Grading of Decision-Making Units with Multi-Period Two-Stage Network Structure: a Method Based on Relative Data Envelopment Analysis
محورهای موضوعی : Operation Research
مقصود احمد خانلو قراخانلو
1
(دانشجوی دکتری، گروه ریاضی کاربردی، دانشگاه آزاد اسلامی واحد تبریز. تبریز- ایران.)
نیما آذرمیر شتربانی
2
(استادیار گروه ریاضی کاربردی، دانشگاه آزاد اسلامی واحد تبریز. تبریز- ایران.)
قاسم توحیدی
3
(دانشیار گروه ریاضی، دانشگاه آزاد اسلامی واحد تهران مرکز. تهران- ایران.)
شبنم رضویان
4
(دانشیار گروه ریاضی، دانشگاه آزاد اسلامی واحد تهران جنوب. تهران- ایران.)
روح اله عباسی
5
(استادیار گروه ریاضی، دانشگاه قم. قم- ایران.)
کلید واژه: Multi-period, Efficiency, network, Grading, relative data envelopment analysis,
چکیده مقاله :
Data envelopment analysis is always considered as a non-parametric method for measuring the efficiency of a set of decision units. The efficiency number obtained from standard models is a criterion for comparing the performance of each decision unit with other units. Despite the many strengths of these models, one of their weaknesses is the lack of distinction between efficient units. Also, these models do not pay attention to the internal structure of the units and have a black box view. To solve these problems, relational data envelopment analysis models are used, which are much more cost-effective in terms of time and cost; But these models are static and do not take time into evaluation. In this paper, a method has been proposed for grading of the decision making units with multi- period two stages network structure using relative data envelopment analysis. Three different perspective are introduced for assessment of efficiency in time periods via relative data envelopment analysis. Proportionate with each perspective, an efficiency number is obtained for any decision making unit. Then three efficiency numbers obtained in the mentioned method is combined with Shannon entropy method and a total efficiency criterion is defined for each unit. Finally, this measure is considered as the main indicator for the units grading. The results of implementation of the mentioned algorithm on the real example and comparison with the similar methods clarify the strength of this algorithm.
تحلیل پوششی داده ها به عنوان یک روش غیرپارامتریک برای اندازه گیری کارایی مجموعه ای از واحدهای تصمیم گیری همواره مورد توجه می باشد . عدد کارایی حاصل از مدل های استاندارد ، معیاری برای مقایسه عملکرد هر واحد تصمیم گیری با بقیه واحدها می باشد. علی رغم نقاط قوت فراوان این مدل ها، از نقاط ضعف آنها می توان به عدم تمایز بین واحدهای کارا اشاره کرد. همچنین، این مدل ها به ساختار داخلی واحدها توجه نمی کنند و دیدگاه جعبه سیاه دارند. در جهت رفع این مشکلات، مدل های تحلیل پوششی داده های نسبتی که هم از لحاظ زمان و هزینه بسیار مقرون به صرفه تر است مورد استفاده قرار می گیرند؛ اما این مدلها ایستا هستند و زمان را در ارزیابی لحاظ نمی کنند. در‌این مقاله، روشی برای رتبه‌بندی واحدهای تصمیم‌گیری با ساختار شبکه دو مرحله‌ای چند زمانی با استفاده از تحلیل پوششی داده‌های نسبتی پیشنهاد می‌شود. با استفاده از مدل‌های تحلیل پوششی داده‌های نسبتی، سه دیدگاه متفاوت برای ارزیابی کارایی در دوره‌های زمانی معرفی می‌شود و متناظر با هر دیدگاه، یک عدد کارایی برای هر واحد تصمیم‌گیری به دست می‌آید. سپس، سه مقدار کارایی منتج از سه روش مذکور، با استفاده از روش آنتروپی شانون با یکدیگر ترکیب شده و یک معیار کارایی کلی برای هر واحد تعریف می‌شود. این معیار در نهایت به عنوان شاخص اصلی برای رتبه‌بندی واحدها درنظر گرفته می‌شود. نتایج اجرای الگوریتم پیشنهادی بر روی مثال واقعی و مقایسه آن با نتایج روش‌های مشابه، قوت‌این الگوریتم را آشکار می‌سازد.
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