7. Conclusion
Evaluation the performance of a system and its component processes over multiple periods requires a model that measures the efficiency of network considering its extension on a time span. In this paper, the relational DNDEA model is developed to incorporate the dynamic effect in network systems. This model has two advantages; first, considering the internal structure of DMU helps to detect the inefficient processes and improve them. Second, the temporal dimension of production processes is included. The relational model of this paper measures the efficiency of processes in connected time periods, properly and there is a mathematical relationship between processes over the time. Comparing the relational and SBM approaches, it's obvious that SBM approach uses slack variables for calculating the efficiency scores and there is no relationship between the efficiency scores of system and subsystems. This paper develops the two-stage form of the dynamic DEA model. The formulation of two-stage model can be extended to multi-stage networks. To illustrate the capability of the proposed model, the efficiencies of 8 airlines in Iran were measured over 2010 to 2012 with considering the interaction between time periods and divisions. The results obtained from the model help us to identify the divisions which cause the system to have lower efficiency. Decomposition the performance of a company to the component processes in a time span produces meaningful results. In the Iranian airlines, Ata airline has the highest rank between other airlines during 2010e2012 in both of two stages. The average of efficiency scores shows that the airlines have had the better performance in stage 2. Also, since the airlines have poor performance in stage 1, so, the final efficiency scores for airlines system are low.
