Inverse cost and revenue efficiency in network processes with uncontrollable inputs

Inverse data envelopment analysis (IDEA) estimates the inputs/outputs of each decision-making unit (DMU) based on the perturbations in the outputs/inputs while maintaining relative efficiency. When the cost of inputs or the price of outputs is available, it is possible to calculate cost, revenue, and profit efficiencies. This study develops an inverse network DEA that includes uncontrollable measures. For this purpose, models are presented for calculating relative, cost, and revenue efficiencies. Then, an algorithm is proposed to estimate the inputs of the first stage, considering unchanged technical and cost efficiencies. Also, an algorithm is presented to estimate the outputs of the second stage, considering unchanged output-oriented technical efficiency and revenue efficiency. Then, the introduced algorithms are applied to a numerical example and a dataset related to salmon farming, obtaining logical results. Finally, the proposed method is compared with one of the existing methods, and their differences are discussed.