Optimal Allocation of Resources Using the Ideal-Solutions

Document Type: research paper


1 Department of Mathematics, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Isfahan, Iran.

2 Department of Mathematics, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Isfahan, Iran


This paper proposes a new method based on the ideal input vector to estimate inputs of a given decision making unit (DMU) when some or all of its outputs are increased to maintain its current efficiency level. In other words, this paper studied the following question: How much would be the increase in the inputs of the DMU if the decision maker increases certain outputs to a particular unit in which the DMU maintains its current efficiency level? In this study, unlike other proposed methods, the above question was addressed using just the single-objective linear programming (LP) problems. The problem of estimation of inputs was investigated based on the non-radial models. Necessary and sufficient conditions are proposed for estimation of inputs using just the single-objective LP problems. In addition, the level of deficiency (if any exists) in each of the output components is specified. An example with real data is presented to illustrate our proposed method.


Article Title [Persian]

تخصیص بهینه منابع با بکارگیری جوابهای ایده آل

Authors [Persian]

  • سعید قبادی 1
  • سعید جهانگیری 2
1 گروه ریاضی، واحد خمینی شهر، دانشگاه آزاد اسلامی، خمینی شهر، اصفهان، ایران
2 گروه ریاضی، واحد خمینی شهر، ، دانشگاه آزاد اسلامی، خمینی شهر، اصفهان، ایران
Abstract [Persian]

این مقاله یک روش جدید بر اساس بردار ورودی ایده آل برای تخمین ورودی ها تحت حفظ اندازه کارایی از یک واحد تصمیم گیرنده وقتی که برخی یا همه خروجی های آن افزایش یافته است، پیشنهاد می دهد. بعبارت دیگر، این مقاله سوال زیر را مطالعه کرده است: تحت حفظ کارایی، به چه میزانی می بایستی ورودی های یک واحد تصمیم گیرنده افزایش یابد در شرایطی که برخی یا همه خروجی های آن افزایش داده شده باشد؟ در روش ارایه شده در این مقاله، برخلاف روش های پیشنهاد شده دیگر، سوال فوق فقط بر پایه مسایل برنامه ریزی خطی تک هدفی پاسخ داده شده است. مساله تخمین ورودی ها بر پایه مدل غیر شعاعی راسل پیشرفته مورد بررسی قرار گرفته است. شرایط لازم و کافی برای تخمین ورودی ها بر پایه برنامه ریزی خطی پیشنهاد گردیده است. بعلاوه، اگر کمبودی در هر یک از مولفه های خروجی واحد تصمیم گیرنده وجود داشته باشد شناسایی می شود. یک مثال با داده های واقعی برای توضیح از روش پیشنهادی ارایه شده است.

Keywords [Persian]

  • تحلیل پوششی داده های معکوس(DEA)
  • برنامه ریزی خطی(LP)
  • تخصیص منابع
  • اندازه راسل پیشرفته(ERM)
  • جوابهای ایده آل
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