An Entropy Based Shapley Value for Ranking in Data Envelopment Analysis
محورهای موضوعی : 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.)
کلید واژه: Data envelopment analysis, Ranking, Entropy, Cooperative Game, Shapley value,
چکیده مقاله :
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.
در تحلیل پوششی داده های معمولی، واحدهای تصمیم گیرنده (DMU) به دو دسته کارا و ناکارا تقسیم می شوند، اما امتیاز همه واحدهای کارا برابر با یک است و هیچ تمایزی بین آنها وجود ندارد. بنابراین روش های رتبه بندی متعددی برای افزایش قدرت تمایز پیشنهاد شده است. این مقاله یک چارچوب یکپارچه از بازی های همکارانه و آنتروپی را برای رتبه بندی واحدهای کارا با در نظر گرفتن واحدهای کارا به عنوان بازیکنان در یک بازی همکارانه پیشنهاد می کند، زیر مجموعه ای از این بازیکنان به عنوان ائتلاف S تعریف می شود. مجموع کارایی DMUهای ناکارا با توجه به مجموعه امکان تولید شامل DMUهای ناکارا و اعضای کارای عضو ائتلاف S به عنوان تابع مشخصه ائتلاف S تعریف می شود که برای تعیین تاثیر حاشیه ای DMUهای کارا استفاده می شود. سپس، یک مقدار شپلی جدید، حاصل از تجمیع وزن دار شده تاثیرات حاشیه ای DMUهای کارا با آنتروپی شانون برای رتبه بندی DMUهای کارآمد استفاده می شود. برای اولین بار، از آنتروپی برای ایجاد یک مقدار شپلی برای محاسبه رتبه واحدهای کارا استفاده می کنیم. دو مثال برای نشان دادن کاربرد مدل پیشنهادی ارائه شده است
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