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Zoran Gligorić
Faculty of Mining and Geology, University of Belgrade, Đušina 7, 11 000 Belgrade, Serbia

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Journal article
Published: 19 August 2021 in Mathematics
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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.

ACS Style

Katarina Urošević; Zoran Gligorić; Igor Miljanović; Čedomir Beljić; Miloš Gligorić. Novel Methods in Multiple Criteria Decision-Making Process (MCRAT and RAPS)—Application in the Mining Industry. Mathematics 2021, 9, 1980 .

AMA Style

Katarina Urošević, Zoran Gligorić, Igor Miljanović, Čedomir Beljić, Miloš Gligorić. Novel Methods in Multiple Criteria Decision-Making Process (MCRAT and RAPS)—Application in the Mining Industry. Mathematics. 2021; 9 (16):1980.

Chicago/Turabian Style

Katarina Urošević; Zoran Gligorić; Igor Miljanović; Čedomir Beljić; Miloš Gligorić. 2021. "Novel Methods in Multiple Criteria Decision-Making Process (MCRAT and RAPS)—Application in the Mining Industry." Mathematics 9, no. 16: 1980.

Journal article
Published: 21 June 2021 in Energies
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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).

ACS Style

Luka Crnogorac; Rade Tokalić; Zoran Gligorić; Aleksandar Milutinović; Suzana Lutovac; Aleksandar Ganić. Gate Road Support Deformation Forecasting Based on Multivariate Singular Spectrum Analysis and Fuzzy Time Series. Energies 2021, 14, 3710 .

AMA Style

Luka Crnogorac, Rade Tokalić, Zoran Gligorić, Aleksandar Milutinović, Suzana Lutovac, Aleksandar Ganić. Gate Road Support Deformation Forecasting Based on Multivariate Singular Spectrum Analysis and Fuzzy Time Series. Energies. 2021; 14 (12):3710.

Chicago/Turabian Style

Luka Crnogorac; Rade Tokalić; Zoran Gligorić; Aleksandar Milutinović; Suzana Lutovac; Aleksandar Ganić. 2021. "Gate Road Support Deformation Forecasting Based on Multivariate Singular Spectrum Analysis and Fuzzy Time Series." Energies 14, no. 12: 3710.

Journal article
Published: 13 August 2020 in Sustainability
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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.

ACS Style

Zoran Gligorić; Miloš Gligorić; Dževdet Halilović; Čedomir Beljić; Katarina Urošević. Hybrid Stochastic-Grey Model to Forecast the Behavior of Metal Price in the Mining Industry. Sustainability 2020, 12, 6533 .

AMA Style

Zoran Gligorić, Miloš Gligorić, Dževdet Halilović, Čedomir Beljić, Katarina Urošević. Hybrid Stochastic-Grey Model to Forecast the Behavior of Metal Price in the Mining Industry. Sustainability. 2020; 12 (16):6533.

Chicago/Turabian Style

Zoran Gligorić; Miloš Gligorić; Dževdet Halilović; Čedomir Beljić; Katarina Urošević. 2020. "Hybrid Stochastic-Grey Model to Forecast the Behavior of Metal Price in the Mining Industry." Sustainability 12, no. 16: 6533.

Journal article
Published: 01 January 2020 in Podzemni radovi
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The Grey Model (GM) is a powerful tool in the Grey System Theory for estimating the behavior of partially unknown systems or systems with limited information. In the Grey System Theory, GM(1,1) is the most widely used model for prediction. The applicability of this model for the purpose of buildings deformation forecasting in a vertical plane was tested on the case of the deformation forecasting of the building of Faculty of Mining and Geology in Belgrade. The non-equidistance grey model (1,1) was utilized, since the measurements on which the model was formed, were performed in various time intervals. The Grey Model; forecasting; deformation

ACS Style

Aleksandar Milutinović; Zoran Gligorić; Zoran Gojković; Aleksandar Ganić. Forecasting the building deformation using the non-equidistance Grey Model (1,1). Podzemni radovi 2020, 49 -59.

AMA Style

Aleksandar Milutinović, Zoran Gligorić, Zoran Gojković, Aleksandar Ganić. Forecasting the building deformation using the non-equidistance Grey Model (1,1). Podzemni radovi. 2020; (36):49-59.

Chicago/Turabian Style

Aleksandar Milutinović; Zoran Gligorić; Zoran Gojković; Aleksandar Ganić. 2020. "Forecasting the building deformation using the non-equidistance Grey Model (1,1)." Podzemni radovi , no. 36: 49-59.

Research article
Published: 27 June 2019 in Mathematical Problems in Engineering
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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.

ACS Style

Miloš V. Gligorić; Zoran M. Gligorić; Čedomir R. Beljić; Suzana Lutovac; Vesna M. Damnjanović. Long-Term Room and Pillar Mine Production Planning Based on Fuzzy 0-1 Linear Programing and Multicriteria Clustering Algorithm with Uncertainty. Mathematical Problems in Engineering 2019, 2019, 1 -26.

