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

Livro de atas do XVI Congresso da Associação Portuguesa de Investigação Operacional

Fundação para a Ciência e Tecnologia - FC

Efficiency and frontier analysis with extension to strategic planning.

Whatever the economic entity, firm, industry, or nation, intensified worldwide competition has increased the need for effective competitive strategies and renders more pressing the need for methods to analyze swelling volumes of information prior to making any decision. A successful strategy is the equivalent of an efficient production plan, allowing a player to operate on the frontier of its feasible achievements. In practice however, such frontiers are not known and have to be estimated empirically. Locating an empirical frontier is at the core of Data Envelopment Analysis (DEA), a mathematical programming technique developed by Charnes, Cooper et al. in 1978 to evaluate the relative performance of decision-making units (DMUs). Several models have since emerged, all aiming at the identification of which of n DMUs, each characterized by s outputs and m, determine an envelopment surface. DEA therefore represents a methodological opportunity for the strategy field. The viability of DEA rests on its ability to foster sound economic decisions and the economic principles embedded in DEA performance evaluations must be clearly enunciated. The overall purpose of this research is hence twofold: (1) the integration of DEA with production theory via the concepts of efficiency; (2) the formalization of DEA as a tool for strategic planning. This dissertation develops a new measure of efficiency that is shown to be superior to existing measures in terms of the number of properties it satisfies and also with respect to the economic interpretation it affords. A unifying perspective of DEA models is offered by means of a taxonomy which affords systematic connections between the various models and production theory, hence providing a consistent interpretation of all models and their limitations. A new model, called the Frontier model, is developed which strengthens the bridge between DEA and economics and addresses the measurement of economic efficiency. All developments are supported by numerical illustrations. Finally a new model, the Comparative Advantage model, is developed that adapts the methodology of DEA to identify a DMU\u27s competitors and derive information regarding the DMU\u27s comparative strengths and weaknesses to assist the unit in formulating its strategy. An application to regional economics using Census of Manufactures data is presented

A computationally efficient procedure for data envelopment analysis.

This thesis is the final outcome of a project carried out for the UK's Department for Education and Skills (DfES). They were interested in finding a fast algorithm for solving a Data Envelopment Analysis (DEA) model to compare the relative efficiency of 13216 primary schools in England based on 9 input-output factors. The standard approach for solving a DEA model comparing n units (such as primary schools) based on m factors, requires solving 2n linear programming (LP) problems, each with m constraints and at least n variables. At m = 9 and n = 13216, it was proving to be difficult. The research reported in this thesis describes both theoretical and practical contributions to achieving faster computational performance. First we establish that in analysing any unit t only against some critically important units - we call them generators - we can either (a) complete its efficiency analysis, or (b) find a new generator. This is an important contribution to the theory of solution procedures of DEA. It leads to our new Generator Based Algorithm (GBA) which solves only n LPs of maximum size (m x k), where k is the number of generators. As k is a small percentage of n, GBA significantly improves computational performance in large datasets. Further, GBA is capable of solving all the commonly used DEA models including important extensions of the basic models such as weight restricted models. In broad outline, the thesis describes four themes. First, it provides a comprehensive critical review of the extant literature on the computational aspects of DEA. Second, the thesis introduces the new computationally efficient algorithm GBA. It solves the practical problem in 105 seconds. The commercial software used by the DfES, at best, took more than an hour and often took 3 to 5 hours making it impractical for model development work. Third, the thesis presents results of comprehensive computational tests involving GBA, Jose Dula's BuildHull - the best available DEA algorithm in the literature - and the standard approach. Dula's published result showing that BuildHull consistently outperforms the standard approach is confirmed by our experiments. It is also shown that GBA is consistently better than BuildHull and is a viable tool for solving large scale DBA problems. An interesting by-product of this work is a new closed-form solution to the important practical problem of finding strictly positive factor weights without explicit weight restrictions for what are known in the DEA literature as "extreme-efficient units". To date, the only other methods for achieving this require solving additional LPs or a pair of Mixed Integer Linear Programs