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In this work, we propose a 3D dynamic optimization model that enables the design of an underground mine ore pass system with uncertainties. Ore transportation costs and ore pass development costs are quantified by triangular fuzzy numbers. Transportation costs are treated as production costs, and they vary over the duration of mining operation, while development costs of ore passes are treated as an investment, and they are treated as constant. The developed model belongs to the class of fuzzy 0–1 linear programming models, where the fuzzy objective cost function achieves a minimum value, with respect to given set of techno-dynamic constraints. Searching for optimal value in the fuzzy environment is a hard task, and because of that, we developed a new ranking function which transforms the fuzzy optimization model into a crisp one. A triangular fuzzy number can be presented as a triangular graph G(V,E) composed of vertices and edges. The x-coordinate of the Torricelli point of a triangular graph presents the crisp value of a triangular fuzzy number. The use of this model lets us know the optimal number of ore passes, optimal location of ore passes, and optimal dynamic ore transportation plan.

Excessive delays of railway traffic at border crossing points as a consequence of poor planning of border crossing procedures lower the performance of train service, increase its cost and reduce the satisfaction of shippers. Mid-term prediction of traffic flows may improve the process of planning border-crossing activities. In this paper, we model the intensity of cross-border railway traffic on the Alpine-Western Balkan Rail Freight Corridor (AWB RFC). For each of the four border crossing points: Dimitrovgrad, Presevo, Sid and Subotica, time series composed of 102 monthly export and import railway freight traffic observations are used for training and testing of alternative forecasting models. Traditional ARIMA, Long-Short-Term Memory (LSTM) neural network, hybrid ARIMA-LSTM and Singular Spectrum Analysis (SSA) models, are fitted to each of the eight time series. To enable the practical applicability of the proposed approach the “Best fit forecast” tool is developed.

М60 М64

Multiple criteria decision making (MCDM) is a supporting tool which is widely spread in different areas of science and industry. Many researchers have confirmed that MCDM methods can be useful for selecting the best solution in many different problems. In this paper, two novel methods are presented and applied on existing decision-making processes in the mining industry. The first method is multiple criteria ranking by alternative trace (MCRAT) and the second is ranking alternatives by perimeter similarity (RAPS). These two novel methods are demonstrated in decision-making problems and compared with the ranking of the same alternatives by other MCDM methods. The mining process often includes drilling and blasting operations as the most common activities for exploitation of raw materials. For optimal blasting design it is important to select the most suitable parameters for the blasting pattern and respect characteristics of the working environment and production conditions. By applying novel methods, how to successfully select the most proper blasting pattern respecting all conditions that must be satisfied for economic aspects and the safety of employees and the environment is presented.

12 3710 14 M20 М22 Underground mining engineers and planners in our country are faced with extremely difficult working conditions and a continuous shortage of money. Production disruptions are frequent and can sometimes last more than a week. During this time, gate road support is additionally exposed to rock stress and the result is its progressive deformation and the loss of functionality of gate roads. In such an environment, it is necessary to develop a low-cost methodology to maintain a gate road support system. For this purpose, we have developed a model consisting of two main phases. The first phase is related to support deformation monitoring, while the second phase is related to data analysis. To record support deformations over a defined time horizon we use laser scanning technology together with multivariate singular spectrum analysis to conduct data processing and forecasting. Fuzzy time series is applied to classify the intensity of displacements into several independent groups (clusters).

Accurate metal price forecasting is the precondition for optimal and sustainable mine production planning. This paper combined two methods for time series analysis. The developed model represents the combination of the Grey System Theory and a Stochastic differential equation. More precisely, we added stochastic term to the first-order whitenization differential equation. Solution of this equation represents the time response function which is capable of creating artificial evolving paths of the metal price. The simulation process resulted in a distribution and adequate expected value at every single point. Further, model efficiency was increased by adding residuals modeled by the Singular Spectrum Analysis method. The model was tested on the monthly lead metal price series. Mean absolute percentage error is 4.37% and the model can be classified as a high-performance model.

