Čedomir Beljić

Shaft location selection at deep multiple orebody deposit by using fuzzy TOPSIS method and network optimization

A shaft is a vertical passageway connecting the surface to ore deposit located deep under surface. The decision on the shaft location is a critical element in the strategic planning for underground mine development system design. Ore deposit is often composed of few independent orebodies located in different places in the space that must be interconnected into one integrated system. In this paper, we examine the case when access points to orebodies lay in the Euclidean plane. We apply fuzzy techniques to incorporate data related to ore reserve and costs into shaft location problem. Fuzzy TOPSIS method is used for the multi-criteria evaluation of the location of the base of the shaft. To identify candidate points (alternatives), we use network optimization based on applying Kruskals algorithm and adding Steiner points. The set of candidate points is given by the union of access and Steiner points.

Evaluation of Underground Zinc Mine Investment Based on Fuzzy-Interval Grey System Theory and Geometric Brownian Motion

Underground mine projects are often associated with diverse sources of uncertainties. Having the ability to plan for these uncertainties plays a key role in the process of project evaluation and is increasingly recognized as critical to mining project success. To make the best decision, based on the information available, it is necessary to develop an adequate model incorporating the uncertainty of the input parameters. The model is developed on the basis of full discounted cash flow analysis of an underground zinc mine project. The relationships between input variables and economic outcomes are complex and often nonlinear. Fuzzy-interval grey system theory is used to forecast zinc metal prices while geometric Brownian motion is used to forecast operating costs over the time frame of the project. To quantify the uncertainty in the parameters within a project, such as capital investment, ore grade, mill recovery, metal content of concentrate, and discount rate, we have applied the concept of interval numbers. The final decision related to project acceptance is based on the net present value of the cash flows generated by the simulation over the time project horizon.

Hybrid model of evaluation of underground lead-zinc mine capacity expansion project using Monte Carlo simulation and fuzzy numbers

Large capital intensive projects, such as those in the mineral resource industry, are often associated with diverse sources of both endogenous and exogenous risks and uncertainties. These risks can greatly influence the project profitability. Having the ability to plan for these uncertainties is increasingly recognized as critical to long-term mining project success. In the mining industry in particular, the relationships between input variables that are controllable, and those that are not, and the physical and economic outcomes are complex and often nonlinear. The value of managerial flexibility is assessed using data on prices, costs, discount rates, grades, ore extraction, and metal output. Monte Carlo simulation of the mean reversion process is used to forecast revenue data based on an initial metal price, by using annualized volatility. Monte Carlo simulation of the Geometric Brownian Motion is used to forecast operating costs. To quantify the uncertainty in the parameters within a project such as capital investment, ore grade, and mill recovery, we used triangular, uniform, and normal statistical distribution, respectively. To decrease uncertainty related to selection of the appropriate discount rate, we have applied the concept of fuzzy sets theory. The result is a Net Present Value (NPV) based on the cash flows generated by the simulation over the timeframe of the project. When using fuzzy numbers, the fuzzy NPV itself is the payoff distribution from the project. The model explains investment behavior satisfactorily, both from a statistical and from an economic point of view.

Optimization of underground mine development system using fuzzy shortest path length algorithm

Graphic mine design elements denote physical entities such as shafts, declines, and drives. Ore deposits are often composed of independent orebodies that must be interconnected into one integrated system. In this paper, we examine a case where access points to orebodies lie in the Euclidean plane. The key question is how to interconnect these points at minimal cost. This design problem is modeled as a network and the solution technique is outlined. We supposed that the locations of access points had been previously determined. To define the ore reserves in each orebody, we used linguistic variables and their transformation to fuzzy triangular numbers. At first, we used Kruskal’s algorithm to identify the minimum spanning tree. After that, by inserting Steiner points we defined a Steiner minimal tree as the global minimum. In a network created in such a way, it is necessary to locate a point called the major mass concentration point to which excavated ore will be delivered; from there, the excavated ore will be hauled or hoisted to a surface breakout point via an optimal development system. In this paper, we use the fuzzy shortest path length procedure to select an optimal development system.