1استادیار، گروه ریاضی، واحد پارس‌آباد مغان، دانشگاه آزاد اسلامی، پارس‌آباد مغان، ایران
2استاد، گروه ریاضی، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران
3استاد، گروه ریاضی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران
چکیده
در ارزیابی عینی عملکرد واحدهای تصمیم‌گیری (DMUs)، دو مشکل وجود دارد. مشکل اول نحوه کار با خروجی‌های نامطلوب است که در کنار خروجی‌های مطلوب تشکیل می‌شوند و مشکل دوم نحوه کار با متغیرهای غیرقابل‌کنترل است که غالباً تأثیر محیط عملیاتی را حفظ می‌کنند. با توجه به مشکلات ساخت مدل و دسترس‌پذیری داده‌ها، تعداد کمی از مقالات منتشر شده هر دو مشکل فوق را به‌طور هم‌زمان در نظر گرفته‌اند. هدف از مقاله حاضر، پیشنهاد زوج جدیدی از مدل‌های تحلیل پوششی داده‌ها (DEA) برای اندازه‌گیری کارایی‌های نسبی دی‌ام‌یوها در حضور عوامل غیرقابل‌کنترل، عوامل نامطلوب و داده‌های نادقیق است. در مقایسه با DEA سنتی، رویکرد DEA پیشنهادی، کارایی هر دی‌ام‌یو را نسبت به مرز بدترین عملکرد، که به آن مرز ورودی نیز می‌گویند، اندازه‌گیری می‌کند (بدترین کارایی نسبی یا کارایی بدبینانه). مدل‌های DEA پیشنهادی، داده‌های قطعی، اطلاعات ترجیح ترتیبی، بازه‌ای، عوامل نامطلوب و عوامل غیرقابل‌کنترل را به‌طور هم‌زمان برای اندازه‌گیری کارایی‌های نسبی دی‌ام‌یوها در نظر می‌گیرند. یافته‌های این مقاله نه‌فقط برای روش ارزیابی عملکرد مفید است، بلکه برای محققان صنعتی و دانشگاهی نیز مفید بوده و نتایجی از منظر سیاست‌گذاری را نیز دربردارد. در این مقاله، یک مثال عددی نیز برای نشان دادن کاربرد مدل‌های DEA پیشنهادی ارائه خواهد شد.
1Assistant Professor, Department of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran
2Professor, Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
3Professor, Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
چکیده [English]
There are two difficulties in implementing an objective evaluation of the performance of decision-making units (DMUs). The first one is how to treat undesirable outputs jointly produced with the desirable outputs, and the second one is how to treat uncontrollable variables, which often capture the impact of the operating environment. Given difficulties in both model construction and data availability, very few published papers simultaneously consider the above two problems. The objective of the present paper is to propose a novel pair of data envelopment analysis (DEA) models for measurement of relative efficiencies of DMUs in the presence of non-discretionary factors, undesirable factors, and imprecise data. Compared to traditional DEA, the proposed DEA approach measures the efficiency of each DMU relative to the worst practice frontier, also called the input frontier, and is called the worst relative efficiency or pessimistic efficiency. The pair of proposed DEA models simultaneously takes into account the crisp data, ordinal preference information, and interval data, as well as undesirable factors and non-discretionary factors, for measurement of relative efficiencies of DMUs. The results of this study are not only useful for the performance evaluation method, but also have policy implications for industrial and academic researchers. A numeric example has been provided to illustrate the applicability of the DEA models.
کلیدواژه‌ها [English]
Data Envelopment Analysis, pessimistic efficiencies, performance evaluation, imprecise data
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