جستجوی مقالات مرتبط با کلیدواژه "Data Envelopment Analysis" در نشریات گروه "ریاضی"

Although data envelopment analysis models are able to divide decision-making units (DMUs) into efficient and inefficient sets, choosing the best efficient unit has always been a challenge in decision-making issues. Also, various methods have been introduced to find the most efficient unit, most of which are based on solving linear and nonlinear problems, and also according to the related logic, different units are found as the most efficient unit. The relationship between the most efficient and the extreme efficient units has not been discussed yet. In this paper, we show that each extreme efficient unit can be taken as the most efficient one and vice versa. As a result, the properties of an extreme efficient unit are the same as the most efficient ones. Therefore, since the ways of finding extreme efficient units are simpler, we can utilize these methods to find the most efficient DMU.  We also show how to use the proposed method on a popular example used in most studies.

Big Data Envelopment Analysis (Big DEA) and Cross-Efficiency (CE) evaluation are two important topics in Data Envelopment Analysis (DEA).However, it should be noted the CE evaluation can be computationally intensive, particularly when dealing with large data sets or a large number of DMUs. In this research, we propose a numerical approach to CE evaluation that can be applied to data sets of any size and has a reasonable run-time. Additionally, we suggest a complementary method to find the set of efficient units, which is a crucial component of most Big DEA algorithms. To test the proposed methods, we simulated large data sets with different scenarios involving varying numbers of units, inputs, and outputs. We found that the proposed numerical method was successful in CE evaluation and approximating the efficiency of DEA-efficiency with a high degree of confidence for data with dimensions less than five, regardless of the number of units. However, for data with dimensions greater than five to ten, its ability to find the set of efficient units decreased proportionally. This was compensated by the complementary method.

In data envelopment analysis, identifying the most efficient decision-making unit (DMU) is crucial for gaining insights into efficient DMUs. Various approaches have been suggested in the literature to determine the most efficient DMU in data envelopment analysis. These approaches aim to develop a model with enhanced discriminatory ability among DMUs. This study introduces a new model based on a common set of weights approach using mixed integer linear programming to select the most efficient DMU. The proposed model ensures that the efficiency score of only one DMU (the most efficient) is strictly greater than one, while the efficiency scores of other DMUs are less than or equal to one. This model demonstrates a strong discriminatory capability, enabling the full ranking of all DMUs with fewer constraints than models that allow complete ranking. To validate the proposed model and compare its performance with recent approaches, two numerical examples from the literature are utilized.

Data envelopment analysis (DEA) is a non-parametric tool for evaluating the relative efficiency of comparable entities referred to as Decision Making Units (DMUs). Conventional DEA models treat systems as black box and do not consider their internal structure. Network data envelopment analysis (NDEA) is a prominent method for assessing the efficiency of network systems based on radial and non-radial approaches. The special case of network systems are two-stage systems. Many real practices have two-stage structure where is divided into two processes. Conventional NDEA calculates the efficiency of these systems in presence of crisp data. But in real life applications, the observed values of data are often uncertain. In this paper, for the first time, a new non-radial approach (based on slack based measure) is introduced, which evaluates the efficiency of two-stage systems in the presence of triangular fuzzy numbers(TFNs) using cut technique and optimistic and pessimistic procedures. The properties of the suggested models will also be examined. Finally, a numerical example will be provided to illustrate the proposed models.

The data envelopment analysis (DEA), as a nonparametric method in operational research, is used to measure the efficiency of a set of homogeneous decision-making units (DMU) with the help of linear programming. Up to now, this method has been extended to be used in various fields. For example, cross-efficiency evaluation, as a ranking technique, has been developed to address the challenges of traditional models. Moreover, the Fuzzy Data Envelopment Analysis (FDEA) and the Network Data Envelopment Analysis (NDEA) have been proposed to be used in terms of imprecise data and systems with internal processes, respectively. The existing models do not work when a decision maker tries to measure the efficiency under all these conditions, and thus there is a need for a unified model that considers all these conditions. In the present study, we present several models to measure the fuzzy cross efficiency of a general two-stage system. The aim of this study is to use the proposed models in the banking industry. In this regard, a case study is conducted to rank the branches of one of Iranian banks. Finally, we compare the results derived using the proposed models.

