detect and eliminate congestion of the intermediate products in supply chain

data envelopment analysis (dea) is a nonparametric technique that includes models to evaluate the relative efficiency of decision making units (dmus). it has the ability to separate efficient units and inefficient units. one of the applications of this mathematical technique is evaluating performance of supply chain. according to such as the inefficiency factors of one dmu, is existence congestion in its inputs and with regard to the economic concept of congestion that is widely visible in the most phenomenon, therefore, cannot ignore its presence in supply chain. in this paper, at first a network dea model is noted to evaluate the performance of supply chain. then according to the important role of intermediate products in supply chain, the existence of congestion in this product is investigated, finally, an inverse dea model is introduced in order to overcome the problems caused by congestion. so that the amount required input for providing the desired intermediate product can be estimated by that. in this case, no congestion will occur in intermediate products. finally for improving the efficiency of this unit with new intermediate products an inverse dea model is proposed.