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

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

Consistent and robust ranking in imprecise data envelopment analysis under perturbations of random subsets of data

Data envelopment analysis (DEA) is a non-parametric method for measuring the relative efficiency of a set of decision making units using multiple precise inputs to produce multiple precise outputs. Several extensions to DEA have been made for the case of imprecise data, as well as to improve the robustness of the assessment for these cases. Prevailing robust DEA (RDEA) models are based on mirrored interval DEA models, including two distinct production possibility sets (PPS). However, this approach renders the distance measures incommensurate and violates the standard assumptions for the interpretation of distance measures as efficiency scores. We propose a modified RDEA (MRDEA) model with a unified PPS to overcome the present problem in RDEA. Based on a flexible formulation for the number of variables perturbed, MRDEA calculates the empirical distribution for the interval efficiency for the case of a random number of variables affected. The MRDEA approach also decreases the computational complexity of the RDEA model, as well as significantly increases the discriminatory power of the model without additional information requirements. The properties of the method are demonstrated for four different numerical instances

An interval efficiency analysis with dual‑role factors

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) is a data-driven and benchmarking tool for evaluating the relative efficiency of production units with multiple outputs and inputs. Conventional DEA models are based on a production system by converting inputs to outputs using input-transformation-output processes. However, in some situations, it is inescapable to think of some assessment factors, referred to as dual-role factors, which can play simultaneously input and output roles in DEA. The observed data are often assumed to be precise although it needs to consider uncertainty as an inherent part of most real-world applications. Dealing with imprecise data is a perpetual challenge in DEA that can be treated by presenting the interval data. This paper develops an imprecise DEA approach with dual-role factors based on revised production possibility sets. The resulting models are a pair of mixed binary linear programming problems that yield the possible relative efficiencies in the form of intervals. In addition, a procedure is presented to assign the optimal designation to a dual-role factor and specify whether the dual-role factor is a nondiscretionary input or output. Given the interval efficiencies, the production units are categorized into the efficient and inefficient sets. Beyond the dichotomized classification, a practical ranking approach is also adopted to achieve incremental discrimination through evaluation analysis. Finally, an application to third-party reverse logistics providers is studied to illustrate the efficacy and applicability of the proposed approach

An extended multiple criteria data envelopment analysis model

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.Several researchers have adapted the data envelopment analysis (DEA) models to deal with two inter-related problems: weak discriminating power and unrealistic weight distribution. The former problem arises as an application of DEA in the situations where decision-makers seek to reach a complete ranking of units, and the latter problem refers to the situations in which basic DEA model simply rates units 100% efficient on account of irrational input and/or output weights and insufficient number of degrees of freedom. Improving discrimination power and yielding more reasonable dispersion of input and output weights simultaneously remain a challenge for DEA and multiple criteria DEA (MCDEA) models. This paper puts emphasis on weight restrictions to boost discriminating power as well as to generate true weight dispersion of MCDEA when a priori information about the weights is not available. To this end, we modify a very recent MCDEA models in the literature by determining an optimum lower bound for input and output weights. The contribution of this paper is sevenfold: first, we show that a larger amount for the lower bound on weights often leads to improving discriminating power and reaching realistic weights in MCDEA models due to imposing more weight restrictions; second, the procedure for sensitivity analysis is designed to define stability for the weights of each evaluation criterion; third, we extend a weighted MCDEA model to three evaluation criteria based on the maximum lower bound for input and output weights; fourth, we develop a super-efficiency model for efficient units under the proposed MCDEA model in this paper; fifth, we extend an epsilon-based minsum BCC-DEA model to proceed our research objectives under variable returns to scale (VRS); sixth, we present a simulation study to statistically analyze weight dispersion and rankings between five different methods in terms of non-parametric tests; and seventh, we demonstrate the applicability of the proposed models with an application to European Union member countries

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