In many production systems, we can do acquisition and merge operations process to increase productivity. For this purpose, we can use the inverse data envelopment analysis (DEA) approach. In many cases, in addition to producing desirable outputs, we also have the simultaneous production of undesirable outputs. It is important to use a suitable approach in the acquisition and merge operations process. In this paper, we present a new model based on the directed distance function. The new model provides a new unit or a pre-determined target efficiency level by merging two decision-making units (DMUs). Based on this model, level for desirable and undesirable outputs is determined for the newly created unit. In the following, we will show the provided approach with a numerical example and apply it for real world data.

One of the common concerns of investors is determining the suitable field for investment. Due to the attractiveness of online sales in various fields such as clothing, newcomers and even existing companies tend usually to sell online. In this research, the rank of the suitability of an investment for online sales in different fields of clothing in Shiraz City was determined using the data envelopment analysis method. In the beginning, we form an expert team. Also, we recognized ten fields of clothing as investment alternatives for online sales (DMUs). Then, we defined suitable inputs and outputs by reviewing the literature and obtaining the opinions of expert team members. Also, we determine an epsilon-based input-oriented BCC model as a suitable DEA model for DMU ranking. Then, we obtained the input and output values from the expert team members and considered the average values as the inputs and outputs of the DEA models. Formulating and solving epsilon-based input-oriented BCC models showed that three DMUs were inefficient, and the other seven DMUs were efficient. Therefore, the rank of these three DMUs was determined. Next, to determine the rank of the other seven DMUs, we formed and solved the Andersen-Peterson epsilon-based input-oriented BCC models. The results of solving the DEA models showed that the fields of "Designing, producing, and selling of wedding dresses", "Designing, producing, and selling suits and formal dresses", and "Designing, producing, or selling local clothing" have the first to third ranks, respectively.

Deprivation and elimination of deprivation from different regions of the country to achieve sustainable development is one of the important issues in Iran. Therefore, the country's budget structure needs to be reformed. The purpose of this research is to evaluate the special view of the Islamic Consultative Assembly towards deprived areas in the amendment of the plan for eliminating deprivation, Note 14 of the budget law of the year 1401, using Data Envelopment Analysis (DEA) method. Since the decision-making units are the provinces of Iran, we have used the output-oriented CCR model to determine the efficiency of design modification, and then we have ranked it with the MAJ model. We have also determined important indicators in the allocation of credit to eliminate deprivation in provinces by using the AHP approach. Therefore, it is suggested that the note of this table should be deleted based on the text presented in a double-urgency plan agreed upon by main factions of the Parliament, and its credit should be distributed according to valid deprivation indicators. As well as this, we suggest that the requirements of each region should be met based on the latest statistics and relevant information.

Performance measurement is always considered one of the most important tasks of managers. Hence, management knowledge is measurement knowledge and if we cannot measure something, we certainly cannot control it and consequently we cannot manage it. In this paper, we examine data envelopment analysis models for improving inefficient units. In this study, 20 bank branches in Tehran were selected and mathematical models were presented for estimating inputs with interval data. The findings of this research highlight the importance of integrating advanced analytical tools like DEA into management practices. By quantifying inefficiencies and offering clear pathways for improvement, DEA empowers managers to make data-driven decisions that enhance overall performance. This approach is particularly valuable in competitive environments, such as the banking sector, where efficiency and service quality directly impact customer satisfaction and profitability.

Productivity, a crucial aspect of economics, refers to the efficient use of resources to maximize output. In today’s world, enhancing productivity is vital for economic growth and competitiveness in global markets. Improvements in productivity lead to cost reductions, increased profitability, and better quality of products and services. This study analyzes changes in total factor productivity by examining data from 20 manufacturing companies in the construction sector listed on the stock exchange. It aligns with the country’s Fifth Development Plan and uses the Malmquist Index as the primary tool for measuring productivity. The Malmquist Index assesses technical and scale efficiency to identify productivity changes over time. The investigation covers the period from 2010 to 2013, reflecting various economic and market conditions. The findings can help managers and policymakers pinpoint strengths and weaknesses in production processes, offering strategies to enhance productivity and efficiency in the construction industry. Additionally, these results provide valuable insights for researchers and practitioners interested in productivity and efficiency. Given the importance of the topic, this article contributes to understanding the factors affecting productivity in manufacturing and aids in developing strategies to improve the country’s economic performance.

