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The aim of this paper is to present an original approach for ranking of DEA-efficient DMUs based on the cross efficiency and analytic hierarchy process (AHP) methods. The approach includes two basic stages. In the first stage using DEA models the cross efficiency value of each DEA-efficiency DMU is specified. In the second stage, the pairwise comparison matrix generated in the first stage is utilized to rank scale of the units via the one-step process of AHP. The advantage of this proposed method is its capability of ranking extreme and nonextreme DEA-efficient DMUs. The numerical examples are presented in this paper and we compare our approach with some other approaches.

Data envelopment analysis (DEA) is a technique to measure the performance of decision-making units (DMUs). Conventional DEA treats DMUs as black boxes and the internal structure of DMUs is ignored. Two-stage DEA models are special case network DEA models that explore the internal structures of DMUs. Most often, one output cannot be produced by certain input data and/or the data may be expressed as ratio output/input. In these cases, traditional two-stage DEA models can no longer be used. To deal with these situations, we applied DEA-Ratio (DEA-R) to evaluate two-stage DMUs instead of traditional DEA. To this end, we developed two novel DEA-R models, namely, range directional DEA-R (RDD-R) and (weighted) Tchebycheff norm DEA-R (TND-R). The validity and reliability of our proposed approaches are shown by some examples. The Taiwanese non-life insurance companies are revisited using these proposed approaches and the results from the proposed methods are compared with those from some other methods.

The calculation of the overall profit Malmquist productivity index (MPI) requires precise and accurate information on the input, output, input-output prices of each decision making unit (DMU). However, in many situations, some inputs and/or outputs and input-output prices are imprecise. As such, we consider the overall profit MPI problem when the input, output, and input-output prices are imprecise and vary over intervals, showing that method (MCM 54: 2827-2838, 2011) has some shortfalls. To remedy these shortfalls, we propose another method for measuring the overall profit MPI when the inputs, outputs, and price vectors vary over intervals. That is, to calculate the overall profit efficiency intervals, cone-ratio data envelopment analysis models can be applied to the incorporated information as weight restrictions. Further, we provide a new approach to calculating the upper bound of the overall profit efficiency of each DMU. A numerical example is provided for illustrating the proposed method.

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