Finding the Most Preferred Decision-Making Unit in Data Envelopment Analysis

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.

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.

A simplistic approach without epsilon to choose the most efficient unit 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.

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

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

Prioritization models for frontier decision making units in DEA

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

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.

Detecting the weak and strong congestion statuses of decision-making units (DMUs) and measuring them via data envelopment analysis (DEA) is an important issue that has been discussed in several studies and with different views. The efficiency frontier is a concept derived from the underlying production possibility set (PPS), and the congestion concept is related to them. Still, researchers have defined congestion for each DMU in many previous studies and ignored that congestion is linked with the underlying production technology. In the congestion measurement matter, this paper presents two new insights into a congestion area and non-congestion area for production technology and two new mathematical definitions of congestion based on the PPS properties and detecting the weak and strong congestion status of DMUs (CSOD). We prove our definitions are equal to the original definition of congestion. First, we describe the congestion and non-congestion areas based on the PPS; then provide full details of how to measure congestion built on these new insights. Our approaches are very accurate and fast to calculate; they are theoretically elementary and efficient in performance. Our proposed methods can deal with both non-negative and negative data. Finally, an empirical example is provided to illustrate our approaches.

Data envelopment analysis (DEA), introduced in Charnes, Cooper, and Rhodes (1978), provides a new approach to the estimation of relative efficiencies of decision making units (DMUs). As described by Banker (1980b) and Banker, Charnes, and Cooper (1984), DEA also encompasses estimation of production frontiers making minimal assumptions—such as convexity—about the production possibility set. DEA may be employed to estimate technical and scale efficiencies as in Banker, Charnes, and Cooper, rates of substitution between inputs as in Banker, Charnes, and Cooper and Charnes, Cooper, and Rhodes (1978), and returns to scale and most productive scale sizes as in Banker (1984) and Banker, Charnes, and Cooper (1984). These estimates of different production characteristics pertain to the efficient production surface, unlike the commonly employed regression techniques which estimate the average production correspondence. In this chapter, we report on the results of a simulation study in which DEA was employed to estimate the production frontier from input and output data randomly generated from a known technology.

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.

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.

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.