A Mathematical Approach for Technology Selection in the Presence of Slightly Non-homogeneous Technologies

The assumption of classical technology selection models is based on complete homogeneity of technologies. In spite of this assumption in many applications some technologies do not comprehensively consume common inputs to comprehensively supply common outputs. The objective of this paper is to propose a model for selecting slightly non-homogeneous technologies. A numerical example demonstrates the application of the proposed method

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

PRINCIPAL COMPONENT ANALYSIS TO RANKING TECHNICAL EFFICIENCIES THROUGH STOCHASTIC FRONTIER ANALYSIS AND DEA

The Stochastic Frontier Analysis permits evaluating the Technical Efficiency scores for one output variable to obtain the corresponding Technical Efficiency of n Decision-Making Units (DMU). The objective of this work is a comparison between a Stochastic Frontier Analysis, with same input and different output variables, and the Data Envelopment Analysis. You get k Technical Efficiency TE(yi) which are unified by a Principal Component Analysis and compared with the results of a DEA on the same data

A geometrical approach for fuzzy DEA frontiers.

Interval DEA frontiers are here used in situation where one input or output is subject to uncertainty in its measurement and is presented as an interval data. We built an efficient frontier without any assumption about the probability distribution function of the imprecise variable. We take into account only the minimum and the maximum values of each imprecise variable. Two frontiers are constructed: the optimistic and the pessimistic ones. We use fuzszy relationships to introduce a new efficiency index based on a set of some Fuzzy T Norms. We will explore only the case where only on single variable presents a certain degree of uncertainty

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

Supplier's total cost of ownership evaluation: a data envelopment analysis approach

Supplier Total Cost of Ownership (TCO) is a widely-known approach for determining the overall cost generated by a supplier relationship, but its adoption is still limited. The complex calculations involved - and in particular the activity-based costing procedure for computing the cost of managing the relationship - pose a major obstacle to widespread TCO implementation. The purpose of this work is to formulate a Data Envelopment Analysis application (denoted 'TCO-based DEA') that can act as a proxy for TCO, and to test its ability to approximate the results of TCO with less effort. The study is based on the analysis of two categories of suppliers (74 in total) of a medium-sized Italian mechanical engineering company. The results show that TCO-based DEA is able to significantly approximate the outcomes of TCO, for both the efficiency indexes and rankings of suppliers, whilst requiring substantially less effort to perform the analysis. To our knowledge, this is the first study to develop a DEA-based tool for approximating TCO and to test it in a real-world setting. The research shows significant potential within the supply chain management field. In particular, TCO-based DEA can be used for analysing suppliers' performance, rationalising and reducing the supplier base, assisting the negotiation process

Economic efficiency of EMBRAPA’S research centers and the influence of contextual variables

Neste artigo é medida a eficiência econômica dos centros de pesquisa da Empresa Brasileira de Pesquisa Agropecuária (Embrapa). É usado o modelo DEA BCC, cuja medida de eficiência é modelada como função linear das variáveis contextuais capacidade de geração de receita, intensidade de parcerias, melhoria de processos administrativos, racionalização de custos, tamanho e tipo de centro. O modelo é do tipo painel dinâmico, assume correlação intra-temporal estruturada entre os centros de pesquisa e inter-temporal não estruturada. Para desempatar as unidades eficientes é usado um índice heurístico de eficiência que agrega os resultados de eficiência em relação às fronteiras DEA clássica e invertida. O efeito positivo das parcerias na medida de eficiência, invalida as críticas de que o processo de avaliação prejudica a integração e cooperação entre os centros de pesquisa. A melhoria de processos administrativos é a variável mais importante do ponto de vista da significância estatística das variáveis contextuais. _________________________________________________________________________________ ABSTRACTIn this paper we measure, with a DEA BCC model, the economic efficiency of Embrapa’s (Brazilian Agricultural Research Corporation) research centers. We model the DEA economic efficiency as a linear function of the contextual variables revenue generation capacity, partnership intensity, improvement of administrative processes, cost rationalization, size and type of research centers. The model used is of the type dynamic panel and assumes a structured correlation matrix intra times and unstructured inter times. In order to better discriminate the efficient units we used a heuristic efficiency score that aggregates the efficiencies in relation to the original and inverted DEA frontiers. Partnerships positive effect in the efficiency scores does not confirm the thoughts that Embrapa’s performance evaluation process discourages the integration and cooperation of its research centers. From the point of view of statistical significance, the improvement of administrative processes is the most important indicator among the contextual variables

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