Multiobjective centralized DEA approach to Tokyo 2020 Olympic Games

"Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License...."There exist two types of Data Envelopment Analysis (DEA) approaches to the Olympic Games: conventional and fixed-sum outputs (FSO). The approach proposed in this paper belongs to the latter category as it takes into account the total number de medals of each type awarded. Imposing these constraints requires a centralized DEA perspective that projects all the countries simultaneously. In this paper, a multiobjective FSO approach is proposed, and the Weighted Tchebychef solution method is employed. This approach aims to set all output targets as close as possible to their ideal values. In order to choose between the alternative optima, a secondary goal has been considered that minimizes the sum of absolute changes in the number of medals, which also renders the computed targets to be as close to the observed values as possible. These targets represent the output levels that could be expected if all countries performed at their best level. For certain countries, the targets are higher than the actual number of medals won while, for other countries, these targets may be lower. The proposed approach has been applied to the results of the Tokyo 2020 Olympic Games and compared with both FSO and non-FSO DEA method

Determining the Optimal Carbon Tax Rate based on Data Envelopment Analysis

Carbon tax policy is widely used to control greenhouse gases and how to determine a suitable carbon tax rate is very important for policy makers considering the trade-off between environmental protection and economic development. In an industry regulated by carbon tax policy, we consider two competing firms who sell ordinary products and green products respectively. In order to promote the firm who sells ordinary product to reduce carbon emissions, the government of China imposes carbon tax on the ordinary products. For the government, three objectives are considered when it makes carbon tax policy. They are increasing the government revenue, reducing the government expenditure and decreasing the carbon emissions. For the firms, it is important to explore their pricing strategies taken into account of the government tax policy. To find an optimal carbon tax rate and to achieve the three objectives simultaneously, we consider this as a multiple criteria decision-making problem. Hence, we propose to use a centralized data envelopment analysis (DEA) approach to solve it. We find that when one firm produces ordinary products and the other produces green products, the government may set a high tax rate. While when both firms sell ordinary products, the optimal tax policy for each firm is different and the government may impose a higher tax rate for one firm and a lower tax rate for the other firm

Centralized DEA approach to assess efficiency scores of bank branches with foreign exchange transactions

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

A Review of DEA-based Resource and Cost Allocation models: Implications for services

Data envelopment analysis (DEA), by its design, was not intended for resource allocation but for measuring relative efficiency of decision-making units. Despite this, many researchers have successfully applied this modelling technique to a variety of resource and cost allocation decisions in order to improve operational efficiencies. This paper is a comprehensive review and classification of such articles. The papers were classified by industry and by DEA model-orientation. The findings of this paper show that existing models predominately apply DEA to mass service industries (e.g., banking), thus, revealing the opportunity for researchers to further develop DEA-based resource allocation modelling toward improving the operational efficiencies of other service industries (e.g., professional services). To guide researchers to this end, we offer a discussion of the use of DEA modelling when the service provider and the customer are both resources needing to be allocated, in other words, using DEA to model professional or co-created services

Ein DEA-basierter Ansatz zur Messung der Performance bei zentralisierten Managementstrukturen

Traditional performance measurement approaches are usually characterized by a number of different limitations. Among other things, these approaches require the subjective determination of weights to aggregate a set of indicators to an overall performance score. Furthermore, traditional approaches are usually not able to incorporate additional improvement potentials that can be received from a centralized management. A performance measurement framework which can overcome these limitations is called data envelopment analysis (DEA). Against this background, this thesis provides a thorough overview of how different degrees of centralization are modeled in the current DEA literature. The systematic literature review identified 135 different approaches that assume a centralized or partially centralized management structure. A concluding discussion of the respective DEA approaches showed two fundamental research gaps. In response to this, this thesis has two fundamental objectives: The first objective is to propose a DEA-based performance measurement approach for measuring performance changes over time. The second objective is to develop another DEA-based approach for comparing the performance of management groups. In contrast to so far developed DEA-models, the here proposed approaches explicitly incorporate the respective management structure. Both DEA approaches thus developed are based on the combination of the metafrontier concept and the Malmquist index. The first approach evaluates productivity changes of operating entities over time and, hence, may indicate potential sources for performance changes. Thereby, the proposed approach preserves the individual characteristics of each local group technology. The second DEA approach proposed here uses the Malmquist index for comparing the performance of management groups. This index accounts for the existence of a central decision maker who can, e.g., undertake resource reallocations to improve the overall performance of its managed group. The applicability and usefulness of both proposed approaches is empirically shown with real-world data from KONE Corporation.Traditionelle Performance Measurement Ansätze gehen mit einer Reihe von Herausforderungen einher. So erfordert die Aggregation unterschiedlicher Kennzahlen zu einem einzelnen Performancemaß die Verwendung von subjektiven Gewichtungen. Darüber hinaus lassen sich in traditionellen Ansätzen nur schwer etwaige Verbesserungspotentiale modellieren, die aus zentralisierten Managementstrukturen resultieren. Eine betriebswirtschaftliche Methode, welche die genannten Limitationen nicht aufweist, ist die Data Envelopment Analysis (DEA). Aufgrund dieser Vorteile wird in dieser Arbeit zunächst ein umfassender Literaturüberblick erarbeitet, wie unterschiedliche Managementstrukturen in einer DEA modelliert werden können. Mithilfe der Literaturrecherche wurden insgesamt 135 unterschiedliche Ansätze ermittelt, die entweder ein vollkommen zentralisiertes oder teilweise zentralisiertes Managementmodell unterstellen. Eine abschließende Diskussion der verschiedenen DEA-Ansätze zeigte allerdings eine Forschungslücke, woraus die beiden folgenden Forschungsziele für diese Arbeit abgeleitet wurden: Einerseits soll ein DEA-basierter Ansatz erarbeitet werden, der zur Messung von Effizienzveränderungen einzelner Produktiveinheiten über die Zeit geeignet ist. Andererseits soll eine DEA-basierte Methode entwickelt werden, welche bei Performancevergleichen zwischen Managementgruppen anwendbar ist. Im Gegensatz zu den bisher in der Literatur diskutierten Ansätzen sollten die entwickelten Methoden dabei die jeweils vorliegende Managementstruktur berücksichtigen. Die entwickelten DEA-Ansätze basieren auf der Kombination des Metafrontier-Konzepts mit dem Malmquist-Index. Der erste Ansatz erlaubt es, Performanceveränderungen von einzelnen Produktiveinheiten über mehrere Zeitperioden zu messen. Im Gegensatz zu konventionellen Metafrontier-basierten Malmquist-Indizes berücksichtigt der vorgeschlagene Ansatz die individuellen Eigenschaften der lokalen Produktionstechnologien. Der zweite vorgeschlagene DEA-Ansatz nutzt den Malmquist-Index für den Vergleich der Performance von Managementgruppen. Der Index berücksichtigt dabei explizit, dass eine zentrale Entscheidungsinstanz existiert, welche Ressourcenumverteilungen durchführen kann. Beide Ansätze werden anhand eines Datensatzes des Unternehmens KONE illustriert

