It is inevitable for a manager to consider the performance effects of each component of a multi-stage financial equity capital. These components serve as inputs in the first stage to raise ...investments. The investments, as outputs of the first stage, become inputs for the second stage and are used in bank services, such as bank facilities, which are outputs of the second stage. Therefore, when evaluating bank performance, the connectivity between the stages must be considered; otherwise, efficiency may not be calculated correctly. Traditional methods often assess multi-stage systems as black boxes, neglecting the potential connectivity that may exist among the stages. We delve into the system and propose models to improve overall efficiency and the efficiency of each stage. Additionally, the continuity and relationships among stages introduce numerous variables and constraints to linear programming for evaluating the entire system. A centralized approach calculates the efficiency score of units simultaneously by solving only one linear programming problem, significantly reducing computational complexity. This approach, especially in large organizations, is commonly employed by central managers. In this paper, we introduce a centralized method for evaluating units with a multi-stage structure. We apply the proposed models to evaluate the efficiencies of bank branches and insurance companies, demonstrating the superiority of the improved network approach and centralized method in enhancing overall system efficiency. Bank branches typically have a two-stage structure, involving labor, physical capital, and other factors.IntroductionBank branches operate under the supervision of a central management team. The central manager, acting as the decision-maker, allocates resources such as labor and financial equity capital as inputs for these branches. The goal is to optimize the overall efficiency of the branches by minimizing the total consumption of resources while maximizing the desired outputs, such as security investments. A common approach to enhancing the performance of banks involves evaluating each branch separately. However, this method does not guarantee the minimization of total resource consumption and can be time-consuming. Since all bank branches are under the control of central management, the decision-maker can optimize the efficiency scores of branches by allocating resources to them simultaneously. This approach, known as centralized Data Envelopment Analysis (DEA), is particularly relevant when certain variables are controlled by a central authority, such as a Head Office, rather than individual unit managers. DEA is a mathematical programming technique used to assess the performance of homogeneous Decision Making Units (DMUs). However, in cases where DMUs have a network structure, such as banks, where the outputs of one division or sub-process serve as inputs for the next sub-process, traditional DEA models treat two-stage DMUs as black boxes and overlook potential connectivity among the stages. In our approach, we consider the internal activities within the system and propose a non-radial model to optimize multi-stage DMUs by taking into account the connectivity among the stages. Furthermore, in previous network DEA models, constraints related to intermediate activities were treated as inequalities, which, as we will demonstrate in this paper, can lead to contradictions in optimality. We address this issue by carefully considering the connectivity among stages. The presence of connectivity among stages introduces numerous variables and constraints to the corresponding model. This model, when used to measure the overall efficiency scores of all DMUs, would traditionally require solving as many problems as there are DMUs, which can be highly time-consuming. In our paper, we introduce a centralized approach that measures the efficiency scores of multi-stage structure DMUs by solving only one linear programming problem. We have applied these proposed models to evaluate bank branches and insurance companies. This approach provides a more comprehensive and efficient way to assess and improve the performance of multi-stage organizations like banks, taking into account the interconnected nature of their operations.MethodologyWe employ the Data Envelopment Analysis approach to evaluate systems with a multi-stage structure, often referred to as a network structure. Traditional DEA models treat two-stage DMUs as black boxes and overlook the potential for connectivity among these stages. In contrast, we delve into the internal activities of the system and propose a model that optimizes multi-stage DMUs by considering the interconnections among the stages. Moreover, in previous models designed to assess network systems, constraints related to intermediate activities were typically treated as inequalities, which could lead to inconsistencies in optimization. In our approach, we enhance these constraints associated with intermediate activities to ensure more robust optimization. Additionally, we apply a centralized approach to allocate resources to DMUs, allowing for the simultaneous optimization of the efficiency scores of all DMUs through the solution of a single linear programming problem. This centralized method streamlines resource allocation and improves the overall efficiency of the DMUs.ResultsWe evaluated 20 bank branches, treating them as 