An innovative inverse model of network data envelopment analysis

Sensitivity analysis in optimization problems is important for managers and decision maker to introduce different strategies. Data Envelopment Analysis (DEA) is a method based on mathematical programming to evaluate the efficiency of a set of Decision-Making Units (DMUs). Due to the importance of sensitivity analysis in an optimization problem, a development of DEA model called inverse model in DEA is presented. The purpose of this model is to analyze the sensitivity of some inputs or outputs to changes in some other inputs or outputs of the unit under evaluation, provided that the amount of efficiency remains constant or improves at the discretion of the manager. In this research, for the first time, we introduce the inverse model in DEA with network structure. In fact, we examine the extent to which the input parameters are likely to change based on the presuppositions of the problem, for the output changes that are applied as the manager desires. One of the key points of this research is that to make the modeling more consistent with reality, the leader-follower method was used in estimating the parameters in the network. In addition, the opinions of the system manager and the decision maker, who have full control over the system under their management, are included in this modeling to estimate the desired values. Another feature of this modeling is the consideration of uncontrollable factors in the inverse model in DEA with network structure. Finally, using a numerical example, the results obtained are analyzed based on the proposed model.