Evaluación y rediseño de la red pública educativa. Un análisis centralizado

La eficiencia escolar constituye un tema de interés. El número de publicaciones en este campo de investigación se ha incrementado en los últimos años, al intentar explicar qué características del centro y del entorno influyen en los resultados de los alumnos. A la luz de la Post-New Public Management, el objetivo del trabajo es la evaluación y rediseño, a través de técnicas frontera, de una muestra de centros de la red educativa pública de Catalunya. Los resultados obtenidos indican que sería posible mejorar la red y redistribuir de forma óptima los recursos educativos. También se aporta información útil para la toma de decisiones y la puesta en marcha de programas de mejora en los centros docentes

Centralised resource allocation using Lexicographic Goal Programming. Application to the Spanish public university system

Identificador de proyecto: FEDER-UPO UPO-1380624This paper deals with Data Envelopment Analysis (DEA) in centralised settings in which the operating units belong to the same organisation. In such a scenario, a global system-wide perspective may be adopted as regards resource allocation and target setting. In this paper, a new Lexicographic Goal Programming (lexGP) approach is proposed using three priority levels: the aggregated input consumption and output production goals; the input and output goals of the individual operating units; and the technical efficiency of the computed targets. It is assumed that the goals for the overall organisation are established by the Central Decision-Maker (CDM) and that they are consistent with those of the individual operating units. The proposed approach has been applied to the Spanish public university system, comprising 47 institutions. Given the CDM preferences in terms of input and output aggregate goals and relative importance weights, specific technical efficient targets have been computed for each university. The results show that the proposed approach is more suitable than the non-centralised DEA approach and produces targets that are more effective than other centralised resource allocation approaches in the sense that they are much closer to both the aggregate goals of the CDM and the specific goals of each university.Universidad de Sevill

Stochastic performance measurement in two-stage network processes: A data envelopment analysis approach

summary:In classic data envelopment analysis models, two-stage network structures are studied in cases in which the input/output data set are deterministic. In many real applications, however, we face uncertainty. This paper proposes a two-stage network DEA model when the input/output data are stochastic. A stochastic two-stage network DEA model is formulated based on the chance-constrained programming. Linearization techniques and the assumption of single underlying factor of the data are used to construct the equivalent deterministic linear programming model. The relationship between the stochastic efficiency of each stage and stochastic centralized efficiency of the whole process, at different confidence levels, is discussed. To illustrate the real applicability of the proposed approach, a real case on 16 commercial banks in China is given

A Scenario-based Model for Resource Allocation with Price Information

In this paper, we consider the problem of allocating resources among Decision Making Units (DMUs). Regarding the concept of overall (cost) efficiency, we consider three different scenarios and formulate three Resource Allocation (RA) models correspondingly. In the first scenario, we assume that overall efficiency of each unit remains unchanged. The second scenario is related to the case where none of overall efficiency scores is deteriorated. We improve the overall efficiencies by a pre-determined percentage in the last scenario. We formulate Linear Programming problems to allocate resources in all scenarios. All three scenarios are illustrated through numerical and empirical examples

Cost Constrained Industry Inefficiency

In this paper a definition of industry inefficiency in cost constrained production environments is introduced. This definition uses the indirect directional distance function and quantifies the inefficiency of the industry in terms of the overall output loss, given the industry cost budget. The industry inefficiency indicator is then decomposed into sources components: reallocation inefficiency arising from sub-optimal configuration of the industry; firm inefficiency arising from a failure to select optimal input quantities (given the prevalent inputs prices); firm inefficiency due to lack of best practices. The method is illustrated using data on Ontario electricity distributors. These data show that lack of best practices is only a minor component of the overall inefficiency of the industry (less than 10 percent), with reallocation inefficiency accounting for more than 75 percent of the overall inefficiency of the system. An analysis based on counter-factual input prices is conducted in order to illustrate how the model can be used to estimate the effects of a change in the regulation regime