Finding units with the most productive scale size (MPSS) is very important. The use of MPSS in ranking is thus the main idea in this paper. We propose an algorithm in DEA that ranks all extreme and non-extreme efficient DMUs in a number of steps. In this method, units with the most productive scale size are identified in each step and are then ranked. We finally show the application of the method using a numerical example.

In traditional Data Envelopment Analysis (DEA) approaches, inputs and outputs are usually considered as exact and real values. The relative efficiency of the Decision Making Units (DMUs) is evaluated and it is known that the factors are inputs and/or outputs. However, there are some conditions under which the efficiency of DMUs should be calculated while the data are integer and ambiguous. Therefore, various integer DEA models have been proposed to determine the performance of DMUs when integer data and fuzzy factors are available. In addition, there are cases where the efficiency of DMUs should be determined when integer data and flexible factors are available. Therefore, some integer DEA methods have been proposed to calculate the performance of DMUs and specify the role of flexible measures when some of the data are integer and flexible factors are available. However, there are some situations where there are integer data, fuzzy integer measures and flexible factors. Therefore, this paper sheds light on the nature of the model to determine the efficiency of DMUs when there are integer inputs and/or outputs, flexible factors and fuzzy integer measures, and determines the role of factors with uncertain inputs or outputs. In fact, slacks are addressed and a slack-based efficiency measure (SBM) is defined to compute the performance of DMUs in the presence of flexible factors, integer data and fuzzy integer measures. The proposed approaches are demonstrated and illustrated using an example.

In order to improve the performance of inefficient decision-making units (DMU), it is important to find an efficient target. This target determines the amount of changes in inputs and outputs; by applying these changes, efficiency is achieved. The usual models in DEA always considered the problem of improving inefficient DMU and in this regard, they present a target as an efficient DMU. But in action, for some DMUs achieving that target in one step is difficult and even impossible. For this reason, finding intermediate target is very important. In this way, instead of an inefficient DMU becoming efficient in one step, this work is done in several steps and in this case the improvement is obtained gradually. In this paper, the efficiency of DMUs is evaluated using the CCR model, and then a sequence of intermediate targets is provided for each inefficient DMU. Moving in this direction will reduce the inefficiency of these DMUs.

The efficiency score of the decision making units (DMUs) depends on the input and output values. The efficiency score of the DMU in the presence of undesirable outputs is greater or equal to the efficiency score of this DMU in the absence of undesirable outputs. To face this problem, we present a new ratio based data envelopment analysis (DEA-R) model to measure the effects of undesirable outputs on the efficiency of production units. In this regard, we first introduce the counterpart (hypothetical) units corresponding to the original DMUs. These units use the same amount of input to produce the same desirable outputs as the original DMUs, but produce a small amount of undesirable outputs compared to the original units. In the following, we use non-radial DEA-R models based on slacks corresponding to all the ratios of input components to desirable output and the ratios of undesirable output to desirable output to measure efficiency in the presence of undesirable outputs. Also, let's use the efficiency ratio of the main units to their corresponding counterpart units as a reduction factor to show the impact of undesirable outputs. To show the validity of the proposed approach, we evaluate the performance of thirty paper mills and present the results.

