An evaluation of cross-efficiency methods: With an application to warehouse performance

Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a selection of methods popular in the literature. These methods are applied to performance measurement of European warehouses. We develop a cross-efficiency method based on a rank-order DEA model to accommodate the ordinal nature of some key variables characterizing warehouse performance. This is one of the first comparisons of methods on a real-life dataset and the first time that a model allowing for qualitative variables is included in such a comparison. Our results show that the choice of model matters, as one obtains statistically different rankings from each one of them. This holds in particular for the multiplicative and game-theoretic methods whose results diverge from the classic method. From a managerial perspective, focused on the applicability of the methods, we evaluate them through a multidimensional metric which considers their capability to rank DMUs, their ease of implementation, and their robustness to sensitivity analyses. We conclude that standard weight-restriction methods, as initiated by Sexton et al. [48], perform as well as recently introduced, more sophisticated alternativesSpanish Ministry of Science and Innovation (Ministerio de Ciencia e Innovación), the State Research Agency (Agencia Estatal de Investigación) and the European Regional Development Fund (Fondo Europeo de Desarrollo Regional) under grants EIN2020-11226

Robustness analysis based on weight restrictions in data envelopment analysis

Includes bibliographical references.Evaluating the performance of organisations is essential to good planning and control. Part of this process is monitoring the performance of organisations against their goals. The comparative efficiency of organizations using common inputs and outputs makes it possible for organizations to improve their performance so that can operate as the most efficient organizations. Resources and outputs can be very diversified in nature and it is complex to assess organizations using such resources and outputs. Data Envelopment Analysis models are designed to facilitate this of assessment and aim to evaluate the relative efficiency of organisations. Chapter 2 is dedicated to the basic Data Envelopment Analysis. We present the following: * A review of the Data Envelopment Analysis models; * The properties and particularities of each model. In chapter 3, we present our literature survey on restrictions. Data Envelopment Analysis is a value-free frontier which has the of yielding more objective efficiency measures. However, the complete freedom in the determination of weights for the factors and products) relevant to the assessment of organisations has led to some problems such as: zero-weights and lack of discrimination between efficient organizations. Weight restriction methods were introduced in order to tackle these problems. The first part of chapter 3 in detail the motivations for weight restrictions while the second part presents the actual weight restriction rnethods

Evaluating cost and profit efficiency: a comparison of parametric and nonparametric methodologies

The objective of this article is 2-fold. First, it provides an empirical assessment of the cost and profit stochastic frontiers based on a panel dataset of Greek commercial banks over the period 1993 to 2005. Second, on the basis of the same sample, it also compares the most widely used parametric and nonparametric techniques to cost efficiency measurement, namely, the Stochastic Frontier Approach and Data EnvelopmentAnalysis. The results suggest greater similarities between the predictions of cost and profit efficiency methods than between parametric and nonparametric techniques. Such evidence is new in the literature and calls for a more technically level playing field for estimating bank efficiency.Bank cost and profit efficiency; Parametric and non-parametric methods

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

Eficiencia y persistencia de los fondos de retorno absolutos españoles

URL del artículo en la web de la Revista: https://www.upo.es/revistas/index.php/RevMetCuant/article/view/2703Performance measurement is an area of crucial interest in asset valuation and investment management. High volatility as well as time aggregation of returns, amongst other characteristics, may distort the results of conventional measures of performance. In this work, we study the performance of 115 Spanish Absolute Return Funds in the period 2010-2015, using the Sharpe, Treynor, Jensen and Modified Sharpe ratios. We then apply Data Envelopment Analysis to classify the funds in order to avoid the problems arising from the non-normality of their returns, since non-gaussian returns do not pose a problem in Data Envelopment Analysis implementation. In addition, we apply the Malkiel, Brown and Goetzman test and the Rude and Khan test in annual periods to determine the existence of persistence. Finally, we study the relationship between efficiency and persistence in order to determine the relationship between both measures and to support decision-making processes. The results show a significant relationship between cross efficiency and Modified Sharpe ratios as well as the existence of persistence for annual periods. Nevertheless, the results do not allow concluding any relationship amongst efficiency and persistence.La medida de la performance es un área de crucial interés en la valoración de activos y selección de inversiones. Elevadas volatilidades, así como la agregación temporal de rendimientos, entre otras características, pueden distorsionar los resultados de las medidas convencionales de performance. En este trabajo, estudiamos la performance de 115 fondos de retorno absoluto españoles en el periodo 2010¿2015 usando los ratios de Sharpe, Treynor y Jensen y el ratio de Sharpe modificado. Posteriormente, para clasificar los fondos se aplica el Análisis Envolvente de Datos (Data Envelopment Analysis, DEA) en aras de evitar los problemas derivados de la no normalidad de los rendimientos, dado que rendimientos no gaussianos no suponen un problema a la hora de implementar el Análisis Envolvente de Datos. Adicionalmente, se aplica el test de Malkiel, Brown y Goetzman y el test de Rude y Khan en periodos anuales para determinar la existencia de persistencia. Finalmente. se estudia la relación entre eficiencia y persistencia con objeto de determinar la relación entre ambas medidas y apoyar el proceso de toma de decisiones. Los resultados muestran una significativa relación entre eficiencia cruzada y el ratio de Sharpe modificado así como la existencia de persistencia en periodos anuales. No obstante, los resultados no permiten concluir en ninguna relación directa entre eficiencia y persistencia.Universidad Pablo de Olavid

