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

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

Chance-constrained cost efficiency in data envelopment analysis model with random inputs and outputs

Data envelopment analysis (DEA) is a well-known non-parametric technique primarily used to estimate radial efficiency under a set of mild assumptions regarding the production possibility set and the production function. The technical efficiency measure can be complemented with a consistent radial metrics for cost, revenue and profit efficiency in DEA, but only for the setting with known input and output prices. In many real applications of performance measurement, such as the evaluation of utilities, banks and supply chain operations, the input and/or output data are often stochastic and linked to exogenous random variables. It is known from standard results in stochastic programming that rankings of stochastic functions are biased if expected values are used for key parameters. In this paper, we propose economic efficiency measures for stochastic data with known input and output prices. We transform the stochastic economic efficiency models into a deterministic equivalent non-linear form that can be simplified to a deterministic programming with quadratic constraints. An application for a cost minimizing planning problem of a state government in the US is presented to illustrate the applicability of the proposed framework

Smart Growth Principles Combined with Fuzzy AHP and DEA Approach to the Transit-oriented Development (TOD) Planning in Urban Transportation Systems

The research for a land use and transportation planning has always been an important study area among the urban planning field. Since the 20th century, automobiles had become the main media as the transportation vehicle. However, the automobile-oriented development (AOD) also caused the sever urban sprawl problem during the past years. In order to reduce the problems of urban sprawl, the Smart Growth concepts have been proposed and applied to transportation planning process. In recent years, with the up to date sustainable development concept, the transit-oriented development (TOD) model has become one of the novel transport planning strategies utilized to improve the urban environment by means of Smart Growth principles. This study tries to integrate smart growth principles into the urban transportation planning development strategies and utilize objective scientific method to the empirical study. This study will include the following sections. First of all, we try to study and classify the category of smart growth principles based on literature review. Followed by applying fuzzy Delphi technique (FDT) to obtain individual expert’s opinions and to screen the most important criteria of proposed principles in our research. And then the empirical study of Taipei Metro Transit System will be demonstrated to show the application of our proposed methodology. Finally, the utilization of data envelopment analysis (DEA) model combined with assurance region analysis will be applied to select the most suitable MRT stations as the suggested strategies for public sectors. Keywords: Smart Growth, Transit-oriented Development (TOD), Fuzzy Delphi Technique (FDT), Data Envelopment Analysis (DEA

Measurement of Returns-to-Scale using Interval Data Envelopment Analysis Models

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 linkThe economic concept of Returns-to-Scale (RTS) has been intensively studied in the context of Data Envelopment Analysis (DEA). The conventional DEA models that are used for RTS classification require well-defined and accurate data whereas in reality observations gathered from production systems may be characterized by intervals. For instance, the heat losses of the combined production of heat and power (CHP) systems may be within a certain range, hinging on a wide variety of factors such as external temperature and real-time energy demand. Enriching the current literature independently tackling the two problems; interval data and RTS estimation; we develop an overarching evaluation process for estimating RTS of Decision Making Units (DMUs) in Imprecise DEA (IDEA) where the input and output data lie within bounded intervals. In the presence of interval data, we introduce six types of RTS involving increasing, decreasing, constant, non-increasing, non-decreasing and variable RTS. The situation for non-increasing (non-decreasing) RTS is then divided into two partitions; constant or decreasing (constant or increasing) RTS using sensitivity analysis. Additionally, the situation for variable RTS is split into three partitions consisting of constant, decreasing and increasing RTS using sensitivity analysis. Besides, we present the stability region of an observation while preserving its current RTS classification using the optimal values of a set of proposed DEA-based models. The applicability and efficacy of the developed approach is finally studied through two numerical examples and a case study

Fuzzy clustering of homogeneous decision making units with common weights in data envelopment analysis

Data Envelopment Analysis (DEA) is the most popular mathematical approach to assess efficiency of decision-making units (DMUs). In complex organizations, DMUs face a heterogeneous condition regarding environmental factors which affect their efficiencies. When there are a large number of objects, non-homogeneity of DMUs significantly influences their efficiency scores that leads to unfair ranking of DMUs. The aim of this study is to deal with non-homogeneous DMUs by implementing a clustering technique for further efficiency analysis. This paper proposes a common set of weights (CSW) model with ideal point method to develop an identical weight vector for all DMUs. This study proposes a framework to measuring efficiency of complex organizations, such as banks, that have several operational styles or various objectives. The proposed framework helps managers and decision makers (1) to identify environmental components influencing the efficiency of DMUs, (2) to use a fuzzy equivalence relation approach proposed here to cluster the DMUs to homogenized groups, (3) to produce a common set of weights (CSWs) for all DMUs with the model developed here that considers fuzzy data within each cluster, and finally (4) to calculate the efficiency score and overall ranking of DMUs within each cluster

The Use of AR-IDEA Approach for Supplier Selection Problems

Abstract: To select the best suppliers in the presence of both cardinal and ordinal data and considering weight restrictions, this paper proposes a method, which is based on Assurance RegionImprecise Data Envelopment Analysis (AR-IDEA). A numerical example demonstrates the application of the proposed method

Efficiency Evaluation in Two-stage Data Envelopment Analysis under a Fuzzy Environment: A Common-Weights Approach

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.Data envelopment analysis (DEA) has been genuinely known as an impeccable technique for efficiency measurement. In practice, since many production systems such as broadcasting companies, banking and R&D activities include two processes connected in series, we have need of utilizing two-stage DEA models to identify the sources of inefficiency and explore in turn appropriate options for improving performance. The lack of the ability to generate the actual weights is not only an ongoing challenge in traditional DEA models, it can have serious repercussion for the contemporary DEA models (e.g., two-stage DEA). This paper presents a common-weights method for two-stage structures that allows us to consider equality of opportunity in a fuzzy environment when evaluating the system efficiency and the component process efficiencies. The proposed approach first seeks upper bounds on factor weights and then determines a set of common weights by a single linear programming problem. We illustrate the approach with a data set taken from the literature

Life settlement pricing with fuzzy parameters

Existing literature asserts that the growth of life settlement (LS) markets, where they exist, is hampered by limited policyholder participation and suggests that to foster this growth appropriate pricing of LS transactions is crucial. The pricing of LSs relies on quantifying two key variables: the insured's mortality multiplier and the internal rate of return (IRR). However, the available information on these parameters is often scarce and vague. To address this issue, this article proposes a novel framework that models these variables using triangular fuzzy numbers (TFNs). This modelling approach aligns with how mortality multiplier and IRR data are typically provided in insurance markets and has the advantage of offering a natural interpretation for practitioners. When both the mortality multiplier and the IRR are represented as TFNs, the resulting LS price becomes a FN that no longer retains the triangular shape. Therefore, the paper introduces three alternative triangular approximations to simplify computations and enhance interpretation of the price. Additionally, six criteria are proposed to evaluate the effectiveness of each approximation method. These criteria go beyond the typical approach of assessing the approximation quality to the FN itself. They also consider the usability and comprehensibility for financial analysts with no prior knowledge of FNs. In summary, the framework presented in this paper represents a significant advancement in LS pricing. By incorporating TFNs, offering several triangular approximations and proposing goodness criteria of them, it addresses the challenges posed by limited and vague data, while also considering the practical needs of industry practitioners