DEA

Cluster analysis in data envelopment analysis (DEA) is determining clusters for the units under evaluation regarding to their similarity. which measure of distances define their similarities. Over the years, researches have been carried out in the field of clustering of DMUs. In this paper, an algorithm for clustering units using projecting them on the frontier is presented. In fact, we gained for every decision making unit (DMU), nearest most productive scale size (MPSS) as target, to find number of clusters 2 method applied. Silhouette index was used to measure similarity value for our clustering. Numerical examples are provided to illustrate the proposed method and its results.

A line location problem as a subdivision of facility location problem deals with finding a straight line in the plane, so that sum of weighted distances or maximum weighted distances from the line to the demand points is minimized. This paper provides a novel approach to study the semi-obnoxious median line location problem with Euclidean norm by using data envelopment analysis method. Since the presented procedure would consider lines as decision making units, so efficiency of lines is taken into account instead of their optimality. Moreover, due to the inherent uncertainty of the parameters of the line location problem in the real world such as weights or/and coordinates of demand points, the problem under interval data is studied in viewpoint of data envelopment analysis as well. Furthermore, some propositions and a numerical example are provided to investigate the problem. Finally, conclusion is given.

DEA is a nonparametric method for calculating the relative efficiency of a DMU that yields to a reference target for an inefficient DMU. However, it is very hard for inefficient DMUs to be efficient by benchmarking a target DMU which has different inputs. Finding appropriate benchmarks based on the similarity of inputs makes it easier for an inefficient DMU to try to be like its target DMUs. But it is rare to discover a target DMU, which is both the most efficient and similar in inputs, in real situation. Therefore, it is necessary to find the most similar and closest real DMU in terms of inputs on the strong efficiency frontier, which has the highest possible output. In this paper, a combination of the Enhanced Russell model and the additive model is proposed as a new model to improve the efficiency of the inefficient DMUs. The proposed model is applied on a dataset of a large Canadian Bank branches. The target introduced by the proposed method is more practical target for the evaluated unit. The inefficient unit can improve its efficiency more easily by this benchmark.

It is very important to choose an appropriate and efficient monitoring system to evaluate the performance of a bank’s financial distress, including the most important monitoring systems that have been proposed to evaluate the performance of a bank’s financial distress; The use of CAMELS monitoring system, which includes six indicators of capital adequacy, asset quality, management soundness, earning quality, liquidity, market risk sensitivity, so the purpose of this study is to evaluate the financial distress of banks based on CAMELS indicators. In this regard, 12 financial variables based on CAMELS indices have been used, which have been implemented on 17 banks listed on the Tehran Stock Exchange. The sample selected in the model fit includes two groups of healthy and financially distressed, which are separated based on the CAMELS index. The accuracy of both models has been investigated. The results indicate that the overall accuracy of the logistic regression model is higher than the Data Envelopment Analysis model in assessing financial distress. Also, the results of this study showed that CAMELS financial ratios can be a good assessor for banks’ financial distress.

Data Envelopment Analysis (DEA) is a non-parametric mathematical programming method used to assess performance and measure the efficiency of Decision-making Units (DMUs) that operate with multiple concurrent inputs and outputs. The performance of these units is influenced by the utilization of input resources. While an increase in input utilization typically leads to higher production levels, there are scenarios where increased input usage results in decreased outputs. This phenomenon is termed congestion. Given that alleviating congestion can reduce costs and enhance production, it holds significant importance in economics. This paper introduces a method for identifying congestion based on a defined modeling framework. A DMU is considered congested when reducing inputs in at least one component leads to increased outputs in at least one component, and increasing inputs in at least one component can be achieved by reducing outputs in at least one component, without improvement in other indicators. The paper explores congestion in DMUs with both increasing and decreasing inputs.

