A simplistic approach without epsilon to choose the most efficient unit in data envelopment analysis

One of the major research streams in data envelopment analysis (DEA) is ranking decision-making units (DMUs). Utilizing a multicriteria decision-making technique, we develop a novel approach to fully rank all units. Motivated by the convex cone-based total order for multiple criteria alternatives proposed by Dehnokhalaji et al. (Nav Res Logist 61(2):155–163, 2014), we consider DMUs in DEA as multiple criteria alternatives and obtain their total ordering. Initially, some pairwise preference information is provided by the decision maker for units and the concepts of convex cones and polyhedral sets are defined in a DEA framework, correspondingly. We apply a modification of Dehnokhalaji et al. method to extract additional preference information for each pair of units and consequently obtain a full ranking (strict total ordering) of DMUs. The benefit of our approach to their method is that we apply non-radial models to overcome the instability drawback of radial models and their infeasibility occurring in DEA applications. The proposed approach is implemented for two numerical examples, and the accuracy of it is investigated through a computational test.

Compensating for non-homogeneity in decision-making units in data envelopment analysis

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 selection-based problem is a type of decision-making issue which involves opting for a single option among a set of available alternatives. In order to address the selection-based problem in data envelopment analysis (DEA), various integrated mixed binary linear programming (MBLP) models have been developed. Recently, an MBLP model has been proposed to select a unit in DEA with variable returns-to-scale technology. This paper suggests utilizing the linear programming relaxation model rather than the MBLP model. The MBLP model is proved here to be equivalent to its linear programming relaxation problem. To the best of the authors’ knowledge, this is the first linear programming model suggested for selecting a single efficient unit in DEA under the VRS (Variable Returns to Scale) assumption. Two theorems and a numerical example are provided to validate the proposed LP model from both theoretical and practical perspectives.

Prioritization models for frontier decision making units in DEA

Discriminating extreme efficient decision making units in DEA using random weight vectors

A cross-dependence based ranking system for efficient and inefficient units in DEA

Data envelopment analysis (DEA) evaluates the efficiency of the transformation of a decision-making unit’s (DMU’s) inputs into its outputs. Finding the benchmarks of a DMU is one of the important purposes of DEA. The benchmarks of a DMU in DEA are obtained by solving some linear programming models. Currently, the obtained benchmarks are just found by using the information of the data of inputs and outputs without considering the decision-maker’s preferences. If the preferences of the decision-maker are available, it is very important to obtain the most preferred DMU as a benchmark of the under-assessment DMU. In this regard, we present an algorithm to find the most preferred DMU based on the utility function of decision-maker’s preferences by exploring some properties on that. The proposed method is constructed based on the projection of the gradient of the utility function on the production possibility set’s frontier.

Efficiency and performance evaluation is an important task in governmental decision making. This paper aims in application of analytic hierarchy process (AHP) for efficiency analysis of a general set of decision making units (DMUs). Conventional tool for analysis of efficiency of DMUs is data envelopment analysis (DEA). DEA models allow splitting the set of DMUs into two subsets - efficient and inefficient. The inefficient ones can be ranked according to their efficiency scores given by the DEA model but the efficient units cannot be ranked easily as their have identical maximal efficiency score. Various models have been proposed for ranking of efficient units in DEA. The aim of the paper is to discuss the possibility of application of AHP models for ranking of efficient or entire set of DMUs. The proposed approach is illustrated on performance evaluation of 19 Czech economic faculties. The results given by the AHP ration model are compared to those given by conventional approaches.

The paper aims in application of analytic hierarchy process (AHP) for efficiency analysis of the set of decision making units (DMUs).Conventional tool for analysis of efficiency of DMUs is data envelopment analysis (DEA).DEA models allow splitting the set of DMUs into two subsets -efficient and inefficient.The inefficient ones can be ranked according to their efficiency scores given by the DEA model but the efficient units cannot be ranked easily as their have identical maximal efficiency score.Many models have been proposed for ranking of efficient units in DEA models.The aim of the paper is to discuss the possibility of application of AHP models for ranking of efficient or entire set of DMUs.Numerical experiments are realized on the set of 20 commercial banks operating on the Czech financial market.The study is based on a real data set containing financial characteristics of the banks.

The development of the pallet rental industry is moving at a rapid pace. However, there is no literature on the performance evaluation of pallet rental companies except our previous study. This paper contributes to extending our previous super-efficiency integer-valued DEA (data envelope analysis) model to a group of integer-valued DEA models with generalized reference sets (G-IDEA). According to the proposed approach, the reference sets for decision-making units (DMUs) are composed of proper efficient sample units instead of efficient DMUs. These sample units, which may or may not be the same as DMUs, can be selected by decision-makers according to their demand. The advantages of the G-IDEA models are as follows: (1) they can be applied to find the projections of pallet rental companies with real-valued and integer-valued variables on the efficient frontier; (2) they are able to help the decision-makers in inefficient pallet rental companies make a step by step efficiency improvement scheme. Particularly, we develop a non-oriented integer-valued DEA model with generalized reference sets (NG-IDEA). The NG-IDEA model can be used to figure out how to improve the performance of inefficient pallet rental companies by simultaneously decreasing inputs and increasing outputs. The proposed models are applied to the performance evaluation of ten pallet rental companies. The results of the case study prove the effectiveness of our models. Furthermore, some valuable suggestions on how to improve the efficiency of inefficient pallet rental companies are presented based on the results.

Data Envelopment Analysis (DEA) is a well-known method for calculating the efficiency of Decision-Making Units (DMUs) based on their inputs and outputs. When the data is known and in the form of an interval in a given time period, this method can calculate the efficiency interval. Unfortunately, DEA is not capable of forecasting and estimating the efficiency confidence interval of the units in the future. This article, proposes a efficiency forecasting algorithm along with 95% confidence interval to generate interval data set for the next time period. What’s more, the manager’s opinion inserts and plays its role in the proposed forecasting model. Equipped with forecasted data set and with respect to data set from previous periods, the efficiency for the future period can be forecasted. This is done by proposing a proposed model and solving it by the confidence interval method. The proposed method is then implemented on the data of an automotive industry and, it is compared with the Monte Carlo simulation methods and the interval model. Using the results, it is shown that the proposed method works better to forecast the efficiency confidence interval. Finally, the efficiency and confidence interval of 95% is calculated for the upcoming period using the proposed model.

Efficiency evaluation is crucial for providing decision support in both target setting and competency recognition. In many practical applications, flexible measures that can be classified as either input or output often lead to inconsistent results due to distinct classifications. Conventional classification methods may identify many efficient decision making units (DMUs), which cannot provide us with the best alternative and reduces the discriminating power of associated models. In this study, we develop a novel integrated approach by identifying the single efficient DMU considering flexible measures. Specifically, our proposed approach guarantees the feasibility of the associated efficiency estimation model under relatively mild conditions. Moreover, the weight scheme and non-dominated classification result can be uniquely determined via a revised min-max computational procedure. We validate and illustrate the proposed approach by applying it to evaluate the efficiencies of Chinese commercial banks before and during the pandemic. Our findings suggest that the pandemic does have an impact on bank efficiency, and different banks respond differently to the pandemic shock. More specifically, the best-performing bank that stands out before and during the pandemic can be identified as a unique benchmark, and the others could learn from this alternative to mitigate the pandemic shock.

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.