Traditional cost models ignore the internal structure of decision-making units (DMUs), so, may produce ambiguous outcomes and provide a biased assessment. In this paper, we evaluate the performance of the units by considering their internal structures. We proposed a new cost Malmquist index for measuring the cost productivity change of the units with bi-level structures. The bi-level structure is a special case of hierarchical structures with two levels, where the leader unit is positioned at the upper level and followers are located at the lower level. The overall system of bi-level units tries to use inputs and produce outputs in a cost-efficient way. However, each subunit performs according to its goals and limited resources. This research tries to develop a bi-level cost model that is suitable for measuring the cost efficiency of bi-level units. Based on this model, a new cost Malmquist index (CMI) is suggested to evaluate the productivity changes of bi-level units. This index presents a new aspect of CMI and provides the productivity changes of units by considering the impact of the leader's and the subunits' performance. In addition, similar to the traditional CMI, it decomposes into various components, such as cost efficiency changes and cost technological changes. The developed CMI is applied to a real-world case study to evaluate eight management regions which all together manage 198 branches. The results show that the proposed CMI provides a more meaningful evaluation of DMUs compared to the conventional CMI.

This research aims to develop data envelopment analysis (DEA) for predicting the supply chain sustainability of the concrete industry using stochastic variables. In the first phase, the mines and companies that organized the four supply chains of the Guilan concrete industry based on competitive elements were identified. After that, based on economic, social, and environmental indexes, the sustainability of the supply chains was chosen using the Fuzzy Delphi model and input and output of mines and concrete companies, which include controllable, uncontrollable, and undesirable inputs and outputs. Finally, data envelopment analysis was used to measure the supply chain sustainability of the concrete industry employing crisp data and a linear model. The errors were entered into the model with a stochastic element based on the probability of the errors. In other words, according to stochastic data envelopment analysis, all input and output data were considered randomly. The output data shows that none of the four supply chains of the Guilan concrete industry is sustainable.

  In the traditional data envelopment analysis (DEA) models, the role of measures from input and output aspects is known. However, in many cases, we face a situation where some measures can play the role of input or output. The role of these measures is determined as input or output with the aim of maximizing the efficiency of the decision making unit (DMU) under evaluation. In this paper, we present a novel inverse DEA model to classify these inputs and outputs. We determine the new level of inputs and outputs and flexible measures by choosing the target efficiency for the DMUs. In this regard, the new model may choose flexible measures as input or output, but the main goal is to reach the target efficiency level. In the following, we will illustrate the presented approach with a simple numerical example. Finally, a numerical real example propose in the banking industry in Indonesia to clarify and demonstrate the suggested approach. We also bring the results of the models.

In this paper, we evaluate the performance of decision-making units (DMUs) in semi-additive production technology in the presence of production trade-offs. We introduce the semi-additive production technology. The semi-additive technology is based on all the DMUs observed and the set of aggregated DMUs corresponding to these DMUs in data envelopment analysis (DEA). We obtain production trade-offs on input and output components in the production process in semi-additive technology. We present a single-stage model to measure efficiency in the presence of production trade-offs in semi-additive production technology. This model also identifies inefficiencies in all input and output components. We show an application of the presented model in the banking industry and at the end we bring the results of the paper.

This Evaluation of fuzzy networks with imprecise data is crucial. In this article, we propose fuzzy two-stage network models based on the structure of central resource allocation models. Firstly, we obtain the target for the fuzzy decision-making units in the two-stage network by using central resource allocation models, with a maximum of one two-phase model in each stage of the network. Then, we determine the overall target for the network. The probability function approach is used in the two-stage fuzzy network models to rephrase the proposed models and find the target. In conclusion, we calculate the target for Iranian airlines using fuzzy data and the proposed model.

The primary models in data envelopment analysis (DEA), consider the inputs and outputs of the decision-making units (DMUs) as non-negative. However, in the real world, we face many cases where the data is negative. In this paper, we investigate the inverse DEA models to estimate the optimal level of inputs and outputs of DMUs based on target efficiency scores. We also assume that some input and output components are negative. In this way, we propose three different models in variable returns to scale (VRS) to determine optimal levels. In order to solve each model, we determine the counterpart DMU corresponding to the DMUs under evaluation. This DMU is obtain based on the additive model, and then we get the level of the target and the observed outputs corresponding to the DMU under evaluation to determine which of these three models to use to measure the efficiency of the DMU under evaluation. We apply the proposed approach with a numerical example and consider it to measure the optimal levels of inputs and outputs of bank branches. Also we propose the results of paper.