Ranking Decision Making units in Data Envelopment Analysis based on cooperative games

Subject Areas : Statistics

sanaz asadi rahmati ¹ , Reza Fallahnejad ²

1 - Department of Mathematics, Khorramabad branch, Islamic Azad University, Khorramabad, Iran
2 - Department of Mathematics, Khorramabad branch, Islamic Azad University, Khorramabad, Iran

Received: 2020-02-26 Accepted : 2021-05-15 Published : 2021-09-23

Keywords: مقدار شپلی, بازی همکارانه, تحلیل پوششی داده‌ها, رتبه‌بندی واحدهای کارا,

Abstract :

Evaluation of decision-making units is very importantin economic and management systems. Data envelopment analysis is one of the scientific and practical techniques for evaluating decision making units. In the conventional models of data envelopment analysis, the units are divided into efficient and inefficient categories, where the efficiency of each efficient unit is one and there is no distinction between efficient units.This study intends to propose a new way of ranking efficient units based on the concepts of cooperative game. The proposed method is that efficient units are considered as players of a cooperative game. A subset of these players is defined as the coalitionS.Then the sum of the efficiency of the inefficient units according to the production possibility set that is created by the inefficient units and the members of the coalitionS is defined as the characteristic function of S, which is used to determine the marginal effect of the efficient units in the various coalitions. Finally, the Shapley value is used to determine the cooperative game solution and rank the efficient units.In the same way that it is able to rank non-extreme units, inefficient units are also effective in ranking, alsois feasiblein any circumstances of return to scale.

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