Data envelopment analysis (DEA) obtains the relative eciency of decision-making units (DMUs) based on their inputs and outputs. In many situations, some variables can play the role of input or output for a DMU. It is important to provide a suitable model that can maximize the eciency of the unit under evaluation by correctly choosing the role of these variables. One of the production technologies in DEA is semi-additive production technology. In addition to the observed DMUs, this technology also considers the set of all aggregations corresponding to these DMUs in the evaluation of eciency. In this paper, we presented the semi-additive production technology in DEA in the presence of exible measures. This technology is created based on the observed DMUs and their corresponding aggregations DMUs. We have shown that we can provide semi-additive production technology in the presence of exible measures based only on the observed DMUs by removing the region with decreasing returns to scale from the production possibility set (PPS). In the following, we present two dierent approaches for measuring the eciency of DMUs in the presence of exible measures in semi-additive production technology. These two approaches allocate exible measure as input or output in such a way that the eciency of the unit under evaluation is maximized. Also, we use the proposed approach to evaluate the eciency of data sets related to academic units.

For an optimal system design (OSD), data envelopment analysis (DEA) treats companies as black boxes disregarding their internal processes. Considering the effect of these processes into account companies can upgrade their internal mechanisms of optimal budgeting allocation. The internal processes can be defined as series and parallel networks or a combination of them. In the literature, DEA is utilized as an approach for OSD in order to determine the optimal budget for a company's activities in a system of series network production; but it is shown that this model is not suitable for budgeting parallel systems. To fill this gap, a new model is presented in this paper to evaluate a company's optimal budgeting which has a parallel network system. The presented parallel network OSD via DEA models, allocates the optimal budget to each of the internal processes of the decision-making units (DMU) based on the efficiency of the parallel internal processes. The model, with a limited budget, also is able to identify the amount of budget deficit and congestion. In this regard, two real cases are studied using the suggested model, which is presented in the parallel network OSD via DEA and Forest production in Taiwan. The optimal budget, budget deficit and congestion, and also the advantages of the proposed model are discussed in these examples as well.

Data Envelopment Analysis (DEA) is an extremely flexible and useful methodology, which provides a relative efficiency score for each decision-making unit.Classic DEA models only evaluate the performance efficiency of units and they cannot provide any information about the progress and regress of units in two periods. Also, they suppose that all inputs and outputs are positive real numbers. But in the real world, due to the existence of uncertainty, this assumption may not always be true. So, the DEA models with fuzzy data (FDEA models) can more realistically represent real-world problems than the conventional DEA models. In this paper, we assume all inputs, outputs and efficiency measures are triangular fuzzy numbers. So we present a method for obtaining the fuzzy Malmquist productivity index on fuzzy data, and finally, we can determine progress and regression for units with fuzzy data.

In the present world, calculating the efficiency of systems with an internal structure, suchas two-stage systems, is principally imperative. Conventional Data envelopment analysis (DEA) is a non-parametric approach that measures the efficiency of comparable black box systems. There is a weakness in traditional DEA that does not survey the internal structure of systems. Hence, for evaluating the efficiency of the systems with internal structure, Network DEA (NDEA) was presented. Two-stage systems are a special case of network systems. Many procedures were suggested to measure the efficiency of these systems such as slacks-based measure (SBM) approach. In this paper, we will focus on two-stage systems with shared inputs between stages and final output in stage 1 and we shall propose non-cooperative models to calculate the efficiency of these systems based on SBM procedure. Also, we shall indicate the overall efficiency of these systems as the product of the efficiency scores of stages. In the end, to explain the proposed approach, a numerical example will be presented.

The measurement of organizational efficiency has always been discussed by various researchers. Data envelopment analysis, taking the inputs and outputs of the decision-making units into account, makes it possible to calculate the relative efficiency for each unit. Many organizations have a two-stage structure, and their performance in successive periods depends on each other. In evaluating such a structure, partial and periodic efficiency must be calculated. Early models and network and dynamic models are not able to calculate this performance alone. Models of existing dynamic networks are also unable to provide a projection for inefficient units or solve all challenges. In this study, by defining the PPS, an input-oriented dynamic two-stage DEA was developed.  In this model, the optimal value of the intermediate and carryover variables is determined by the next stage and period, and the stages and periods become efficient backward from the last stage of the last period. In addition to the total structure, the model makes efficient all stages and periods and only becomes an efficient unit if it is efficient in all stages and periods. It was also proved that the projection of the unit to be evaluated is partial, periodic, and total efficient. How to use the model to calculate efficiency was expressed by a practical three periodical example.

