Imprecise weights and non-discretionary factors in data envelopment analysis

The aim of this thesis is to investigate and identify the main effect of qualitative and imprecise data, such as knowledge, experience and human judgments, in efficiency evaluation of the real world problems on one hand, and non-discretionary data such as environmental factors in Data Envelopment analysis issues (DEA) on the other hand. In the first part, a fuzzy weighed CCR model is represented to assess decision making units (DMUs) with normal data and fuzzy essence in weights of input and output factors. In this case, incorporation of fuzzy arithmetic and traditional method in DEA is helpful to solve and achieve the interval efficiency scores without additional restrictions for each data which prevents the model from becoming infeasible. The outcome of the model demonstrates the effect of data on the efficiency score. This thesis then offers a non-discretionary fuzzy additive model for cases in efficiency analysis and benchmarking that, decision-maker is confronted with some exogenously fixed data with fuzzy essence. A detailed procedure on a method applying -cut concept is provided to linearize the model with the intention of achieving appropriate benchmarking for inefficient DMUs. In conclusion, the thesis argues that impact of imprecise weights and non-discretionary factors in DEA is essential and requires new modified models. The models offer more informative and persuasive data to assist the manager to be aware of uncertain effects of factors on efficiency score as well as to evaluate and benchmark DMUs with fuzzy nature while non-discretionary factors are taken into account.

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