بهینه‌سازی مدل برنامه‌ریزی تولید بلند مدت با در نظر گرفتن عدم قطعیت عیار با روش آزادسازی لاگرانژی - الگوریتم‌ خفاش

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه مهندسی نفت و معدن، واحد تهران جنوب، دانشگاه آزاد اسلامی

2 گروه مهندسی معدن، دانشگاه کاشان

10.29252/anm.2020.12767.1420

چکیده

یکی از ارکان اصلی برنامه‌ریزی معدن، برنامه‌ریزی تولید بلند مدت است که یک امر بسیار مهم در تحقیقات نظری استخراج معادن روباز بوده و توزیع جریان نقدینگی را در سراسر عمر معدن مشخص می‌نماید. در واقع هدف برنامه‌ریزی، بیشینه‌کردن ارزش خالص فعلی از مجموع سودهایی است که در آینده تولید می‌شوند. برای رسیدن به این هدف باید همه محدودیت‌های عملیاتی از قبیل شیب، آمیختن عیارهای مختلف، تولید ماده معدنی و ظرفیت استخراج راضی‌کننده باشند. طرح‌های تولید بلند مدت بهینه در برابر عدم قطعیت‌های مربوطه با داده‌های مدل بهینه‌سازی دارای حساسیت هستند. در میان عدم قطعیت‌ها، عدم قطعیت عیار، سهم عمده‌ای را در دقت برنامه‌ریزی تولید بلند مدت خواهد داشت. در این مقاله مدل ترکیبی به وسیله روش آزادسازی لاگرانژی و الگوریتم خفاش برای حل مساله برنامه‌ریزی تولید بلند مدت معادن روباز ارائه شده که در آن عدم قطعیت عیار نیز لحاظ گردیده است. رویکردهای جدید پیشنهاد شده براساس بهینه سازی ضرایب لاگرانژ و مقایسه آن با روش سنتی است. الگوریتم خفاش برای به روزرسانی ضرایب لاگرانژ مورد استفاده قرار گرفته شده است. 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 می‌تواند راه‌حل قابل قبولی را نسبت به روش تقریبی سنتی ارائه کند؛ به طوری ‌که، در طول یک دوره معین ارزش خالص فعلی با استفاده از روش ترکیبی پیشنهادی 69/6 درصد بیشتر از روش سنتی موجود است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Optimization of the Long-Term Production Scheduling Model by Considering the Grade Uncertainty by the Lagrangian Relaxation Method - Bat Algorithm

نویسندگان [English]

  • Kamyar Tolouei 1
  • Ehsan Moosavi 1
  • Amirhossein Bangian Tabrizi 1
  • Peyman Afzal 1
  • Abbas Aghajani Bazazi 2
1 Dept. of Petroleum and Mining Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
2 Dept. of Mining Engineering, University of Kashan, Kashan, Iran
چکیده [English]

Summary
One of the main problems of mine planning is long-term production scheduling, which is very important in the theoretical research of open-pit mining and determines the distribution of cash flow throughout the life of the mine. In fact, the purpose is to maximize the net present value of the future profits generated. Among the uncertainties, grade uncertainty will play a major role in the accuracy of long-term production scheduling. In this paper, a hybrid model is presented by the Lagrangian relaxation method and bat algorithm to solve the problem of long-term production of open-pit mines, in which the uncertainty of the grade is also considered. The new approaches proposed are based on optimizing Lagrange coefficients and comparing them with the traditional method. The bat algorithm is used to update the Lagrange coefficients. The results of the case study show that the hybrid strategy can provide an acceptable solution compared to the traditional approximation method so that over a given period the net present value using the proposed hybrid method is 6.69% higher than the traditional one.
 
Introduction
In recent years, a new approach to cheaper computational algorithms, such as meta-heuristic techniques, has attracted more attention from researchers to solve production scheduling problems. Although these techniques do not guarantee optimization as a final solution for production, they can provide suitable solutions for production at a lower computational cost.
 
Methodology and Approaches
In this paper, an optimal hybrid model by the Lagrangian relaxation method and bat algorithm is presented to solve the problem of long-term production of open-pit mines, where the uncertainty of the grade is also considered. The newly proposed approach is based on optimizing Lagrange coefficients and comparing it with the traditional method. The results of the proposed approach are also compared with the combined approach based on the Lagrangian relaxation method and genetic algorithm. The bat algorithm is used to update the Lagrange coefficients.
 
Results and Conclusions
The results of a case study show that the Lagrangian relaxation method can provide a suitable solution to the main problem and the combined strategy can produce a more effective solution than the traditional approximation method. It was also found that the proposed method has advantages, such as stable convergence property and prevention of early convergence. Over a given period, the net present value using the LR-BA hybrid method is 6.69% higher than the traditional method and also 5.58% higher than the LR-GA method.

کلیدواژه‌ها [English]

  • Open pit mine
  • Long-term production scheduling
  • Grade uncertainty
  • Lagrangian relaxation
  • Bat algorithm

در عملیات معدنکاری در ابتدا از طریق پی‌جوئی و اکتشاف، محدوده‌ای که پتانسیل معدن شدن را دارد شناسایی شده و در سراسر منطقه کارهای اکتشافی از قبیل: حفاری، نقشه‌برداری و تفسیر زمین‌شناسی صورت می‌گیرد. در صورتی که روش روباز برای استخراج تأیید شود آنگاه مدل ماده معدنی به وسیله روش‌های مدلسازی عددی بسط داده می‌شود و ذخیره معدنی به زون‌هایی تقسیم‌بندی می‌شود که سرانجام این زون‌ها از طریق بلوک‌های مستطیلی شکل سه بعدی بلوک‌بندی می‌شوند. در هر بلوک عیار و عنصر کانسار و دیگر اطلاعات لازم از طریق مغزه‌گیری گمانه‌های حفاری مشخص می‌شود که در ارزیابی اقتصادی ارزش بلوک‌ها از آنها استفاده می‌شود. سپس از مدل توده معدنی که شامل توزیع کانسار و ارزش اقتصادی مورد انتظار آن می‌باشد در تعیین محدوده نهایی پیت مورد استفاده قرار می‌گیرند، که محدوده اقتصادی معدن را مشخص می‌نماید. به بیان دیگر، برنامه‌ریزی تولید سالانه یک مساله تصمیم‌گیری است که در آن بلوک‌ها در درون محدوده پیت باید به گونه‌ای و در زمانی استخراج شوند که بیشترین ارزش خالص فعلی[i](NPV) با در نظرگرفتن محدودیت‌های موجود حاصل شود. بلوک‌ها در داخل حجم‌های بزرگ‌تری که فاز استخراجی نامیده می‌شوند، جمع می‌شوند که آنها را می‌توان در طول زمان مشخص استخراج نمود. مشکل در یافتن مناسب­ترین راه ممکن برای جمع آوری بلوک‌ها در یک حجم که بتواند بیشترین مقدار ارزش خالص فعلی را بدهد، است.



[i] Net present value

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