Ranking of fire stations is one of the most important issues in urban planning and crisis management. Because ranking increases the speed of service in crises. In the real world, the value of some attributes is non-controllable, so planners and decision makers can't change the values in the ranking process and it must be considered in the ranking. The aim of this study is ranking of fire stations candidates in district ten of Tehran municipality and for this, has used non-radial DEA model. The decision matrix consists of eleven alternatives and twelve attributes. The attributes are controllable (that the decision makers able to change values) and non-controllable (that the decision makers unable to change the values). The results show that station 5 is prioritized among the stations and has higher non-controllable attribute values in decision matrix than the others, and it validates the results.

The healthcare organization is a basic factor for any community, as it highly acts on the socioeconomic development of any country. Beginning of coronavirus disease 2019 (COVID-19) was initial reported in December 2019. Until now, many medicines and plans have been used in the cure of the illness. The COVID-19 became a pandemic around the world and has giant effect on our industrial and social systems, particularly on the healthcare system. Data envelopment analysis (DEA) is a powerful nonparametric engineering tool for estimating technical efficiency and production capacity of service units. Therefore, in this study, to examine a relationship between healthcare and bed suitable in the COVID-19 is evaluated using DEA. In the first step, the efficiency values are calculated based on determines the production capacity of hospitals through data envelopment analysis. In the second, incorporates the complexity of needs in two categories for the reallocation of beds throughout the medical specialties. The proposed approach can provide a direction for governments to expand strategies based on a powerful production capacity measure.

Data Envelopment Analysis is a technique based on mathematical planning for specifying the efficiency of decision making units (DMUs). In some cases, manager is not going to add a new resource but to reallocate one of the previous resources. Reallocating a resource may be done for different purposes and has different benefits. For example, without adding a new resource and only using the same resources, is it possible to increase the efficiency of one unit or even increase the efficiency of the whole system? In this paper, a mathematical model is presented that can be used to reallocate one of the previous available resources between units in such a way that the total efficiency of decision-making units reaches the maximum possible value. In this model, in order to prevent excessive reduction of the share of each unit of the desired source, restrictions have been considered. In these constraints, a lower bound for the share of each unit is specified. Also, reallocating a resource is likely to lead some changes in output values of decision-making units. In the presented model, some constraints are considered that specify an upper bound for outputs produced by the units. There are other restrictions in this model. The first is that the total share of units from the desired resource should not exceed the amount available of it and the second is that the total output produced by all units should be at least equal to the total output produced before reallocation. The model presented in this article, in addition to considering the restrictions described, all of which are unavoidable, has been transformed into a linear programming model that can be solved by many existing software.

One of the major concerns in healthcare management is the optimal allocation of staffing and resources. The global crisis created by the COVID-19 Pandemic has created extreme strains both on the staffing and the resources available to the healthcare systems. It has geometrically added to the number of patients seeking health services. In addition, the Pandemic has dramatically increased the rate of mortality in the hospitals in an unprecedented way. Therefore, in this research, in order not to sacrifice the quality of the services provided, we have used Data Envelopment Analysis (DEA) model to determine the efficiency of the emergency departments in the hospitals and the possible improvements that could be made to them. As traditional DEA models do not seek to reduce the undesirable outputs and increase the undesirable inputs, in addition to determining the efficiency of decision making units (DMU) despite some undesirable input components, the effect of these units on performance is investigated. To this end, considering the problem assumptions, first, a set of proper production possibilities is defined. Finally, a new method is introduced to determine the system’s performance in the presence of some undesirable input components. The impact of undesirable components on determining efficiency is specified, and a real example is provided consisting of emergency rooms in 30 hospitals, in which five desirable inputs and four desirable outputs along with one undesirable input are considered. The example is solved using the presented model, and the efficiency scores are determined.

