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.

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<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>

Data Envelopment Analysis (DEA) is an appropriate tool for estimating various types of efficiency such as cost efficiency. There are two different sates in cost spaces; in the first space prices are equal for all Decision Making Units (DMUs) which is competitive space, and in the second space prices are different form one DMU to another; this is known as non-competitive space. The present paper introduces a new method to assess Cost Efficiency (CE), Revenue Efficiency (RE) and Profit Efficiency (PE) in a non-competitive space. The present paper also proposes a Production Possibility Set (PPS) in which DMUs are evaluated based on both their own prices and the prices of other DMUs in non-competitive space. Moreover, a new decomposition is provided for observed actual cost DMUs based on the cost efficiency model and the proposed PPS, thus the observed actual cost can be shown by summation of several technical, price and allocative efficiency (AE) losses. The biggest advantage of this method comparing to the previous methods is that passive the developed cost efficiency and the cost Production Possibility Set has been developed and the performed decomposition is more accurate; this is because the new inefficiency sources are defined and added to this new decomposition. Therefore, it includes more inefficient sources.

The present study proposes a method for evaluating and ranking the efficiency of decision-making units (DMUs) that has a two-stage network structure in data envelopment analysis (DEA). Measuring the efficiency of two-stage network systems in data envelopment analysis has developed considerably, but ranking it in a logical and accurate analysis is a subject that still needs further study. In the present study, a model is presented that can consider the impact of each efficient DMUs on the whole two-stage network system, as well as using the reference frontier, the impact of each efficient DMUs in each evaluating non-efficient DMUs. It also provided more information to rank and identify the impact of extreme efficient DMUs on non-efficient DMUs by reference frontier. The concept of reference frontier introduced in the present study has the potential to determine the contribution of each extreme efficient DMUs in constructing a reference frontier for each non-extreme efficient DMUs and non-efficient DMUs. These facts have been investigated using logical reasoning and proof of several theorems, and have been discussed with a Practical example.

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