Production planning in an underground mine plays a key activity in the mining company business. It is supported by the fact that mineral industry is unique and volatile environment. There are two uncertain parameters that cannot be managed by planners, metal price, and operating costs. Having ability to quantify and incorporate them in the process of planning can help companies to do their business in much easier way. We quantify these uncertainties by the simulation of mean reverting process and Itô-Doob stochastic differential equation, respectively. Mineral deposit is represented as a set of mineable blocks and room and pillar mining method is selected as a way of mining. Multicriteria clustering algorithm is used to create areas inside of mineral deposit that have technological characteristics required by the planners. We also developed a way to forecast the volatility of economic values of these areas through the planning period. Fuzzy 0-1 linear programming model is used to define the sequence of mining of these areas by maximization of the expected value of the fuzzy future cash flow. Model was tested on small hypothetical lead-zinc mineral deposit and results showed that our approach was able to solve such complex problem.

Meeting investment and operating goals with presence of different sources of uncertainties and operational constraints is critical for a successful underground mining operation and even for a mining company to survive. Small and large mining businesses are all affected by business environment. Production planning that takes into account real strength of the mining company requires from the owner or management of the company to set up acceptable and achievable investment goals (targets). In this paper we propose the production planning model that minimizes deviation from Acceptable Rate Of Return (AROR). Besides the AROR, there are operating goals success that should be also realized with minimum deviation from target values. Accordingly, the production planning can be treated as a multi-objective problem. All these objectives are integrated in multi-variable weighted Frobenius distance function that measures the deviation from established targets. Ore body is represented as a set of mineable blocks and room and pillar mining method is selected as a way of mining. We apply a multi-objective iterated greedy algorithm to define a set of blocks that should be mined every year such that deviations from target values are less than or equal to given errors of minimization. Uncertainty of metal price and operating costs are treated by mean reversion process and Geometric Brownian motion respectively. Algorithm was tested on small hypothetical lead-zinc ore body.

The uncertainty that dominates in the functioning of the electricity market is of great significance and arises, generally, because of the time imbalance in electricity consumption rates and power plants&rsquo, production capacity, as well as the influence of many other factors (weather conditions, fuel costs, power plant operating costs, regulations, etc.). In this paper we try to incorporate this uncertainty in the electricity price forecasting model by applying interval numbers to express the price of electricity, with no intention of exploring influencing factors. This paper represents a hybrid model based on fuzzy C-mean clustering and the interval-valued autoregressive process for forecasting the short-term electricity price. A fuzzy C-mean algorithm was used to create interval time series to be forecasted by the interval autoregressive process. In this way, the efficiency of forecasting is improved because we predict the interval, not the crisp value where the price will be. This approach increases the flexibility of the forecasting model.

The results of multi-criteria decision making (MCDM) for the selection of the optimum sulfide mineral collector and dose rate in a flotation study are presented. Laboratory scale flotation tests were performed to investigate selective flotation of galena from lead–zinc sulfide ores using several different xanthates at different dose rates. The flotation results show that the different tests result in changes lead concentrate grade, lead recoveries and selectivity against zinc. According to the selection criteria to maximize lead concentrate grades and recoveries while minimizing zinc concentrate grades as different factors, decision making and final selection of the optimum collector and dose rates are not simple since there is multiple options and outcomes to consider. A technique for order preference by similarity to ideal solution (TOPSIS), as well-known MCDM method, has been used for ranking xanthates not only using technological, but also economical factors. The results obtained show that MCDM is a useful tool for ranking and selection of tested collectors in flotation because of the ability to evaluate all factors fixed in flotation tests. The final step is a developed mathematical model for selection of optimal collector.

Methodology for long-term underground lead-zinc mine planning based on fuzzy inventory theory is presented in this paper. We developed a fuzzy stochastic model of inventory control problem for planning lead-zinc ore production under uncertainty. The final purpose of this article is to find the optimal quantity of mined ore that should be stockpiled, in order to enable “feeding” of mineral processing plant in cases when the production in underground mine is interrupted, by using Possibilistic mean value of fuzzy number for defuzzing the fuzzy total annual inventory costs, and by using Extension of the Lagrangean method for solving inequality constrain problem. The different types of costs involved in mined ore inventory problems affect the efficiency of production scheduling. Dynamic nature of lead and zinc metal price is described by Ornstein-Uhlenbeck stochastic mean reverting process. The model is illustrated with a numerical example.

