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Efficiency measurement has been an essential topic in banking research. Many studies have used the data envelopment analysis approach as an effective tool for the efficiency measurement of bank branches. Recently, the Network (NDEA) method has been introduced, which involves internal processes and intermediate factors in the efficiency measurement. A few studies have used this method for the efficiency measurement of bank branches; they have considered two processes in branches and used two-stage models. In this study, we will use a more general approach and a more complete network structure consisting of three processes, including the deposit attraction process, deposit allocation process and banking services provision process. Since we want to obtain efficient targets, an envelopment form of the NDEA model had to be used. Therefore, a slack-based NDEA model, as introduced by Tone and Tsutsui (SBM-NDEA), was nominated to support its mathematical model. But according to the new categorization of the efficiency measurement factors introduced in this paper, and also regarding some previous reviews on SBM-NDEA model, the model will be modified to include the desired properties. Finally, by applying the modified model, branches efficiency scores and also efficient targets will be obtained.

Proportional trade-offs-as an enhanced form of the conventional absolute trade-offs-have recently been proposed as a method which can be used to incorporate prior views or information regarding the assessment of decision making units (DMUs) into relative efficiency measurement systems by Data Envelopment Analysis (DEA). A proportional trade-off is defined as a percentage change of the level of inputs/outputs so that the corresponding restriction is adapted with respect to the volume of the inputs and outputs of the DMUs in the analysis. It is well-known that the incorporation of trade-offs either in an absolute form or proportional form may lead in certain cases to serious problems such as infinity or even negative efficiency scores in the results. This phenomenon is often interpreted as a result of defining the set of trade-offs carelessly by the analyst. In this paper we show that this may not always be the case. The existing framework by which the trade-offs are combined mathematically to build a corresponding production technology may cause a problem rather than the definition of the trade-offs. We therefore develop analytical criteria and formulate computational methods that allow us to identify the abovementioned problematic situations and test if all proportional trade-offs are consistent so that they can be applied simultaneously. We then propose a novel framework for aggregating local sets of trade-offs, which can be combined mathematically. The respective computational procedure is shown to be effectively done by a suggested algorithm. We also illustrate how the efficiency can be measured against an overall technology, which is formed by the union of these local sets. An empirical illustration in the context of engineering schools will be presented to explain the properties and features of the suggested approach.

The "trade-offs Data envelopment analysis (DEA)" model is built by adding an extra axiom to the traditional production possibility set. The axiom introduces some replacement relations as production rules between inputs and outputs and leads to some extensions to the production possibility set. It provides more discriminatory power of decision-making units (DMUs) in DEA models, and the results are more adaptable to real conditions. In this paper, these variations are defined in proportional forms, which make the variation proportionate to DMUs' sizes. So we call them proportional tradeoffs, and they offer some advantages in comparison with simple trade-off vectors, which depend on input or output units of measurements. First of all, the proportional trade-offs vectors can fairly consider the DMUs' abilities and their strengths in adapting to the proposed changes. Secondly, it will be seen that proportional trade-off vectors can be used as a generalization of usual returns to scales (RTS), and finally the proportional trade-offs models cover the basic DEA models and their related production possibility set (PPSs) as special cases.Keywords: Data envelopment analysis (DEA); production possibility set (PPS); proportional trade-offs (PTO); returns to scale (RTS). 1250035-1 Asia Pac. J. Oper. Res. 2012.29. Downloaded from www.worldscientific.com by THE UNIV OF WESTERN ONTARIO on 02/07/15. For personal use only. 1250035-2 Asia Pac. J. Oper. Res. 2012.29. Downloaded from www.worldscientific.com by THE UNIV OF WESTERN ONTARIO on 02/07/15. For personal use only. Proportional Production Trade-Offs in DEA Simple Trade-Offs VectorsThe trade-offs model is created by extending the PPS axioms based on trade-offs, which are replacement relations between inputs and outputs (Podinovski, 2004a).

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