Relative efficiency measurement in the public sector with data envelopment analysis

PhDTraditional efficiency measures have two significant drawbacks. Firstly, they fail to recognise that output is the result of all inputs operating in combination; thus output per head is a misleading indicator of intrinsic labour productivity. Secondly, they have often been defined in terms of average levels of performance in least squares production functions. In practice, average performance norms may institutionalise some level of inefficiency. The first of these problems may be overcome in a total-factor view of efficiency. This implies the extension of traditional ratio measures to include all inputs and outputs simultaneously. The second requires the comparison of performance with frontier possibilities. Both of these improvements are embodied in Data Envelopment Analysis (DEA). Two applications of DEA are undertaken on U. K. public sector data. The first of these defines frontier efficiency in local education authorities (LEAs). It develops an 8 variable model with 3 outputs (based on exam pass rates) and 5 inputs. Four of the inputs are uncontrollable background variables allowing for differences in student catchment area; the fifth, teaching expenditure, is under LEA control and can be targeted. The results suggest that 44 authorities are best-practice and at the remainder spending per pupil could have been reduced by an average of 6.8%. These results are replicated on smaller clusters of LEAs to examine the sensitivity of DEA to the size of the performance comparison. The clustering procedure produces marked effects on targets, peer groups and the efficiency status of certain authorities. A second case study investigates the performance of a sample of 33 prisons with a high remand population. The model separately identifies the effects of remand prisoners on costs, and includes separate variables to reflect the levels of overcrowding and offences. In 1984/85 the combined budget of these prisons was overspent by 4.6% vis a vis best-practice costs. Using an alternative constant returns technology this overspend rises to 13.1%. Two aspects of DEA targets are explored. A model of Leibenstein's inert area suggests reasons for the persistence of inefficiency and hence that targets may be unattainable without coercion. Secondly, the literature has justified the recommendation of DEA targets in their being Pareto efficient. This interpretation is disputed and an alternative DEA-Dominance criterion is proposed as a more appropriate basis for targeting

Multi-Dimensional Assessment of Transit System Efficiency and Incentive-based Subsidy Allocation

Over the past several decades, contending with traffic congestion and air pollution has emerged as one of the imperative issues across the world. Development of a transit-oriented urban transport system has been realized by an increasing number of countries and administrations as one of the most effective strategies for mitigating congestion and pollution problems. Despite the rapid development of public transportation system, doubts regarding the efficiency of the system and financing sustainability have arisen. Significant amount of public resources have been invested into public transport; however complaints about low service quality and unreliable transit system performance have increasingly arisen from all walks of life. Evaluating transit operational efficiency from various levels and designing incentive-based mechanisms to allocate limited subsidies/resources have become one of the most imperative challenges faced by responsible authorities to sustain the public transport system development and improve its performance and levels of service. After a comprehensive review of existing literature, this dissertation aims to develop a multi-dimensional framework composed of a series of robust multi-criteria evaluation models to assess the operational and financial performance of transit systems at various levels of application (i.e. region/city level, operator level, and route level). It further contributes to bridging the gap between transit efficiency evaluation and the subsequent subsidy allocation by developing a set of incentive-based resource allocation models taking various levels of operational and financial efficiencies into consideration. Case studies using real-world transit data will be performed to validate the performance and applicability of the proposed models

Robust optimization in data envelopment analysis: extended theory and applications.