AMA Style

Miloš V. Gligorić, Zoran M. Gligorić, Čedomir R. Beljić, Suzana Lutovac, Vesna M. Damnjanović. Long-Term Room and Pillar Mine Production Planning Based on Fuzzy 0-1 Linear Programing and Multicriteria Clustering Algorithm with Uncertainty. Mathematical Problems in Engineering. 2019; 2019 ():1-26.

Chicago/Turabian Style

Miloš V. Gligorić; Zoran M. Gligorić; Čedomir R. Beljić; Suzana Lutovac; Vesna M. Damnjanović. 2019. "Long-Term Room and Pillar Mine Production Planning Based on Fuzzy 0-1 Linear Programing and Multicriteria Clustering Algorithm with Uncertainty." Mathematical Problems in Engineering 2019, no. : 1-26.

Journal article
Published: 23 May 2019 in Symmetry
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When considering data and parameters in hydrogeology, there are often questions of uncertainty, vagueness, and imprecision in terms of the quantity of spatial distribution. To overcome such problems, certain data may be subjectively expressed in the form of expert judgment, whereby a heuristic approach and the use of fuzzy logic are required. In this way, decision-making criteria relating to an optimal groundwater control system do not always have a numerical value. Groundwater control scenarios (alternatives) are identified through hydrodynamic modeling of the aquifer, providing an indication of their effectiveness. The paper develops a fuzzy-stochastic multi-criteria decision-making model to deal with a topical problem: selection of the most suitable groundwater control system for an open-cast mine. Both real numerical and linguistic variables are used to express the values of all criteria that affect the final decision. In particular, it should be pointed out that the values of the criteria are varied over a predefined time horizon. For mathematical calculations, fuzzy dynamic TOPSIS and the stochastic diffusion process—geometric Brownian motion—were used. The proposed method is tested in a case study: the selection of an optimal groundwater control system for an open-cast mine.

ACS Style

Dušan Polomčić; Zoran Gligorić; Dragoljub Bajić; Miloš Gligorić; Milanka Negovanović. Multi-Criteria Fuzzy-Stochastic Diffusion Model of Groundwater Control System Selection. Symmetry 2019, 11, 705 .

AMA Style

Dušan Polomčić, Zoran Gligorić, Dragoljub Bajić, Miloš Gligorić, Milanka Negovanović. Multi-Criteria Fuzzy-Stochastic Diffusion Model of Groundwater Control System Selection. Symmetry. 2019; 11 (5):705.

Chicago/Turabian Style

Dušan Polomčić; Zoran Gligorić; Dragoljub Bajić; Miloš Gligorić; Milanka Negovanović. 2019. "Multi-Criteria Fuzzy-Stochastic Diffusion Model of Groundwater Control System Selection." Symmetry 11, no. 5: 705.

Journal article
Published: 10 September 2018 in Resources Policy
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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.

ACS Style

Zoran Gligoric; Milos Gligoric; Bojan Dimitrijevic; Ines Grozdanovic; Aleksandar Milutinovic; Aleksandar Ganic; Zoran Gojkovic. Model of room and pillar production planning in small scale underground mines with metal price and operating cost uncertainty. Resources Policy 2018, 65, 1 .

AMA Style

Zoran Gligoric, Milos Gligoric, Bojan Dimitrijevic, Ines Grozdanovic, Aleksandar Milutinovic, Aleksandar Ganic, Zoran Gojkovic. Model of room and pillar production planning in small scale underground mines with metal price and operating cost uncertainty. Resources Policy. 2018; 65 ():1.

Chicago/Turabian Style

Zoran Gligoric; Milos Gligoric; Bojan Dimitrijevic; Ines Grozdanovic; Aleksandar Milutinovic; Aleksandar Ganic; Zoran Gojkovic. 2018. "Model of room and pillar production planning in small scale underground mines with metal price and operating cost uncertainty." Resources Policy 65, no. : 1.

Journal article
Published: 22 July 2018 in Energies
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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’ 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.

ACS Style

Zoran Gligorić; Svetlana Štrbac Savić; Aleksandra Grujić; Milanka Negovanović; Omer Musić. Short-Term Electricity Price Forecasting Model Using Interval-Valued Autoregressive Process. Energies 2018, 11, 1911 .

AMA Style

Zoran Gligorić, Svetlana Štrbac Savić, Aleksandra Grujić, Milanka Negovanović, Omer Musić. Short-Term Electricity Price Forecasting Model Using Interval-Valued Autoregressive Process. Energies. 2018; 11 (7):1911.

Chicago/Turabian Style

Zoran Gligorić; Svetlana Štrbac Savić; Aleksandra Grujić; Milanka Negovanović; Omer Musić. 2018. "Short-Term Electricity Price Forecasting Model Using Interval-Valued Autoregressive Process." Energies 11, no. 7: 1911.

Journal article
Published: 19 July 2017 in Water
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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.

ACS Style

Dušan Polomčić; Zoran Gligorić; Dragoljub Bajić; Čedomir Cvijović. A Hybrid Model for Forecasting Groundwater Levels Based on Fuzzy C-Mean Clustering and Singular Spectrum Analysis. Water 2017, 9, 541 .

