ارائه یک مدل برنامه‌ریزی عدد صحیح صفر یا یک به منظور رفع پدیده تغییر در رتبه‌های گزینه‌های تصمیم‌گیری

نوع مقاله: مدیریت تولید و عملیات(نوآوری -تحقیق و توسعه -زنجیره تامین -زنجیره اززش -بهره وری)

نویسنده

عضو هیات علمی گروه مدیریت صنعتی-دانشگاه علامه طباطبایی

چکیده

روش‌های مختلف در مسائل تصمیم‌گیری چندشاخصه می‌تواند به رتبه‌بندی‌های گوناگونی بیانجامد. اعتبار روش به این بستگی دارد که با حذف بدترین (بهترین) گزینه، تغییر در رتبه‌بندی‌های قبلی رخ ندهد (رتبه سایر گزینه‌ها به ترتیب قبلی خود یک پله صعود داشته باشند). همچنین روش‌های مختلف نرمال‌سازی بر روی نتایج تاثیر نداشته باشد. در این مقاله یک مدل برنامه‌ریزی ریاضی عددصحیح صفر یا یک با تابع هدف حداقل‌سازی مجموع وزنی انحرافات از معیارها تشکیل شده است. محدودیت‌های متناظر با هر معیار نیازمند متغیر کمکی یا مازاد برای استاندارد شدن است. این محدودیت‌ها همراه با سایر محدودیت‌های واقعی نظیر محدودیت بودجه تشکیل دهنده محدویتهای مسئله است. با بررسی سه مسئله از ادبیات موضوع مدل مزبور با طرق مختلف نرمال‌سازی بررسی شده و جواب آنها به‌دست آمده است. نتایج حاصله نشان می‌دهد که پدیده تغییر در رتبه‌ها نه تنها با حذف بدترین گزینه اتفاق نمی‌افتد، بلکه با حذف بهترین گزینه، سایر گزینه‌ها به ترتیب رتبه‌های قبلی خود با یک پله صعود مواجه می‌شوند

کلیدواژه‌ها


عنوان مقاله [English]

A Zero-One Programming Model for Preventing Rank Reversal Phenomena in Ranking of Decision Alternatives

نویسنده [English]

  • Seyed Mohammad Ali Khatami Firouzabadi
Faculty Member-Industrial Management Group, Management and Accounting Department, Allameh Tabataba'i University
چکیده [English]

Many methods have been proposed in the literature for solving Multiple Attribute Decision Making (MADM) problems, which may create different prioritization for a unique problem. The validity of the methods depends on preserving the rankings in the case of adding or removing irrelevant alternatives. Irrelevant alternatives are those which their evaluations regard to any attribute is worse than the best selected alternative or any other alternative which has not been chosen. In other words, the validity of prioritization not only depends on not to create a different prioritization with removing the worst alternative, but also depends on to create an upward prioritization for other alternatives when the best alternative elemintates from the set of alternatives. Furthermore, when diverse normalization process use for the problem, the results must not change. Furthermore, different normalization processes do not have any effect on the rankings. In this paper, a zero-one programming model with a weighted sum minimization objective function has been constructed. Any constraint which relates to each attribute needs to have a slack or surplus variable for standardization. These constraints with real world constraints (for instance, budget constraint) forms the model constraints. Three case studies adapted from literature review, which have been normalized with different normalization procedures, solved with new model. The results demonstrate rank reversal phenomena has not been occurred.

کلیدواژه‌ها [English]

  • MADM
  • Rank Reversal
  • Prioritization
  • Zero-One Programming

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