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In this paper, a three-stage network with optimal desirable and undesirable inputs and outputs has been taken into consideration by us. This network comprises of a leader and two followers. Four diverse models of Data Envelopment Analysis (DEA) to measure the efficiency or the performance, of this three-stage network have been taken under contemplation; these are namely, a Black Box Model and three Stackelberg Game (Theory) Models. A multiplicative DEA, with a double-frontier approach, to measure the efficiency of the entire system and the performances of the decision making units (DMUs), from both the optimistic and pessimistic views have 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 define cooperation between the leader and followers, such that, we are able to include the objectives of the managers in the models. In actual fact, a non-cooperative 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.

Efficiency Evaluation of a Three-Stage Leader-Follower Model by the Data Envelopment Analysis with Double-Frontier Viewpoint