A Bi-level Multi-objective Programming on Data Envelopment Analysis by Penalty Approach

The aim of this paper is to evaluate the structure of a bi-level system, which consists of multiple leaders at the first level and multiple followers at the second. We integrate the bi-level programming and Data Envelopment Analysis with multiple leaders and followers. The proposed model differs from the existing bi-level Data Envelopment Analysis models in that we use a penalty function for evaluating the cost efficiency instead of the Kuhn–Tucker conditions. So, we first explain the bi-level linear multi-objective programming problem and then utilize an exact penalty method to evaluate the cost efficiencies of decision-making units with multiple leaders and followers. One of the features of our proposed method is that it reduces the number of nonlinear constraints and increases the computational speed compared to existing computational methods. Finally, to demonstrate the efficiency of our method, we provide a numerical example. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.