Forecasting the operational efficiency of an existing underground mine plays an important role in strategic planning of production. Degree of Operating Leverage (DOL) is used to express the operational efficiency of production. The forecasting model should be able to involve common time horizon, taking the characteristics of the input variables that directly affect the value of DOL. Changes in the magnitude of any input variable change the value of DOL. To establish the relationship describing the way of changing we applied multivariable grey modeling. Established time sequence multivariable response formula is also used to forecast the future values of operating leverage. Operational efficiency of production is often associated with diverse sources of uncertainties. Incorporation of these uncertainties into multivariable forecasting model enables mining company to survive in today’s competitive environment. Simulation of mean reversion process and geometric Brownian motion is used to describe the stochastic diffusion nature of metal price, as a key element of revenues, and production costs, respectively. By simulating a forecasting model, we imitate its action in order to measure its response to different inputs. The final result of simulation process is the expected value of DOL for every year of defined time horizon.

Large scale mining as a method of extraction of mineral raw materials have a growing application with the aim to increase the quantity of blasted mass, and to reduce costs of production as well. Increasing the quantity of blasted mass requires the use of large amounts of explosives, leading to an increase in the negative effects of mining. Under negative effects of mining the seismic effect of blasting, effect of air waves, sound effect, scattering the blasted rock mass, and similar are assumed. In order both to evaluate and control the seismic effect of blasting, as well as to plan it, the determination of soil oscillation law is required, with the strike: mine field - facilities to be protected. One of the most commonly used equations is that of M.A. Sadovski defining the law of alteration in the oscillation velocity of the soil depending on distance, explosive amount, and conditions of blasting and geologic characteristics of the soil, being determined on the basis of test blasting for the specific work environment. The Sadovsky equation is determined based on trial minings for a specific work environment. In this paper, a special attention was paid to the seismic effect of blasting. In accordance with this, an analysis of the method for determining the soil oscillation law parameters, proposed by the Russian professor M.A. Sadovsky, was performed. For determination of parameters in the Sadovsky equation, in addition to the usual model - the least squares method, one more model is shown with the use of Lagrange's theorem. Thereby, it has been stated that both models can be used to calculate the oscillation velocity of the rock mass.

In this paper, a fuzzy programming model, incorporating fuzzy measures of costs and ore reserves, is developed to evaluate different design alternatives in the context of the selection of the underground mine development system. The bauxite deposit is usually mined using the sublevel mining method. This method extracts the ore via sublevels, which are developed in the ore body at regular vertical spacing. In such an environment, we consider the development system as a weighted network interconnecting all sublevels with surface breakout point using the minimum cost of development and haulages. Selection of the optimal development system is based on the application of Convex Index and composite rank. The uncertainties related to the future states of transportation costs are modeled with a special stochastic process, the Geometric Brownian Motion. The results indicate that this model can be applied for solving underground mine development problems.

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 wi...

This paper gives an analysis the method for determining the parameters of soil oscillation law, suggested by Professor M. A. Sadovski as well as the level of its applicability for blasting with commercial explosives for the needs of mining and other economic activities. The applicability of this law was analyzed on examples of mass blasting at the Open Pit 'Drenovac' that are carried out for deposit mining. As the relation between the soil oscillation velocity and basic parameters affecting its magnitude, are the following: the amount of explosive, distance from the blasting site, characteristics of the rock material and type of blasting, the equation of M. A. Sadovski, where the oscillation velocity v is given in the form of of the function, is most frequently used: v = K . R-n , where R is reduced distance, and K and n parameters conditioned by soil characteristics and blasting conditions, thereby v is decreasing and convex function of variable R. To determine parameters in the equation of Sadovski, in addition to the common method of least squares, another model was applied. There by, it has been stated that both models can be used to calculate the oscillation velocity of the rock mass.

There are typically many of variables, which are directly or indirectly associated with the value of underground mine project. Having the ability to plan for uncertainties of input variables is increasingly recognized as critical to longterm mining project success. Large capital intensive projects, such as those in the mineral resource industry, are often associated with diverse sources of both internal and external uncertainties. One of the most external influencing uncertainties is related to the future states of metal price. There are many methods which are applied to forecast the future metal prices, but Mean Reversion Process is one of the most applying methods. This paper analyzes the possibility of using of Grey System Theory to metal price forecasting by examining the correlation between results obtained by these two methods. Intra-class Correlation Coefficient is used as a measure of reliability.