AMA Style

Dušan Polomčić, Zoran Gligorić, Dragoljub Bajić, Čedomir Cvijović. A Hybrid Model for Forecasting Groundwater Levels Based on Fuzzy C-Mean Clustering and Singular Spectrum Analysis. Water. 2017; 9 (7):541.

Chicago/Turabian Style

Dušan Polomčić; Zoran Gligorić; Dragoljub Bajić; Čedomir Cvijović. 2017. "A Hybrid Model for Forecasting Groundwater Levels Based on Fuzzy C-Mean Clustering and Singular Spectrum Analysis." Water 9, no. 7: 541.

Journal article
Published: 15 December 2016 in Energies
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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.

ACS Style

Miloš Gligorić; Zoran Gligorić; Čedomir Beljić; Slavko Torbica; Svetlana Štrbac Savić; Jasmina Nedeljković Ostojić. Multi-Attribute Technological Modeling of Coal Deposits Based on the Fuzzy TOPSIS and C-Mean Clustering Algorithms. Energies 2016, 9, 1059 .

AMA Style

Miloš Gligorić, Zoran Gligorić, Čedomir Beljić, Slavko Torbica, Svetlana Štrbac Savić, Jasmina Nedeljković Ostojić. Multi-Attribute Technological Modeling of Coal Deposits Based on the Fuzzy TOPSIS and C-Mean Clustering Algorithms. Energies. 2016; 9 (12):1059.

Chicago/Turabian Style

Miloš Gligorić; Zoran Gligorić; Čedomir Beljić; Slavko Torbica; Svetlana Štrbac Savić; Jasmina Nedeljković Ostojić. 2016. "Multi-Attribute Technological Modeling of Coal Deposits Based on the Fuzzy TOPSIS and C-Mean Clustering Algorithms." Energies 9, no. 12: 1059.

Research article
Published: 23 July 2014 in Journal of Applied Mathematics
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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.

ACS Style

Zoran Gligoric; Lazar Kricak; Cedomir Beljic; Suzana Lutovac; Jelena Milojević. Evaluation of Underground Zinc Mine Investment Based on Fuzzy-Interval Grey System Theory and Geometric Brownian Motion. Journal of Applied Mathematics 2014, 2014, 1 -12.

AMA Style

Zoran Gligoric, Lazar Kricak, Cedomir Beljic, Suzana Lutovac, Jelena Milojević. Evaluation of Underground Zinc Mine Investment Based on Fuzzy-Interval Grey System Theory and Geometric Brownian Motion. Journal of Applied Mathematics. 2014; 2014 ():1-12.

Chicago/Turabian Style

Zoran Gligoric; Lazar Kricak; Cedomir Beljic; Suzana Lutovac; Jelena Milojević. 2014. "Evaluation of Underground Zinc Mine Investment Based on Fuzzy-Interval Grey System Theory and Geometric Brownian Motion." Journal of Applied Mathematics 2014, no. : 1-12.

Articles
Published: 21 May 2014 in Journal of the Chinese Institute of Engineers
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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.

ACS Style

Zoran Milan Gligoric; Cedomir Rajko Beljic; Sasa Miladin Jovanovic; Cedomir Miodrag Cvijovic. Optimization of underground mine development system using fuzzy shortest path length algorithm. Journal of the Chinese Institute of Engineers 2014, 37, 965 -982.

AMA Style

Zoran Milan Gligoric, Cedomir Rajko Beljic, Sasa Miladin Jovanovic, Cedomir Miodrag Cvijovic. Optimization of underground mine development system using fuzzy shortest path length algorithm. Journal of the Chinese Institute of Engineers. 2014; 37 (8):965-982.

Chicago/Turabian Style

Zoran Milan Gligoric; Cedomir Rajko Beljic; Sasa Miladin Jovanovic; Cedomir Miodrag Cvijovic. 2014. "Optimization of underground mine development system using fuzzy shortest path length algorithm." Journal of the Chinese Institute of Engineers 37, no. 8: 965-982.

Journal article
Published: 01 January 2014 in Podzemni radovi
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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.

ACS Style

Zoran Gligoric; Aleksandar Ganic; Rade Tokalic; Aleksandar Milutinovic; Gligorić Zoran; Ganić Aleksandar; Tokalić Rade. Optimisation of underground mine decline development system using genetic algorithm. Podzemni radovi 2014, 22, 33 -40.

AMA Style

Zoran Gligoric, Aleksandar Ganic, Rade Tokalic, Aleksandar Milutinovic, Gligorić Zoran, Ganić Aleksandar, Tokalić Rade. Optimisation of underground mine decline development system using genetic algorithm. Podzemni radovi. 2014; 22 (25):33-40.

Chicago/Turabian Style

Zoran Gligoric; Aleksandar Ganic; Rade Tokalic; Aleksandar Milutinovic; Gligorić Zoran; Ganić Aleksandar; Tokalić Rade. 2014. "Optimisation of underground mine decline development system using genetic algorithm." Podzemni radovi 22, no. 25: 33-40.