Performance evaluation of decision-making units (DMUs) via the data envelopment analysis (DEA) is confronted with multi-conflicting objectives, complex alternatives and significant uncertainties. Visualizing the risk of uncertainties in the data used in the evaluation process is crucial to understanding the need for cutting edge solution techniques to organizational decisions. A greater management concern is to have techniques and practical models that can evaluate their operations and make decisions that are not only optimal but also consistent with the changing environment. Motivated by the myriad need to mitigate the risk of uncertainties in performance evaluations, this thesis focuses on finding robust and flexible evaluation strategies to the ranking and classification of DMUs. It studies performance measurement with the DEA tool and addresses the uncertainties in data via the robust optimization technique. The thesis develops new models in robust data envelopment analysis with applications to management science, which are pursued in four research thrust. In the first thrust, a robust counterpart optimization with nonnegative decision variables is proposed which is then used to formulate new budget of uncertainty-based robust DEA models. The proposed model is shown to save the computational cost for robust optimization solutions to operations research problems involving only positive decision variables. The second research thrust studies the duality relations of models within the worst-case and best-case approach in the input \u2013 output orientation framework. A key contribution is the design of a classification scheme that utilizes the conservativeness and the risk preference of the decision maker. In the third thrust, a new robust DEA model based on ellipsoidal uncertainty sets is proposed which is further extended to the additive model and compared with imprecise additive models. The final thrust study the modelling techniques including goal programming, robust optimization and data envelopment to a transportation problem where the concern is on the efficiency of the transport network, uncertainties in the demand and supply of goods and a compromising solution to multiple conflicting objectives of the decision maker. Several numerical examples and real-world applications are made to explore and demonstrate the applicability of the developed models and their essence to management decisions. Applications such as the robust evaluation of banking efficiency in Europe and in particular Germany and Italy are made. Considering the proposed models and their applications, efficiency analysis explored in this research will correspond to the practical framework of industrial and organizational decision making and will further advance the course of robust management decisions

Robust optimization in data envelopment analysis: extended theory and applications.

Performance evaluation of decision-making units (DMUs) via the data envelopment analysis (DEA) is confronted with multi-conflicting objectives, complex alternatives and significant uncertainties. Visualizing the risk of uncertainties in the data used in the evaluation process is crucial to understanding the need for cutting edge solution techniques to organizational decisions. A greater management concern is to have techniques and practical models that can evaluate their operations and make decisions that are not only optimal but also consistent with the changing environment. Motivated by the myriad need to mitigate the risk of uncertainties in performance evaluations, this thesis focuses on finding robust and flexible evaluation strategies to the ranking and classification of DMUs. It studies performance measurement with the DEA tool and addresses the uncertainties in data via the robust optimization technique. The thesis develops new models in robust data envelopment analysis with applications to management science, which are pursued in four research thrust. In the first thrust, a robust counterpart optimization with nonnegative decision variables is proposed which is then used to formulate new budget of uncertainty-based robust DEA models. The proposed model is shown to save the computational cost for robust optimization solutions to operations research problems involving only positive decision variables. The second research thrust studies the duality relations of models within the worst-case and best-case approach in the input – output orientation framework. A key contribution is the design of a classification scheme that utilizes the conservativeness and the risk preference of the decision maker. In the third thrust, a new robust DEA model based on ellipsoidal uncertainty sets is proposed which is further extended to the additive model and compared with imprecise additive models. The final thrust study the modelling techniques including goal programming, robust optimization and data envelopment to a transportation problem where the concern is on the efficiency of the transport network, uncertainties in the demand and supply of goods and a compromising solution to multiple conflicting objectives of the decision maker. Several numerical examples and real-world applications are made to explore and demonstrate the applicability of the developed models and their essence to management decisions. Applications such as the robust evaluation of banking efficiency in Europe and in particular Germany and Italy are made. Considering the proposed models and their applications, efficiency analysis explored in this research will correspond to the practical framework of industrial and organizational decision making and will further advance the course of robust management decisions