The main aim of a coal deposit model is to provide an effective basis for mine production planning. The most applied approach is related to block modeling as a reasonable global representation of the coal deposit. By selection of adequate block size, deposits can be well represented. A block has a location in XYZ space and is characterized by adequate attributes obtained from drill holes data. From a technological point of view, i.e., a thermal power plant’s requirements, heating value, sulfur and ash content are the most important attributes of coal. Distribution of attributes’ values within a coal deposit can vary significantly over space and within each block as well. To decrease the uncertainty of attributes’ values within blocks the concept of fuzzy triangular numbers is applied. Production planning in such an environment is a very hard task, especially in the presence of requirements. Such requirements are considered as target values while the values of block attributes are the actual values. To make production planning easier we have developed a coal deposit model based on clustering the relative closeness of actual values to the target values. The relative closeness is obtained by the TOPSIS method while technological clusters are formed by fuzzy C-mean clustering. Coal deposits are thus represented by multi-attribute technological mining cuts.

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 Kruskal's algorithm and adding Steiner points. The set of candidate points is given by the union of access and Steiner points.

Having the ability to forecast groundwater levels is very significant because of their vital role in basic functions related to efficiency and the sustainability of water supplies. The uncertainty which dominates our understanding of the functioning of water supply systems is of great significance and arises as a consequence of the time-unbalanced water consumption rate and the deterioration of the recharge conditions of captured aquifers. The aim of this paper is to present a hybrid model based on fuzzy C-mean clustering and singular spectrum analysis to forecast the weekly values of the groundwater level of a groundwater source. This hybrid model demonstrates how the fuzzy C-mean can be used to transform the sequence of the observed data into a sequence of fuzzy states, serving as a basis for the forecasting of future states by singular spectrum analysis. In this way, the forecasting efficiency is improved, because we predict the interval rather than the crisp value where the level will be. It gives much more flexibility to the engineers when managing and planning sustainable water supplies. A model is tested by using the observed weekly time series of the groundwater source, located near the town of Čačak in south-western Serbia.

When deposit is composed of few ore bodies it is necessary to interconnect them into one integrated system. Suppose the deposit characteristics indicate that decline development system is preferred one. In such environment we treat development of an underground mine as access infrastructure composed of different decline sections. Access infrastructure designing can be treated as spanning the spatial network which will connect all main terminals (points). In our model we defined spatial network by adequate nonlinear constrained objective function representing the cost of mine development and ore haulage. To find the minimum value of the objective function we use Genetic algorithm.

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.

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.

