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|Authors: ||Mensah, Emmanuel Kwasi|
|Internal Tutor: ||ROCCA, MATTEO|
|Tutor: ||TOLOO, MEHDI|
|Title: ||Robust optimization in data envelopment analysis: extended theory and applications.|
|Abstract: ||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.|
|Keywords: ||Robust optimization, data envelopment analysis (DEA), robust efficiency, duality, RDEA, banking efficiency, robust goal programming|
|Subject MIUR : ||SECS-S/06 METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE|
|Issue Date: ||2019|
|Doctoral course: ||Metodi e modelli per le decisioni economiche|
|Academic cycle: ||31|
|Publisher: ||Università degli Studi dell'Insubria|
|Other information: ||Technical University of Ostrava - Czexh Republic|
|Citation: ||Mensah, E.K.Robust optimization in data envelopment analysis: extended theory and applications. (Doctoral Thesis, Università degli Studi dell'Insubria, 2019).|
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