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# رضا فرضی پور

حجت اله رجبی مشتاقی رضا فرضی پور

data envelopment analysis (dea) is a powerful tool for measuring relative efficiency of organizational units referred to as decision making units (dmus). in most cases dmus have network structures with internal linking activities. traditional dea models, however, consider dmus as black boxes with no regard to their linking activities and therefore do not provide decision makers with the reasons of inefficiencies. furthermore, the overall efficiency in multistage processes is composed of the efficiencies of their sub-processes. thus the relationship between the overall efficiency of the network and their components has been the subject of various studies. for example, cook et al. (2010) used the additive weighted average of component efficiencies to calculate the overall efficiency. they used the ratio of total weighted input of a stage to the total weighted input of all the components to find the weight of a component. as an alternative approach to cook et al. (2010), faramarzi et al. (in press) proposed that the other choice for the weights is the ratio of total weighted output at the ith stage to total weighted output of all components. a new method, based on the work of faramarzi et al.,(in press in international journal of management science and engineering management), and two other ones were also proposed and tested in s.p.g.c refineries to measure the weights, wp, of different stages necessary for efficiency calculation {(θ=∑_(p=1)^p▒〖w_p θ_p 〗 , where ∑_(p=1)^p▒w_p =1 ); theta is the efficiency of a process or a stage in a process}. comparisons among five methods of finding the weights of each node were made using data from s.p.g.c refineries. the results of the study showed that all of the decision making units (dmu), that is all four or five refineries considered were efficient. the relative efficiencies of the decision making units and their stages were very close to each other and their respective stages were efficient as well. the results were basically similar in all of these different methods. it is noteworthy, however, that the new method based on the work of faramarzi et al, seems to be very simple and practical and hence deserves further investigation. finally, spearman’s rank correlation coefficients of the five methods used were computed which showed very little difference in these methods. it is suggested that inefficient dmus and sub dmus be recognized by management and corrected to reach efficiency frontier. annual repetition of this research is advisable in order to urge competition among unites and sub unites. it is further recommended that this research be applied to all gas refineries in the country. efficiency of refineries can be measured on the basis of designed capacity and compared with the results obtained in this research.