برنامه‌ریزی استوار استخراج بلوک‌های معدن روباز در شرایط عدم‌قطعیت- رویکرد مبتنی بر مجموعه عدم‌قطعیت جعبه‌ای

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه مهندسی معدن، دانشکده مهندسی معدن و مواد، دانشگاه صنعتی ارومیه

2 دانشکده مهندسی معدن، دانشگاه تهران

10.29252/anm.2019.9426.1328

چکیده

برنامه‌ریزی زمانی استخراج بلوک‌های معادن روباز از کلیدی‌ترین تصمیم‌های مرتبط با این معادن است. غیرقطعی بودن برخی از پارامترها، لزوم توجه به برنامه‌ریزی در شرایط عدم‌قطعیت را ضروری ساخته است. در پژوهش حاضر ضمن بررسی اثر عدم‌قطعیت‌های رایج بر نتیجه برنامه‌ریزی استخراج، مقایسه‌ای بین برنامه‌ریزی قطعی و غیرقطعی استخراج بلوک‌های یک کانسار فرضی مس در حالت سه‌بُعدی صورت گرفته است. برای صورت‌بندی مدل برنامه‌ریزی غیرقطعی از رویکرد بهینه‌سازی استوار مبتنی بر مجموعه‌های محدب عدم قطعیت استفاده شده است. در این مدل، ارزش اقتصادی بلوک به عنوان ضریب متغیرهای تصمیم در تابع هدف و محدودیت ظرفیت استخراج و فرآوری به ‌عنوان مقادیر سمت راست محدودیت‌ها، به صورت غیرقطعی در نظر گرفته شده‌اند. با توجه به ماهیت روش استوار، حول مقادیر اسمی پارامترهای غیرقطعی نرخ اغتشاش و نوسانی با دامنه ثابت در نظر گرفته شده و تدابیر لازم برای کنترل و ارضای محدودیت‌ها در نظر گرفته شده است. در نهایت طی یک برنامه پنج ساله، خروجی مدل در حالت‌های مختلف، شامل زمان استخراج هر بلوک، تناژ استخراج، تناژ فرآوری و عیار متوسط هر دوره با پاسخ مدل برنامه‌ریزی خطی قطعی مقایسه شده است. نتایج حاصل از برنامه‌ریزی استوار نشان می‌دهد که محدوده معدن متناسب با افزایش سطح محافظه‌کاری کوچک‌تر می‌شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Uncertain Production Scheduling Optimization in Open-Pit Mines and Its Box Robust Counterpart

نویسندگان [English]

  • Aref Alipour 1
  • Mojtaba Mokhtarian Asl 1
  • Ali Asghar Khodaiari 2
1 Dept. of Mining and Metallurgy, Urmia University of Technology, Iran
2 Dept. of Mining, University of Tehran, Iran
چکیده [English]

Summary
The block extraction sequence is among the most challenging and important issues that should be considered through whole mining operations to reach the maximum profit value. Such Open-pit Production Scheduling problems can be solved under either deterministic or non-deterministic states. This study aims to model the problem applying robust counterpart linear optimization which uses the box set based counterpart. Block economic value, as the objective function coefficient and operational capacity, as the constraints coefficients, are considered as uncertainty sources. Exact mathematical modeling using CPLEX solver, is applied to solve the box counterpart. The model, which was solved in deterministic and uncertain conditions, terminated in results with some differences in scheduled plans.
 
Introduction
Open-Pit Production Scheduling (OPPS) concentrates on determining a block extraction sequence in a way that maximizes NPV of the venture under access, mining capacity, and processing capacity constraints and some other criteria such as blending constraints (extracted ore grade). Mathematical formulation of OPPS problem has been modeled by the mixed integer programming (MIP) method. Production scheduling problem solutions are very sensitive to price and cost volatility, ore grade uncertainty, operational capacities and etc. Hence, the scheduling process involves a significant degree of uncertainty. In order to deal with uncertainties, various approaches such as chance-constrained programming, stochastic programing with recourse and RSO, fuzzy programing, robust optimization programing, etc., can be recommended. Robust counterpart optimization techniques are commonly used in engineering optimization problems. Set-induced robust counterpart optimization techniques include interval set, combined interval and ellipsoidal, adjustable box, pure ellipsoidal, pure polyhedral, combined interval, ellipsoidal, and polyhedral set. In this paper, robust counterpart optimization formulation based on the box counterpart is applied to the OPPS problem.
 
Methodology and Approaches
In this paper, convex set-based robust formulation is employed to handle the OPPS problem according to the box counterpart. The source of violations/perturbations in block economic value, mining, and processing capacity are considered and these formulations are implemented for hypothetical copper orebody. Several runs were executed on our data sets consisting of 6250 blocks.
 
Results and Conclusions
It has been concluded that the OPPS solutions are sensitive to block economic value volatility and operational capacities in each period of extraction. Based on robust mathematical framework, which quantitatively measures the sensitivity and analyzes its impact on OPPS problems different schedule plans are obtained for 3D blocks of a hypothetical mine; also, terminated in results with some differences in production scheduled NPV.

کلیدواژه‌ها [English]

  • Open-pit
  • Production scheduling
  • Uncertainty
  • Robust optimization
  • Box counterpart

برنامه‌ریزی زمانی معادن روباز و تعیین ترتیب استخراج بلوک­های درون محدوده‌ی نهایی این معادن معمولاً بر مبنای بیشینه­کردن ارزش فعلی خالص[i] صورت می­گیرد. از سال 1960 تاکنون محققین مختلف برای برنامه­ریزی زمانی استخراج بلوک­های معادن روباز الگوریتم­های مختلفی را با پایه­های ابتکاری و ریاضی، و رویکردهای قطعی و غیرقطعی ارائه کرده‌اند. برخی از مهم‌ترین الگوریتم‌ها و روش­های حل ارائه شده برای برنامه‌ریزی با رویکرد قطعی در مراجع [1-11] ارائه شده است.

 



[i] Net present value (NPV)

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