Rudarstvo, a u okviru njega i priprema mineralnih sirovina, se odlikuje složenošću tehnoloških procesa što je posledica velikog broja uticajnih parametara. Samim tim je potrebno biti veoma obazriv prilikom donošenja odluka u oblasti rudarstva. U cilju što efikasnijeg funkcionisanja procesa, moguće je primeniti različite metode koje služe za pojednostavljenje procesa odlučivanja. Jedna od takvih metoda jeste i teorija grubih skupova. Ona predstavlja relativno novu matematičku teoriju koja je pogodna za razumevanje nepreciznih i nepotpunih podataka kao i za otkrivanje međusobnih odnosa između tih podataka.Teorija grubih skupova je pronašla primenu u različitim granama industrije, međutim pregledom literature došlo se do zaključka da primenjivost ove teorije u rudarstvu nije dovoljno ispitana. To je bila polazna osnova doktorske disertacije, ispitivanje mogućnosti njene primene u oblasti rudarstva.U okviru eksperimentalnog dela disertacije izvršeno je testiranje mogućnosti primene teorije grubih skupova za rešavanje tri problema: izbor lokacije za flotacijsko jalovište, izbor flotacijskog kolektora i izbor flotacione mašine. Određeni su parametri koji imaju najviše uticaja prilikom ova tri izbora, odnosno određeni su kriterijumi za izbor. Izabranim kriterijumima su dodeljene odgovarajuće vrednosti, a nakon toga je izvršeno vrednovanje predloženih subjekata. Na taj način je izvršena primena teorije grubih skupova za rešavanje datih problema. Na kraju, nakon analize primenom teorije grubih skupova, izvršena je provera dobijenih rezultata metodama višekriterijumskog odlučivanja: VIKOR, AHP, ELECTRE, PROMETHEE i TOPSIS.Na osnovu dobijenih rezultata se došlo do zaključka da je u sva tri problema uspešno primenjena teorija grubih skupova. Poklapanje rezultata dobijenih metodom grubih skupova sa rezultatima dobijenim ostalim metoda višekriterijumskog odlučivanja se kreće od 100% poklapanja u slučaju izbora lokacije za flotacijsko jalovište, do 40% u slučaju izbora flotacijskog kolektora i flotacione mašine. Visoki koeficijenti korelacija demonstriraju visoku osetljivost metode grubih skupova u uslovima višekriterijumskog odlučivanja i determinišu njenu upotrebljivost u uslovima nedovoljnosti podataka. Mining, and mineral processing within it, is characterized by the complexity of the technological process due to the large number of influential parameters. Therefore it is necessary to be very cautious when making decisions in the field of mining. In order to provide a more efficient functioning of the processes, it is possible to apply methods that are used to streamline the decision-making process. One such method is the rough set theory. It is a relatively new mathematical theory that is suitable for understanding imprecise and incomplete data as well as to detect relationships between these data.The rough set theory has found application in various areas of industry, however, by reviewing literature it was concluded that the applicability of this theory in mining has not been sufficiently investigated. This was the starting point of a doctoral dissertation, examining the possibilities of its application in mining.In the experimental part of the dissertation was done testing the possibilities for application of rough set theory to solve three problems: choosing location for the flotation tailings landfill, choosing flotation collector and choosing flotation machine. The parameters that have the most influence during these three choices were determined, and they represented criteria for selection. The selected criteria were assigned with appropriate value, and subsequently the evaluation of the proposed subjects was carried out. In this way, rough set theory was applied for solving the given problems. Finally, results obtained by rough set theory, were verified by multi-criteria decision-making methods: VIKOR, AHP, ELECTRE, PROMETHEE and TOPSIS.Based on results it was concluded that rough set theory was successfully applied in all three problems. The superposition of the results obtained by the rough set theory with the results from other multi-criteria decision-making methods varies from 100% in the case of the choosing location for the flotation tailings landfill, to 40% in the case of choosing flotation collectors and flotation machines. High correlation coefficients demonstrate the high sensitivity of the rough set theory in terms of multi-criteria decision-making and define its usefulness in terms of insufficiency of data. mining, mineral procesing, rough set theory, multi-criteria decision-making, flotation tailings landfill, flotation collector, flotation machine

Nakon mnogih geoloških istraživanja i eksploatacije Jame – Bor, pristupiće se otkopavanju sulfidnog ležišta bakra „Borska reka“ iznad XIX horizonta. Da bi se postigli najbolji rezultati prilikom eksploatacije ležišta, primenjena je komorno-stubna metoda sa blokovskim otkopavanjem i zasipavanjem otkopa pastom. Tehno-ekonomska ocena opravdanosti eksploatacije rude bakra iz ležišta „Borska reka“ sa očuvanjem površine terena, urađena je na bazi projektovanih parametara datih u tehničkom projektu. Analiziran je i ocenjen vek projekta – prvih 10 godina od 25 godina, koje predstavljaju ukupni vek trajanja eksploatacije. Procenjeno je da je investicioni projekat u celini rentabilan i ekonomski potpuno opravdan.

Investiciono okruženje skopčano sa rudarskom industrijom je veoma svojstveno kada seuporedi sa okruženjima koje susrećemo u tipičnim proizvodnim industrijama. Neke odkarakterisitka rudarstva, koje su često naznačene kao jedinstvene su: visok intenzitetinvesticija, dugi predproizvodni periodi, visok rizik i neobnovljivost resursa.Investiranje u sistem otvaranja rudnika predstavlja dobar primer ireverzibilneinvesticije. Takva investicija zahteva pažljivu analizu, jer nakon njene realizacije ona sene može nadoknaditi bez značajnog gubitka vrednosti. Očigledno je da izbor sistemaotvaranja podzemnog rudnika pripada strateškom planiranju... The investment environment associated with the mining industry is unique whencompared with the environment encountered by typical manufacturing industries. Someof the characteristics of mining which are often proclaimed as unique are as follows:capital intensity, long preproduction periods, high risk and non-renewable resource.Mines’ development system investments provide a good example of irreversibleinvestment. Such investment requires careful analysis because, once the investmenttakes place, it cannot be recouped without significant loss a value. Obviously, theselection of an underground mine development system belongs to strategic planning... mining; development; networks and graphs; fuzzy sets; stochasticprocesses; convex index, decision support systems