production planning

Production planning in underground mines is still a manual process and there are no suitable tools for optimal production planning for these mines. It is impossible to achieve a real optimum result through manual programming because of the complexity of underground mines and production planning problems in these mines. Due to the increasing consumption of minerals on one hand and the depth of mineral reserves, on the other hand, efforts to achieve comprehensive production planning optimization methods in underground mines and especially large-scale production methods with high production rates are inevitable. Among the underground mining methods, sublevel caving is a common method for hard rock mining, and there are very few studies of long-term production planning for this method. In this paper, a new mathematical model with the aim of maximizing the net present value (NPV) is presented to optimize the production planning of the sublevel caving method. The technical and operational constraints of the sublevel caving method such as development constraints, production capacity, sublevels geometry, and storage access are included in this model. The proposed model was implemented on an economic block model and the maximum NPV was determined. A comparison of the results obtained with the results of manual planning shows a significant increase in NPV mining operations.

Production planning defines the drawpoint extraction percentage in order to a deterministic destination (processing factory) according to scheduling objectives. One of the main problems in such planning is related to the lack of integration designing factors. So, there is a need to develop a model for mine scheduling using all factors influencing the strategic plan. In the current study, the Mixed Integer Linear Programming (MILP) has been developed according to metallurgical constraints. The maximum and minimum cut of grade as well as relative grade constraints are used to produce a real production from drawpoints according to the dilution control. The CPLEX software is used as a MILP solving framework, and also MATLAB to develop mathematical models. The application of the models based on metallurgical constraints was validated using 85 drawpoints over 12 periods. The results showed that in usual condition, the reduction of NPV was only 9% with the proportional non-distribution of average grade 24% of the maximum grade in the drawpoints, while by applying the metallurgical constraint this was reduced to 4%. Finally applying the metallurgical constraints with other operational constraints presented the real production planning.

Uncertainties of economic parameters have an indispensable role in mining evaluation projects. Therefore, evaluation of a mining project without considering the available uncertainties is incorrect and unreliable. Metal price uncertainty is the most important parameter in a mine economic uncertainty. Many researchers have studied the role of economic uncertainties in the production planning. But majority of these studies are conducted in one-element deposits and the two-element deposits are rarely investigated. In this research the binomial tree technique valuation is used to compute the production planning evaluation in two element deposits for price uncertainty. It is concluded that the mine evaluation suggests greater net present value when price uncertainty is considered for both element. 

The main sources of uncertainty arising at the beginning of a mine project can be categorized into three groups: geology uncertainties, engineering uncertainties and economic uncertainties. Many researchers studied these types of uncertainties. In majority of the aforementioned researches, price uncertainty effect was investigated only for one- element deposits, which can result in an inaccurate valuation. Therefore, in this paper, the binomial tree method was used for determining the effect of price uncertainty in valuation of two-element deposits. 

In this research the binomial tree technique valuation is used to compute the production planning evaluation in two element deposits for price uncertainty in four scenarios: Assuming price certainty for both elements; assuming price uncertainty for first element and price certainty for second element; assuming price certainty for first element and price uncertainty for second element; assuming price uncertainty for both elements. 

It is concluded that the mine evaluation suggests least NPV of 245.05 thousand dollars when price certainty is considered for both elements and greater NPV of 349.6 thousand dollars when price uncertainty is considered for both elements. The sensitivity analysis showed that even by changing input economic parameters, the NPV, which was computed in price uncertain for both elements, was the greatest.