ارائه مدل برنامه‌ریزی ریاضی عدد صحیح برای مسئله زمان‌بندی استخراج در معادن روباز تحت شرایط عدم قطعیت عیار و حل آن با استفاده از الگوریتم کرم شب‌تاب

نوع مقاله : علمی - پژوهشی

نویسندگان

1 دانشجوی دکتری ، دانشکده مهندسی نفت و معدن، واحد تهران جنوب، دانشگاه آزاد اسالمی،

2 استادیار، دانشکده مهندسی نفت و معدن، واحد تهران جنوب، دانشگاه آزاد اسالمی،

3 دانشیار، دانشکده مهندسی نفت و معدن، واحد تهران جنوب، دانشگاه آزاد اسالمی،

4 استادیار، دانشکده مهندسی معدن، دانشگاه کاشان

چکیده

برنامه‌ریزی تولید بلند‌مدت در معادن روباز یک امر بسیار حیاتی در برنامه‌ریزی معدن است و توزیع جریان نقدینگی را در سراسر عمر معدن مشخص می‌کند. هدف برنامه‌ریزی، بیشینه‌کردن ارزش خالص فعلی با در نظر گرفتن همه محدودیت‌های عملیاتی از قبیل شیب، آمیختن عیارهای مختلف، تولید ماده معدنی و ظرفیت استخراج است. عدم قطعیت‌های مرتبط با داده‌های مدل، نقش به سزایی در بهینه‌سازی برنامه‌های تولید بلند‌مدت دارند. در میان عدم قطعیت‌ها، عدم قطعیت عیار، سهم عمده‌ای را ایفا می‌کند. در این مقاله مدل‌های ترکیبی به وسیله روش آزادسازی لاگرانژی (LR)، روش آزادسازی لاگرانژی تعمیم‌یافته (ALR) و الگوریتم کرم شب‌تاب (FA) برای حل مساله برنامه‌ریزی تولید بلند مدت معادن روباز با فرض قطعیت و همچنین، با در نظر گرفتن عدم قطعیت عیار ارایه شده‌اند. الگوریتم کرم شب‌تاب برای به روزرسانی ضرایب لاگرانژ مورد استفاده قرار گرفته شده است. رویکردهای جدید پیشنهاد شده با نتایج روش‌های ترکیبی حاصل از آزادسازی لاگرانژی و آزادسازی لاگرانژی تعمیم‌یافته با الگوریتم ژنتیک (GA) و روش سنتی زیرگرادیان (SG) مقایسه شده‌اند. برای حل و اعتبارسنجی مدل به دست‌آمده، معدن سنگ آهن چادرملو به عنوان مورد مطالعاتی مناسب، در نظرگرفته شده است. نتایج حاصل از مطالعه موردی نشان می‌دهد که استراتژی‌ ترکیبی
 ALR-FA می‌تواند راه‌حل بهینه را نسبت به روش‌های دیگر ارایه کند؛ به‌طوری‌که، در طول یک دوره زمان‌بندی دوازده ساله، میانگین ارزش خالص با استفاده از روش ترکیبی پیشنهادی 11/20 درصد بیشتر از روش سنتی موجود است. همچنین، سرعت CPU از مدل پیشنهادی، 7/4 درصد بیشتر از دیگر روش‌ها حاصل شد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

An Integer Mathematical Programming Model for Production Scheduling Problem in Open-Pit Mines under Grade Uncertainty and Solving Using the Firefly Algorithm

نویسندگان [English]

  • Kamyar Tolouei 1
  • Ehsan Moosavi 2
  • Amir Hossein Bangian Tabrizi 2
  • Peyman Afzal 3
  • abbas Aghajani Bazzazi 4
1 Department of Petroleum and Mining Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
2 Department of Petroleum and Mining Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
3 Department of Petroleum and Mining Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
4 Department of mining engineering, University of Kashan, kashan, Iran
چکیده [English]

Long-term production scheduling in open-pit mines is a crucial issue in mining planning and determines the distribution of cash flow throughout the life of the mine. The purpose of the planning is to maximize the net present value by taking into account all operational constraints such as slope, mixing of different grades, mineral production, and extraction capacity. The uncertainties associated with model data play an important role in optimizing long-term production plans. Among the uncertainties, grade uncertainty plays a major role. In this paper, hybrid models are presented by the Lagrangian relaxation (LR) method, augmented Lagrangian relaxation (ALR) method, and firefly algorithm (FA) to solve the long-term production scheduling problem of open-pit mines with the assumption of deterministic and also considering the grade uncertainty. The firefly algorithm is used to update the Lagrange multipliers. The newly proposed approaches are based on optimizing Lagrangian multipliers and comparing them with the results of combined Lagrangian relaxation method and augmented Lagrangian relaxation with the Genetic Algorithm (GA), and the traditional sub-gradient (SG) method. For solving and validating the obtained model, Chadarmelo iron ore mine is considered as a suitable case study. The results of the case study show that the combined strategy (ALR-FA) can provide a near-optimal solution over other methods such that, over a given period, the net present value using the proposed hybrid approach is 20.11% higher than the traditional method is available. Also, the CPU speed of the proposed model is 4.7% more than the other methods.

کلیدواژه‌ها [English]

  • Open-pit mine
  • long-term production scheduling
  • Grade Uncertainty
  • Lagrangian relaxation
  • firefly algorithm
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