مدل سازی ریاضی دوسطحی مساله مکان‌یابی و استحکام‌سازی تسهیلات سلسله مراتبی با محدودیت ظرفیت و بودجه تحت شرایط تخریب و حل آن با الگوریتم ژنتیک

نوع مقاله : مقاله پژوهشی

نویسنده

استادیار گروه ریاضی و آمار، دانشکده علوم پایه و فنی مهندسی، دانشگاه گنبد کاووس، گلستان، ایران

چکیده

DOR : 20.1001.1.24766291.1399.5.3.3.8
اهمیت مکان یابی و استحکام سازی تسهیلات سلسله مراتبی در شرایط عملیات خرابکارانه، بسیاری از محققین را به اتخاذ تصمیمات مناسب ترغیب نموده است. در این مقاله، یک مدل برنامه ریزی دوسطحی معرفی شده که با در نظرگرفتن عملیات ممانعتی و از کارافتادگی تسهیلات سلسله مراتبی در دو سطح، استراتژی های مناسب جهت مکان‌یابی و استحکام سازی آنها انتخاب می نماید. با توجه به منابع مکان‌یابی موجود، تقاضای خدمات و بدترین سناریوی خرابی تسهیلات در هر دوسطح، تصمیمات تخصیص، مکان‌یابی و استحکام سازی تسهیلات موجود تعیین می شوند. برای نزدیکی بیشتر به واقعیت سیستم سلسله مراتبی از مفاهیم ظرفیت و بودجه استفاده شده‌است. هدف مدل کمینه سازی هزینه مکان یابی و فاصله خدمات رسانی بین نقاط تقاضا و تسهیلات در هر دو سطح است. در ادامه، چند نمونه عددی از مساله ارایه و با رویکردهای ترکیبی دوسطحی مبتنی بر الگوریتم‌های فراابتکاری ژنتیک و کوچ پرندگان برای مساله سطح اول و روش دقیق برای مساله سطح دوم ‎حل شده است.

کلیدواژه‌ها


عنوان مقاله [English]

Bi-level mathematical modeling of the location and fortification problem of hierarchical facilities with capacity and budget constraints under destruction conditions and solving it with genetic algorithm

نویسنده [English]

  • Raheleh Khanduzi
Assistant Professor-Department of Mathematics and Statistics-Applied Mathematics - Operations Research (Optimization)-Gonbad Kavous University
چکیده [English]

The importance of locating and fortifying hierarchical facilities in the face of sabotage operations has encouraged many researchers to make appropriate decisions. In this paper, a bi-level programming model has been introduced, which, considering the interdiction operations and failure of hierarchical facilities at two levels, selects appropriate strategies to locate and fortify them. Depending on available location resources, service demand, and the worst-case scenario of facility failure at both levels, the decisions as to the allocation, location, and fortification of existing facilities are determined. The concepts of capacity and budget have been used to bring the hierarchical system closer to reality. The model aims at minimizing the location cost as well as service distance between demand points and facilities at both levels. In the following, a number of numerical examples of the problem have been presented and solved with two-level combined approaches based on genetic and particle swarm algorithms for the first level and the exact method for the second level problem.

کلیدواژه‌ها [English]

  • Hierarchical network
  • Bi-level model
  • Fortification
  • Interdiction
  • genetic algorithm
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