No abstract

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 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.

The efficiency evaluation of laboratories as one of the most significant areas of healthcare plays a key role in the quality of laboratories management. In this paper, a three-stage structure with optimal desirable and undesirable inputs and outputs has been taken into consideration by us. This network comprises of a leader and two followers. The suggested model simulates the internal structure of a diagnostic lab (pre-test, test and post-test). The criteria for evaluation are achieved by using the Fuzzy Delphi technique. Due to the environmental, economic and social impacts of health care systems, the significance of sustainability criteria is obvious in the case study indicators. We use the non-cooperative method multiplicative DEA technique to evaluate the efficiency of the network from both the optimistic and pessimistic views. Moreover, a heuristic technique was used to convert non-linear models into linear ones. Finally, we suggest to use a k-means method to cluster DMUs into several groups with similar characteristics based on double-frontier Standpoint.