20 DMUs with a two-stage structure. In the first stage, inputs included paid interest, personnel costs, paid interest related to foreign currency transactions, and personnel costs related to foreign currency transactions. The first stage produced intermediate outputs in the form of raised funds and raised funds related to foreign currency transactions. In the second stage, the outputs consisted of loans and common incomes. Notably, some loans in the second stage might become non-performing, where borrowers are unable to make full or even partial repayments. To address this, we considered non-performing loans as undesirable or bad outputs and transformed them into inverse values to treat them as good outputs. To calculate the efficiency scores of the bank branches, we employed both our improved network model and the traditional DEA approach. Our network-based method revealed that many of the bank branches under evaluation were inefficient, in contrast to the traditional method, which inaccurately identified many of the bank branches as efficient. Subsequently, we extended our network method to a centralized case, significantly reducing computation time. The network-based assessment of bank branches took nearly 5 seconds, whereas solving the centralized model required only 0.1 second. In addition to evaluating bank branches, we applied our methods to assess insurance companies. The results demonstrated that our model provided more accurate efficiency scores compared to previous network-based approaches.ConclusionIn multi-stage production systems, the production process comprises several stages. Banks, for example, operate with a network structure in which labor, physical capital, and financial equity capital serve as inputs in the first stage to generate deposits as intermediate outputs. In the second stage, these banks utilize the deposits obtained from the first stage to create loans and security investments. We have introduced models to assess the efficiency of each stage, whether it's the first, intermediate, or final stage, individually. Additionally, we have developed a non-radial SBM model designed for evaluating DMUs with multi-stage structures. The Centralized DEA approach is a valuable method for central managers, particularly in large organizations like bank branches, to allocate resources effectively. We have extended our network-based method to a centralized approach, allowing us to calculate efficiency scores by solving just one linear programming problem. The results obtained from applying our proposed models to evaluate bank branches and insurance companies, both exhibiting network structures as DMUs, demonstrate the superiority of the network centralized approach over previous models.
Traditional DEA models deal with measurements of relative efficiency of DMUs regarding multiple-inputs vs. multiple-outputs. One of the drawbacks of these models is the neglect of intermediate ...products or linking activities. After pointing out needs for inclusion of them to DEA models, we propose a slacks-based network DEA model, called Network SBM, that can deal with intermediate products formally. Using this model we can evaluate divisional efficiencies along with the overall efficiency of decision making units (DMUs).
In data envelopment analysis, there are several methods for measuring efficiency changes over time, e.g. the window analysis and the Malmquist index. However, they usually neglect carry-over ...activities between two consecutive terms and only focus on the separate time period independently aiming local optimization in a single period, even if these models can take into account the time change effect. In the actual business world, a long time planning and investment is a subject of great concern. For these cases, single period optimization model is not suitable for performance evaluation. To cope with long time point of view, the dynamic DEA model incorporates carry-over activities into the model and enables us to measure period specific efficiency based on the long time optimization during the whole period. Dynamic DEA model proposed by Färe and Grosskopf is the first innovative contribution for such purpose. In this paper we develop their model in the slacks-based measure (SBM) framework, called dynamic SBM (DSBM). The SBM model is non-radial and can deal with inputs/outputs individually, contrary to the radial approaches that assume proportional changes in inputs/outputs. Furthermore, according to the characteristics of carry-overs, we classify them into four categories, i.e. desirable, undesirable, free and fixed. Desirable carry-overs correspond, for example, to profit carried forward and net earned surplus carried to the next term, while undesirable carry-overs include, for example, loss carried forward, bad debt and dead stock. Free and fixed carry-overs indicate, respectively, discretionary and non-discretionary ones. We develop dynamic SBM models that can evaluate the overall efficiency of decision making units for the whole terms as well as the term efficiencies.
•We investigate the factors in influencing the variations in overall efficiency of additive network DEA approach.•Variation in overall efficiency can be associated with constant stage ...efficiencies.•We examine relation of overall efficiency to the stage efficiencies and weights.•We propose a new of overall efficiency to reflect entirely on the stage efficiencies.