In this paper, we develop the revenue and cost efficiency models based on the FDH model. In the following, we will develop the proposed models for the two-stage network structure and obtain the desired scores of inputs and outputs by considering the input and output prices. An algorithm for measuring the revenue and cost efficiency is presented based on the ratio of inputs and outputs.

Some researchers deals to estimation of some of the influences factors in efficiency score in which the DMU, maintains or improves its current efficiency level. This problems are considered in a general framework which is called inverse DEA. This paper studies the inverse data envelopment analysis. The issue of input or output estimation has been examined with improvement in unit efficiency.Therefore, in this paper, by increasing the level of undesirable inputs and the level of desired outputs of decision-making units along with improvements in the efficiency of the decision-maker, the level of changes in the level of desired inputs and the level of undesirable outputs is estimated. To do this, we consider the data as Interval data and then use the inverse DEA method using a multi-objective linear programming model (MOLP), so that the unit performance under evaluation is improved. The following is an applied example of the proposed method.

Data envelopment analysis (DEA) is used as a handy tool to evaluate a set of decision-making units (DMUs) forming a sustainable supply chain (SSC). Furthermore, the Malmquist Productivity Index (MPI) is used to determine the level of progress or regression in the DMUs. In this paper, we calculate the MPI in a sustainable supply chain using non-radial DEA models. Generally speaking, we are after the sustainability of economic, environmental and social conditions in a supply chain, and the subject of sustainable supply chain is quite important in this respect. Thus, in this paper, MPI is calculated in a sustainable supply chain using the non-radial Enhanced Russell Measure (ERM). Moreover, our applied study involves an evaluation of sustainable supply chains in Iranian oil refineries.

It is necessary to make use of scientific methods when merging the Decision-Making Units (DMUs) in any organization. Tools such as Data Envelopment Analysis (DEA) and network DEA (NDEA) are quite useful for unit mergers in two-stage network processes. In this paper, a two-stage network inverse DEA (InvDEA) process is proposed for the merger of university and bank branches based on linear programming models. It is generally crucial to prioritize the inputs and outputs and find the intermediate vectors in multi-stage networks. Therefore, a two-stage network inverse DEA model is used for the purposes of this study. Finally, some applications of the proposed model are provided in DMU mergers based on vector prioritization using Shannon’s entropy, namely the mergers of 5 universities, 24 insurance companies, and 20 commercial banks.

Data envelopment analysis (DEA) is a body of research methodologies to evaluate overall efficiencies, identify the sources, and estimate the amounts of inefficiencies in inputs and outputs.efficient DMUs all have an efficiency of one, so that for these units no ranking can be given. Since in evaluating by traditional DEA models many DMUs are classified as efficient, a large number of methods for fully ranking both efficient and inefficient DMUs have been proposed. In the last decade, ranking DEA efficient units has become the interests of many DEA researchers and a variety of models (called super-efficiency models) were developed to rank DEA efficient units. Super efficiency data envelopment analysis model can be used in ranking the performance of efficient DMUs. While the models developed in the past are interesting and meaningful, they have the disadvantages of being infeasible or instable occasionally. But the main problem of super-efficient models is lack of differentiation between non- extreme efficient DMUs, so these models cannot rank these DMUs. In this paper, we propose a new method for Ranking Non-extreme Efficient Decision making units in Data Envelopment Analysis based on benchmark. One of the main advantages of our approach is that, this method doesn’t apply any new models, rather this model applies a combination of the well-known models for ranking DMUs. Therefore, understanding our proposed method is easy for readers. One numerical example is examined to illustrate the potential applications of the proposed method.