a set of peer decision making units (DMUs) with multiple inputs and outputs. The efficient frontier is characterized by the DMUs with an unity efficiency score. The performance of inefficient DMUs is characterized with respect to the identified efficient frontier. If the performance of inefficient DMUs deteriorates or improves (up to the frontier), the efficient DMUs still have an unity efficiency score. However, the performance of DMUs may be influenced by the context — e.g. a product may appear attractive against a background of less attractive alternatives and unattractive when compared to more attractive alternatives. With an application to Tokyo public libraries, the current paper presents and demonstrates a context-dependent DEA which measures the relative attractiveness of libraries on a specific performance level against libraries exhibiting poorer performance. The set of libraries are grouped into different levels of efficient frontiers. Each efficient frontier (on a specific performance level) is then used as evaluation context for the relative attractiveness. The performance of the efficient libraries changes as the inefficient libraries change their performance. The context-dependent DEA can also be used to differentiate the performance of efficient DMUs. The context-dependent DEA provides finer DEA results with respect to the performance of all DMUs.

Efficiency evaluations with context-dependent and measure-specific data envelopment approaches: An application in a World Bank supported project

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.

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.

Traditional DEA models allow individual decision-making units (DMUs) to arbitrarily determine the weights of all variables to calculate their efficiencies. This flexibility in selecting the weights is a great advantage for many DMUs, but it also brings some defects such as non-uniqueness of weights sets and the appearance of zero-value weights. Different sets of weights to calculate efficiencies violate the requirement that DMUs should be compared on the same base, leading to the efficiency ranking being not accepted by decision-makers. In this paper, we provide a DEA-based approach for obtaining DMUs’ efficiencies, which assumes that DMUs are collective rationality and its objective is to maximise the satisfaction degrees of all the DMUs. Then, we provide a maxmin model and two corresponding algorithms for generating the common set of weights (CSW). Lastly, the proposed approach is applied to the ranking of 17 forest districts and is compared with other methods.

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

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.

The aviation industry has a key role in international trade activities. Most studies measure aviation performance based on airlines or airports. However, the frontline operation is delivered via air routes and more operating characteristics can be revealed with route-based performance evaluation. Further, the traditional data envelopment analysis (DEA) approach cannot rank performance in a particular context which represents an efficiency frontier built by decision making units (DMUs). Therefore, this study uses a context-dependent DEA approach to measure and rank the performance of air routes with a case study of 112 international routes from two airlines in Taiwan. Model results identify eight performance levels with most air routes at efficiency performance level 2 and level 3 and most route destinations in East Asia (e.g., Japan). The results of this study can inform operators about a clear relationship between performance and potential markets as well as improvement strategies.

Energy and environmental efficiency of OECD countries in the context of the circular economy: Common weight analysis for malmquist productivity index

Organizations are interested in exploiting the data from the other organizations for better analyses. Therefore, the data related policies of organizations should be sensitive to the data privacy issue, which has been widely discussed recently. The present study is focused on inter-group data usage for a relative evaluation. This research is based on the data envelopment analysis (DEA), which is used to measure the efficiency of a decision making unit (DMU) relatively employed within a group. In DEA, establishing an efficient frontier consisting of efficient DMUs is essential. We can obtain the efficiency values of a DMU by projecting it to the efficient frontier, and including in the efficiency interval via the interval DEA. When the original data of multiple groups are not open to each other, the alternative is to exchange the information corresponding to the efficient frontiers to estimate the efficiency intervals of a DMU in such a manner that the alternative is in the other groups. Therefore, in this paper, we propose a method to replace the efficient frontier with a weight vector set, from which it is not possible to reconstruct the original data. Considering the weight vector sets of multiple groups, a DMU has three types of efficiency intervals: in its own group, in each of the other groups, and in the integrated group. They provide rich insights on the DMU from a broad perspective, and this encourages inter-group data usage. In this process, we focus on two types of information reduction: one is from the efficient frontier to the weight vector set, and the other is from a union of the groups to the integrated group.

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.

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

The research aims to analyze the technical efficiency of the chocolate industry, which has outstanding performance in producing chocolate products in East Java, Indonesia. The research sample includes all small and large-scale chocolate industries in East Java, with 42 Decision Making Units (DMUs). Efficiency research uses Data Envelopment Analysis (DEA), which is usually used in agricultural production research. However, in this research, DEA was used to analyze the efficiency of the chocolate industry making this concept as an empirical novelty. The analysis results show that there are industries operating at the Constant Returns to Scale (CRS) level (0.971), with a percentage of 66.67%, consisting of 28 DMUs, and the Variable Returns to Scale (VRS) level (0.992), with a percentage of 85.71%, which is represented by 36 DMUs. The Technical Efficiency (TE) is categorized as full technical efficiency at 85.72%, with a high category at 14.28%, and no DMUs fall under the moderate and low categories. This indicates that the allocation of inputs in each DMU is significantly different. Six DMUs require improvement in the distribution of industrial capital and raw materials input to achieve full efficiency category by making decisions based on the DMU's recommendations as a reference (benchmarks). This article concludes that industrial efficiency is a priority for the establishment of a business to achieve its goals easily. When the industry can control the quality and quantity of its products, it can be highly beneficial. The policy implications required for this case research to maintain and improve the efficiency of the chocolate industry in East Java, Indonesia, are for industries to prioritize joint management, increase the scale of operations, increase production frequency, expand innovative chocolate processing technology, prioritize product quality, and be able to penetrate export markets.

Strategic alliances and partnerships based on the semi-additive production technology in DEA

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.