Data envelopment analysis (DEA) is a technique for performance evaluation of peer decision making units (DMUs). The network DEA models study the internal structures of DMUs. Using two-stage network structures as an example, the current paper examines additive efficiency decomposition where the overall efficiency is defined as a weighted average of stage efficiencies and the weights are used to reflect relative importance of individual stages. We show that weights may not affect the calculation of stage efficiency scores and that variation in the overall efficiency resulting from using different weights can be associated with constant stage efficiencies. We demonstrate the need to isolate the impact of weights on the overall efficiency. We propose to use a new overall efficiency index to address some pitfalls in weighted additive efficiency decomposition. Our findings are illustrated using two empirical data sets representing two types of two-stage network structures.
Incorporating undesirable outputs in the operational assessments through the integration of Life Cycle Assessment (LCA) and Data Envelopment Analysis (DEA) has received great attention recently. ...There are many studies throughout literature that apply various methods to integrate LCA and DEA. In this case study, the six most common approaches were employed to assess the winter wheat cropping system in Poland. These six methods were: a) ignoring undesirable outputs, b) treating undesirables as inputs to the DEA model, c) data transformation, d) impact rate, e) ratio model, and f) slack based measurement DEA with undesirable outputs. The environmental impact of wheat production was assessed by determining its carbon footprint (CF). The mean CF equalled 0.45 kg CO2eq per kg wheat grain (ranging from 0.25 to 0.67). According to the model comparison results, a slack based measurement DEA with undesirable outputs could better reflect the performance of undesirable outputs, and was selected as the most appropriate method to maximize the efficiency of winter wheat production while minimizing undesirable outputs. The advantage of applying the slack based model with undesirable outputs was that the targets presented by this model were based on existing efficient farms, as opposed to theoretical results; thus achieving these targets are feasible. The average efficiency score equalled 0.43, whereby few farms were classified as efficient farms. The results of the proposed integrated model showed a high reduction potential for mineral fertilizers (up to 595 kg ha−1 y−1), seed (up to 37 kg ha−1 y−1), and fuel (up to 75 L ha−1 y−1) in winter wheat farms. These results help farmers to obtain a realistic and reliable usage pattern for inputs in a winter wheat production system, whereby the greatest production can be achieved in conjunction with the lowest possible environmental impact.
•The aim was integration of Life Cycle Assessment and Data Envelopment Analysis.•six approaches were tested for efficiency assessment of winter wheat cropping system.•The most appropriate method was a slack based measurement DEA.•The mean carbon footprint was 0.45 kg CO2eq per kg of wheat grain.•High reduction potential for mineral fertilizers, seed, and fuel was reported.
The main aim of this review article is to review of DEA models in regarding to energy efficiency. This paper reviewed and summarized the different models of DEA that have been applied around the ...world to development of energy efficiency problems. Consequently, a review of 144 published scholarly papers appearing in 45 high-ranking journals between 2006 and 2015 have been obtained to achieve a comprehensive review of DEA application in energy efficiency. Accordingly, the selected articles have been categorized based on year of publication; author (s) nationalities, scope of study, time duration, application area, study purpose, results and outcomes. Results of this review paper indicated that DEA showed great promise to be a good evaluative tool for future analysis on energy efficiency issues, where the production function between the inputs and outputs was virtually absent or extremely difficult to acquire.
•A new robust counterpart optimisation with nonnegative decision variables is proposed.•The new robust model is used to propose a new robust DEA model.•A case study of 250 banks in Europe validates ...our new approach.•The proposed robust DEA model reduces 50% of the required computational burden.
Robust optimization has become the state-of-the-art approach for solving linear optimization problems with uncertain data. Though relatively young, the robust approach has proven to be essential in many real-world applications. Under this approach, robust counterparts to prescribed uncertainty sets are constructed for general solutions to corresponding uncertain linear programming problems. It is remarkable that in most practical problems, the variables represent physical quantities and must be nonnegative. In this paper, we propose alternative robust counterparts with nonnegative decision variables – a reduced robust approach which attempts to minimize model complexity. The new framework is extended to the robust Data Envelopment Analysis (DEA) with the aim of reducing the computational burden. In the DEA methodology, first we deal with the equality in the normalization constraint and then a robust DEA based on the reduced robust counterpart is proposed. The proposed model is examined with numerical data from 250 European banks operating across the globe. The results indicate that the proposed approach (i) reduces almost 50% of the computational burden required to solve DEA problems with nonnegative decision variables; (ii) retains only essential (non-redundant) constraints and decision variables without alerting the optimal value.
