Eciency evaluation of a three-stage leader-follower model by data envelopment analysis with double-frontier viewpoint

In this paper, a three-stage network with optimal desirable and undesirable inputs and outputs has been taken into consideration. This network is comprised of a leader and two followers. Four diverse models of Data Envelopment Analysis (DEA) to measure the eciency or performance of this three-stage network have been taken under consideration. These are, namely, a Black Box Model and three Stackelberg Game (theory) Models. A multiplicative DEA, with a double-frontier approach, to measure the eciency of the entire system and the performance of the Decision Making Units (DMUs), from both optimistic and pessimistic views has been utilized. In this paper, attempts have been made to present the goals of the managers in the models. Hence, aspects of goal programming have been manipulated so as to dene cooperation between the leader and followers, such that the objectives of the managers are included in the models. In actual fact, a noncooperative collaboration is deliberated upon. In addition to which, in the second and third scenarios, the leader-follower, nonlinear models are present. Thereby, a heuristic approach is suggested to convert the nonlinear models into linear ones.