Data Envelopment Analysis for Target Setting with Imprecise Data

In this thesis, a new aspect of target setting in data envelopment analysis is presented. The existing data envelopment analysis (DEA) target models are defined just for exact data. Considering the importance of imprecise data such as fuzzy, ordinal and interval data in organizations, DEA target models and method are proposed with some advantages over the previous ones, and also defined for imprecise data. The suggested target models for imprecise data are originally non-linear mathematical programming problems, but two proposed methods are used to convert them to the linear ones. The different aspects of target setting in DEA are discussed. By these new approaches, the drawbacks of the existing methods and models defined for target setting process in DEA are rectified. The problems in which the centralized decision makers encountered limited or constant resources for total input consumption or total output production are solved in this thesis. A new DEA target model which solves and deals with such a situation is also established. The relation between the multiple objective linear programming and data envelopment analysis is discussed. The existing models established during the investigation of the relations between the output-oriented dual DEA model and the mini-max reference point formulations are the super-ideal point model, the ideal point model and the shortest distance model. Through these models, the decision maker's preferences will be considered by interactive trade-off analysis procedures in multiple objective linear programming. These models considered only the output-oriented dual DEA model which is a radial model that concentrates the increase in outputs. These models are also improvements to the cases which consider the decrease of total input consumption and the increase of total output production simultaneously which results in solving only one rather than n mathematical programming problems. Numerical illustrations are provided at each chapter of this thesis to show the advantages of the established imprecise target models over the existing ones. Considering the wide application of data envelopment analysis in organizations, one of the established models is applied to the evaluation of efficiency and resource allocation of commercial banks in Malaysia. Finally, the discussions on some approaches in our researches are presented. Future studies and potential improvements are also given to conclude this thesis.

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