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Mathematical Problems in Engineering
Volume 2015, Article ID 610307, 18 pages
Research Article

Operational Efficiency Forecasting Model of an Existing Underground Mine Using Grey System Theory and Stochastic Diffusion Processes

1The School of Electrical and Computer Engineering of Applied Studies, Vojvode Stepe 283, 11000 Belgrade, Serbia
2Belgrade University College of Applied Studies in Civil Engineering and Geodesy, Department of Geodesy, Hajduk Stanka 2, 11000 Belgrade, Serbia
3Faculty of Mining and Geology, University of Belgrade, Djusina 7, 11000 Belgrade, Serbia

Received 3 August 2015; Revised 28 October 2015; Accepted 29 October 2015

Academic Editor: Paolo Maria Mariano

Copyright © 2015 Svetlana Strbac Savic et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.