Measuring the efficiency of a three-stage network using data envelopment analysis approach considering dual boundary

This paper presents a method for performance evaluation, ranking and clustering based on the double-frontier view to analyze the complex networks. The model allows us to open the structure of the “black box” and can help to obtain important information about efficient and inefficient points of the system. In this paper, we consider a three-stage network, in respect to the additional desirable and undesirable inputs and outputs and utilize the cooperative approach to measure the efficiency of the overall system. Due to the fact that, a conclusion implying only one of these two, optimistic or pessimistic views is one-sided and incomplete, so, in this paper we used the double-frontier to analyze the network. Moreover, a heuristic technique was used to convert non-linear models into linear models. After obtaining the effective and inefficient points of the network, the DMUs are classified into several clusters by the k-means algorithm.Finally, in this article, in order to apply the proposed model a factory producing dairy products with a production area, warehouse premises and a delivery point are simulated. This factory has been regarded as a dynamic network with a time period of 24 intervals. The results of the ranking showed that, the time periods, (10) and (1) were the best and poorest respectively, in context to the efficiency within 24 phases of time.