Finding the appropriate weight for each criterion is one of the main points in

Conventional data envelopment analysis (DEA) is a method for measuring the efficiency of decision-making units (DMUs). Recently, to measure the efficiency of sub-DMUs (Stages), several network DEA models have been developed, in which the results of network DEA models not only provide the overall efficiency of the whole system but also provide the efficiency of the individual stages. This study develops a bargaining game model for measuring the efficiency of DMUs that have a two-stage network structure with non-discretionary inputs, that the model as a method of dealing with the conflict arising from the intermediate measures. Under the Nash bargaining game theory, the two stages in the network DEA are considered as players and network DEA model is a cooperative game model. Here, the non-discretionary additional inputs in the second stage make changes in the cooperative game model, so that managers of units cannot change the value of non-discretionary inputs in measuring the efficiency of the bargaining game model, and this causes the desired and expected output of the managers not to be produced. In addition, it can be stated that the presence of such inputs is capable, significantly affecting the system efficiency score and stages. So that the existence of the inputs in the measuring efficiency of decision-making units reduces the efficiency score of cooperative game. In this study, linearizing the model in the presence of the non-discretionary input is a new idea in the bargaining game model. A numerical example shows the applicability of the new model.

Data envelopment analysis (DEA), which is used to determine the efficiency of a decision-making unit (DMU), is able to recognize the amount of input congestion. Moreover, the relative importance of inputs and outputs can be incorporated into DEA models by weight restrictions. These restrictions or a priori weights are introduced by the decision maker and lead to changes in models and efficiency interpretation. In this paper, we present an approach to determine the value of congestion in inputs under the weight restrictions. Some discussions show how weight restrictions can affect the congestion amount.

No abstract

<abstract><p>Data Envelopment Analysis (DEA) is a prominent technique for evaluating the performance and ranking of a set of decision-making units (DMUs) that transform multiple inputs into multiple outputs. However, one of the challenges of the primary DEA models is facing imprecise data in real practical problems. To address this issue, fuzzy DEA have been proposed, which have been successfully applied in many real fields. On the other hand, in some real-world DEA applications, the primary objective of performance evaluation is the ranking of a group that consists of several DMUs that are typically under the control of a centralized management. In this paper, we try to use the theory of cooperative games and Shapley value method as a fair method to solve such games in order to rank groups in DEA. In this way, the resulting rank for groups is based on the average marginal shares of groups in different coalitions that are formed based on the theory of cooperative games. We applied the proposed method to rank groups of airlines considering fuzzy data. To the best of authors' knowledge, so far, no method has been presented in DEA literature for ranking groups in fuzzy environment and using game theory techniques.</p></abstract>