Frequent droughts have caused severe disaster losses in China. Such events can be minimized by enhancing the country's resilience and reducing its vulnerability, where this can ensure socioeconomic ...stability and sustainable development. Evaluating the vulnerability and resilience to drought is thus crucial for effectively managing the risk of disasters and promoting sustainable socioeconomic development. In this study, we constructed a comprehensive framework to assess the spatiotemporal characteristics of China's vulnerability and resilience to drought at the provincial scale from an input-output perspective by using the Super-efficiency Data Envelopment Analysis (DEA) model and the Super-efficiency Slacks-Based Measure DEA (SBM-DEA) model. This study focused on drought drivers, the disaster-forming environment, drought bearers, disaster intensity, and recovery. The results showed that the vulnerability to drought of 42 % of China's provinces decreased from 2010 to 2022, that of only 29 % of the provinces increased, while the status of a majority of provinces improved in general. The center of gravity of the vulnerability to drought moved toward the southwest over time and a spatial clustering of vulnerability was observed, with High-High clusters moving from the north to the south. Moreover, the resilience to drought declined in 36 % of provinces and increased in only 20 %, reflecting poor resilience overall. The center of gravity of China's overall resilience to drought moved northward, with a relatively stable spatial pattern and prominent clusters of Low-Low resilience indicating a pressing need for improvement. Areas with high vulnerability and low resilience were concentrated in inland western and eastern regions, and this highlights the importance of drought prevention and mitigation in provinces like Xinjiang, Inner Mongolia, Jiangxi, and Fujian. The findings here provide valuable insights for mitigating the risk of drought and promoting sustainable socioeconomic development.
Display omitted
•An assessment framework for drought vulnerability and resilience is proposed.•China's drought vulnerability has improved and resilience needs to be strengthened.•The high-risk areas for drought are in western inland and eastern China.•The DEA model-based assessment framework is portable and efficient to use.
•We define a fuzzy multi-objective multi-period network Data Envelopment Analysis model.•The model is applied to evaluate the dynamic efficiency of several Iranian oil refineries.•Their enhancement ...of the environmental scope of the production process is also measured.•The performance of oil refineries is evaluated in the presence of undesirable outputs.•A real-life case study illustrates the efficacy and applicability of the proposed method.
We define a fuzzy multi-objective multi-period network DEA model customized to evaluate the dynamic performance of oil refineries in the presence of undesirable outputs. In particular, we use a standard fuzzy operator to define the efficiency levels so as to integrate multiple objectives and periods of time within a unique maximization framework. Managers and decision makers are provided with a model characterized by its operational simplicity that allows for the straightforward implementation of standard spreadsheet software. The model is applied to a real-life case study, where the capacity of refineries to optimize their performance through the refining process is analyzed together with the introduction of value-added products that preserve and enhance the environmental dimensions of the refining process. The inclusion of a real-life case study aims at illustrating the efficacy and applicability of the proposed method relative to those of more conventional models. Moreover, the range of the time period covered allows us to analyze the evolution of efficiency beyond the standard two-period Malmquist framework generally considered in the literature dealing with the behavior of refineries.
One of the most powerful and applicable tools to evaluate the efficiency of decision making units (DMUs) is data envelopment analysis (DEA). In order to evaluate the efficiency of multi-division ...DMUs, it is essential to pay attention to the internal or linking activities among their different divisions, and also, we have presented a model of DEA, due to uncertainty in some input and output indexes of units, which beside paying attention to internal or linking activities, the data have been entered into the model in a fuzzy form. The suggested model is a slacks-based measure (SBM) model which deals with evaluating the efficiency of DMUs. At the end, a case study on the Iran regional power companies using the suggested model is presented. Mean whilst the proposed model is compared with other existing models and the results prove its advantages as well as the validity of our model.
•We developed a new fuzzy network DEA model.•Due to uncertainty in some inputs and outputs, those are presented in fuzzy form.•The new model is applied on a case study of Iran’s regional electricity companies.
PDF
