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

Document Type : Research Article

Authors

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

10.29252/anm.2020.12767.1420

Abstract

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.

Keywords

Main Subjects

Full Text

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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Journal of Analytical and Numerical Methods in Mining Engineering
Volume 10, Issue 24
November 2020
Pages 13-26

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History

  • Receive Date: 07 August 2019
  • Revise Date: 28 December 2019
  • Accept Date: 15 April 2020

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