Projections onto Efficient Frontiers: Theoretical and Computational Extensions to DEA

Data Envelopment Analysis (DEA) has been widely studied in the literature since its inception in 1978 and is a key analytical technique used in Wharton's performance analysis for retail delivery systems. The methodology behind the classical DEA, the oriented method, is to hold inputs (outputs) constant and to determine how much of an improvement in the output (input) dimensions is necessary in order to become efficient. The authors extend this methodology in two substantive ways. First, a method is developed that determines the shortest projection from an inefficient DMU to the efficient frontier in both the input and output space simultaneously, and second, introduces the notion of the "observable" frontier and its subsequent projection. The observable frontier is the portion of the frontier that has been experienced by other DMUs, and thus the projection onto this portion of the frontier guarantees a recommendation that has already been demonstrated by an existing DMU or a convex combination of existing DMUs. A numerical example is used to illustrate the importance of these two methodological extensions.

The role of multiplier bounds in fuzzy data envelopment analysis

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The non-Archimedean epsilon ε is commonly considered as a lower bound for the dual input weights and output weights in multiplier data envelopment analysis (DEA) models. The amount of ε can be effectively used to differentiate between strongly and weakly efficient decision making units (DMUs). The problem of weak dominance particularly occurs when the reference set is fully or partially defined in terms of fuzzy numbers. In this paper, we propose a new four-step fuzzy DEA method to re-shape weakly efficient frontiers along with revisiting the efficiency score of DMUs in terms of perturbing the weakly efficient frontier. This approach eliminates the non-zero slacks in fuzzy DEA while keeping the strongly efficient frontiers unaltered. In comparing our proposed algorithm to an existing method in the recent literature we show three important flaws in their approach that our method addresses. Finally, we present a numerical example in banking with a combination of crisp and fuzzy data to illustrate the efficacy and advantages of the proposed approach

Data Envelopment Analysis, Endogeneity and the Quality Frontier for Public Services

Applying Data Envelopment Analysis (DEA) to real-world public policy issues can raise many interesting complications beyond those considered in standard models of DEA. One of these complications arises if the funding levels of public service providers, and their ability to attract and retain clients and able staff, depend upon the quality of the output which they produce. This dependency introduces additional inter-relationships between inputs and outputs beyond the uni-directional Production Possibility Frontier (PPF) relationship considered by standard DEA models. The paper therefore analyses the multiplier effects which can be generated by these additional relationships, in which key resource inputs become endogenous variables subject to the external environmental variables which the public service provider faces across these different relationships. The magnitude of these multiplier effects can be captured by focusing DEA on the estimation of an Achievement Possibility Frontier, which reveals the wider set of opportunities which are available to a public service provider to improve its own output quality than that revealed by the estimation of the PPF associated with standard models of DEA. In doing so, the paper enables DEA to be still applied, but in modified form, to the estimation of the scope for improved output of any given public service provider in the presence of such resource endogeneity

Measuring hospital efficiency using DEA an investigation into the relationship between scale and efficiency within the South African private hospital environment

Includes abstract.Includes bibliographical references.This paper investigates the relationship between scale and efficiency through the application of Data Envelopment Analysis (DEA) to a set of South African private hospitals over the three year period from 2007 to 2009. As part of the investigation, this paper provides a description of the current research into scale and efficiency with a focus on definition and measurement. It also provides an introduction to DEA as a tool for measuring the relationship between hospital scale and efficiency. Based on the underlying set of private hospitals, this investigation found that scale efficiency improvements are likely to be possible

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

The Administrative Efficiency of Hospitals and the Effect of Electronic Data Interchange: A Critical Evaluation of the Stochastic Frontier and the Data Envelopment Analysis Models to Efficiency Measurement

The investigation and measurement of administrative efficiency is an issue of great concern for health care policy decision makers and has important implications for the efficiency of the overall health care sector itself as well as for the cost containment efforts and the restructuring of the health care system. The administrative cost efficiency of the United States health care system has received much attention during the last years, and has been under continuous criticism since it became widely known that the country\u27s administrative costs are higher than those of any other country in the world. As criticism on administrative inefficiency of the U.S. health care system has intensified, the need for detailed empirical studies has become imperative. To answer the question of administrative efficiency, this study undertakes an empirical investigation of the largest component of the health care sector; the hospital sector. The variety of proposed health care reform proposals that involve the reduction of administrative costs of hospitals consider the application of Electronic Data Interchange as the potential mechanism towards streamlined administration, cost efficiency and cost containment. Efficiency is the main concern of all economic sectors and a variety of models have been developed to examine every aspect of it. In this dissertation, the two leading approaches to efficiency measurement (Stochastic Frontier and Data Envelopment Analysis) are used and compared. To increase the reliability and comparability of estimates, a variety of models are estimated. In addition, an integrated model that incorporates the characteristics of the Stochastic Frontier with Data Envelopment Analysis techniques is developed. The model provides a new approach for incorporating Technologically Consistent information into DEA in the form of weight restrictions. In this integrated framework the extent of administrative efficiency of hospitals is evaluated. In a second stage analysis, the determinants of inefficient performance are assessed with special attention to the effect of Electronic Data Interchange. The results support the common belief that hospital administration is inefficient. Hospital administration appears to be the most significant determinant of hospital inefficiency. Furthermore, the results indicate that Electronic Data Interchange could be used as a mechanism of reducing administrative inefficiency

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