# A Value Efficiency-Based Target Setting Approach in Data Envelopment Analysis

Document Type: research paper

Author

Department of Mathematics-Faculty of Mathematical Science and Statistics-University of Birajnd-Birjand-Iran

Abstract

Basic models of Data Envelopment Analysis are intrinsically preference-free, in the sense that they consider all inputs and outputs and also all decision making units of the same importance. Although this property is beneficial in many ways, it has some drawbacks simultaneously, as the decision makers’ preferences are not taken into account in the process of evaluating units.  To overcome this drawback many researchers have developed several techniques for incorporating the preferences into the evaluation model. One of the underlying approaches is value efficiency analysis, which evaluates decision making units by comparing them with the most preferred unit. The most preferred unit is a unit which satisfies the decision maker most. On the other hand, the issue of benchmarking is an important aspect in data envelopment analysis, as it enables the analyst to choose a target for each inefficient unit. The target unit for each unit is located on the efficient frontier and determines the path of improvement for that inefficient unit. In this paper, the issue of target setting based on the concept of value efficiency is investigated. We aim to develop a target setting model which is able to determine target units that are not only efficient but also value efficient, as well. Moreover, the targets are determined based on closest distance from the evaluated unit. Some properties of the model are also discussed. Finally, we perform the proposed model on a real data set of 42 Spanish Universities.

Keywords

Article Title [Persian]

### الگویابی در تحلیل پوششی داده‌ها با رویکرد کارایی ارزش

Author [Persian]

• نسیم نصرآبادی
گروه ریاضی- دانشکده علوم ریاضی و آمار - دانشگاه بیرجند- بیرجند - ایران
Abstract [Persian]

مدل­های اساسی تحلیل پوششی داده­ها به طور ذاتی بدون ارجحیت هستند، به این مفهوم که در این مدل­ها اهمیت کلیه ورودی­ها و خروجی­ها و نیز اهمیت همه واحدهای تصمیم­گیرنده تحت ارزیابی یکسان در نظر گرفته می­شود. این ویژگی علی­رغم مزیت­های آن دارای نقاط ضعف نیز می­باشد. از این رو موضوع دخیل نمودن ارجحیت­های مدیر در فرآیند ارزیابی و تحلیل عملکرد واحدهای تصمیم­گیرنده به عنوان یک مساله مهم تاکنون توسط بسیاری از پژوهشگران مورد بررسی قرار گرفته است. یکی از راهکارهای وارد نمودن ارجحیت­های مدیر در فرآیند ارزیابی واحدهای تصمیم­گیرنده روش کارایی ارزش است که ارزیابی واحدهای تصمیم­گیرنده را در مقایسه با واحد تصمیم­گیرنده دارای بیشترین ارجحیت انجام می­دهد. از طرف دیگر بحث الگویابی یکی از موضوعات حائز اهمیت در تحلیل پوششی داده­ها است، چرا که بدین طریق می­توان برای هر واحد ناکارا یک واحد الگو را که روی مرز کارایی قرار داشته و جهت بهبود عملکرد را برای آن واحد ناکارا تعیین می­کند، مشخص نمود. در این مقاله موضوع الگویابی در تحلیل پوششی داده­ها مبتنی بر مفهوم کارایی ارزش بررسی می­شود، بدین صورت که در فرآیند الگویابی نقش واحد با بیشترین ارجحیت لحاظ شده و برای هر واحد ناکارای ارزش یک واحد الگو که روی مرز شدنی کارای ارزش قرار دارد، تعیین می­شود. همچنین نقاط قوت و ضعف این روش مورد بحث قرار می­گیرد. در نهایت مدل الگویابی پیشنهاد شده بر روی داده­های یک مثال واقعی اجرا شده و نتایج حاصل تحلیل می­شوند.

Keywords [Persian]

• تابع فاصله جهت‌دار
• مرز کارای ارزش
• واحد الگو
• نزدیک‌ترین الگو
• ارجحیت

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