An Entropy Based Shapley Value for Ranking in Data Envelopment Analysis

Subject Areas : Data Envelopment Analysis

رضا  فلاح نژاد ¹ (Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran)
ساناز  اسدی رحمتی ² (Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran.)
کیوان  مرادی پور ³ (Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran.)

Received: 2022-03-12 Accepted : 2022-07-06 Published : 2022-03-01

Keywords: Data envelopment analysis, Ranking, Entropy, Cooperative Game, Shapley value,

Abstract :

In traditional DEA, DMUs are divided into Efficient and inefficient, but the score of all efficient units are equal to one and there is no discrimination between them. Thus many ranking methods are proposed to increase discrimination power. This paper proposes an integrated framework of cooperative games and entropy to rank efficient units by considering efficient units as players in a cooperative game, A subset of these players is defined as the coalition of S. The sum of the efficiency of inefficient DMUs with respect to the frontier of production possibility set contain inefficient DMUs and the member of coalition S is defined as the characteristic function of the coalition S, which is used to determine the marginal effect of efficient DMUs. Then, a new Shapley Value resulted from aggregating the marginal effects of efficient DMUs weighted by Shannon entropy is used for ranking efficient DMUs. For the first time, we use the entropy to create a Shapley value for calculating the rank of efficient units.. Two examples are provided to illustrate the applicability of proposed model.

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