Finding projection in the two-stage supply chain in DEA-R with random data using (CRA) model

Data envelopment analysis based on mathematical programming for decision-making units determines the efficiency score in addition to the projection of inefficient DMUs on the efficient frontier. Centralized Allocation Resource (CRA) with a two-stage linear programming model captures the projection of DMUs on the efficient frontier. But since the input and output vectors of each DMU in the DEA are crucial, they may be random data that follow a particular distribution. Hence, many applied studies face random data. This paper shows a two-stage supply chain with random data and the CRA model with ratio data has been used to calculate the projection of DMUs. In the end, the supply chain of 11 Iranian Airlines with random data during the period of 2011-2017 was considered concerning sustainability factors.