Robust data envelopment analysis via ellipsoidal uncertainty sets with application to the Italian banking industry

AbstractThis paper extends the conventional DEA models to a robust DEA (RDEA) framework by proposing new models for evaluating the efficiency of a set of homogeneous decision-making units (DMUs) under ellipsoidal uncertainty sets. Four main contributions are made: (1) we propose new RDEA models based on two uncertainty sets: an ellipsoidal set that models unbounded and correlated uncertainties and an interval-based ellipsoidal uncertainty set that models bounded and correlated uncertainties, and study the relationship between the RDEA models of these two sets, (2) we provide a robust classification scheme where DMUs can be classified into fully robust efficient, partially robust efficient and robust inefficient, (3) the proposed models are extended to the additive DEA model and its efficacy is analyzed with two imprecise additive DEA models in the literature, and finally, (4) we apply the proposed models to study the performance of banks in the Italian banking industry. We show that few banks which were resilient in their performance can be robustly classified as partially efficient or fully efficient in an uncertain environment

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

Sustainable R&D portfolio assessment.

Research and development portfolio management is traditionally technologically and financially dominated, with little or no attention to the sustainable focus, which represents the triple bottom line: not only financial (and technical) issues but also human and environmental values. This is mainly due to the lack of quantified and reliable data on the human aspects of product/service development: usability, ecology, ethics, product experience, perceived quality etc. Even if these data are available, then consistent decision support tools are not ready available. Based on the findings from an industry review, we developed a DEA model that permits to support strategic R&D portfolio management. We underscore the usability of this approach with real life examples from two different industries: consumables and materials manufacturing (polymers).R&D portfolio management; Data envelopment analysis; Sustainable R&D;

A novel modified Khatter’s approach for solving Neutrosophic Data Envelopment Analysis

The evaluation of the performance of decision-making units (DMUs) that use comparable inputs to produce related outputs can be accomplished through a non-parametric linear programming (LP) technique called Data Envelopment Analysis (DEA). However, the observed data are occasionally imprecise, ambiguous, inadequate, and inconsistent which may result in incorrect decision-making when these criteria are ignored. Neutrosophic Set (NS) is an extension of fuzzy sets which is used to represent unclear, erroneous, missing, and wrong information. This paper proposes a neutrosophic version of the DEA model, and a novel solution technique for Neutrosophic DEA (Neu-DEA) model. The possibility mean for triangular neutrosophic number (TNN) is redefined and modified the Khatter’s approach to convert directly the Neu-DEA model into its crisp DEA model. As a result, the Neu-DEA model is simplified to a crisp LP problem with a risk parameter (δ ∈ [0, 1]) that represents the attitude of the decision-maker towards taking risk. The efficiency score of the DMUs is computed by using various risk factors and divided into efficient and inefficient groups. The ranking of DMUs is determined by calculating the mean efficiency score of DMUs, which is based on various risk parameters. A numerical example is illustrated here to describe the suggested approach’s flexibility and authenticity and compared with some of the existing approaches

Spin-Off Policy of Sharia Bank: Is It Profitable?

According to Law no. 21 Year 2008, the Sharia Business Unit (SBU) owned by a Conventional Commercial Bank (CCB) is required to separate from its Parent Bank before year 2023. Some Sharia Business Units have initiated a separation step from Conventional Commercial Bank. On the other hand, they are required to keep the level of efficiency in running its business operations. This paper is intended to analyze the efficiency level of Sharia Business Units that have separated from its parent and then compare whether there is difference of efficiency level between before and after separation. The method used is Data Envelopment Analysis (DEA) and Paired Sample t-Test.The results show that based on the total average efficiency of all sharia banks spin off (in this case four sharia banks namely BNI Sharia, BRI Sharia, BJB Sharia and Bukopin Sharia Bank), there occur a decrease in efficiency technically and also pure the technical itself in sharia banks starting from before and after the spin off. This can be read because in the early periods of spin off there was a cost adjustment on the shariah bank spin off. Sharia banks require a 'weaning' from their parents. Nevertheless, there is no statistically significant difference in efficiency levels between before and after the spin off. This should be a booster for other Sharia Business Units to take the decision to spin off immediately, of course, accompanied by careful and prudent planning and implementation

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

A new DEA-GAHP method for supplier selection problem

Supplier selection is one of the most important decisions made in supply chain management. Supplier evaluation problem has been in the center of supply chain researcher’s attention in these years. Managers regard some of these studies and methods inappropriate due to simple, weight scoring methods that generally are based on subjective opinions and judgments of decision maker units involved in the supplier evaluation process yielding imprecise and even unreliable results. This paper seeks to propose a methodology to integrate data envelopment analysis (DEA) and group analytical hierarchy process (GAHP) for evaluating and selecting the most efficient supplier. We develop a methodology, which consists of 6 steps, one by one has been introduced in lecture and finally applicability of proposed method is indicated by assessing 12 suppliers in a numerical example