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A mathematical optimisation approach to modelling the economics of a coal mine
Abstract
A mathematical model of a multi-product coal mining project is proposed to characterise the economics governing coal production. The model accounts for mining cost variation due to varying production levels, changes in reserves available for extraction by means of a cut-off parameter, as well as lead-time delays between investment and when operations begin. The resulting constrained optimisation problem is solved computationally by maximising the net present value of future cash flows from the mining operation subject to physical limitations. We find that the capital investment problem has greater bearing on the overall project configuration decision and that changes in production capital are made throughout the life of the project while production volumes are largely unchanged.
... A similar formulation for capital investment appears as a term in the objective function of the coal mining optimisation presented in Rademeyer et al. (2019). There is however no motivation given for the viability of this formulation. ...
... The models would be useful to commodity analysts for simulating the lag between project investment and commodity production in market studies. This is seen in Rademeyer et al. (2019) where the model appears as a term representing production capacity in the objective function of the cash flow optimisation problem. In fact, it is the right-hand term of Eq. 3 in Section "Deriving a model of capacity investment with lead-time" that is used. ...
... In fact, it is the right-hand term of Eq. 3 in Section "Deriving a model of capacity investment with lead-time" that is used. Rademeyer et al. (2019) solve the cash flow optimisation and this yields results which are consistent with what might be seen for real-life mining operations. ...
In the development of mining projects, there is a period in between commitment of finance and production commencement. Risks are present in various aspects of development such that production start-up could be delayed, thereby affecting the value of the project. This paper demonstrates the application of convolution in the capital investment problem for projects with long lead-times as a means of characterising the relationship between capital invested and the materialisation of capacity for production to begin. The system is functionally similar to that of a causal linear time-invariant system in signal processing. We find that the filter for capital projects, affecting the rate at which capacity becomes available for use, can be approximated by a straight-line function with positive gradient on bounded support contained in the positive time domain. The deterministic version is derived and evaluated, and uncertainty is simulated in the stochastic version, where variance results from the presence of a random process in the form of a standard Brownian motion.
... This is because mining firms are mainly competing in the matter of cost (Bomsel et al., 1996). Cost estimates are significant in the decisions regarding whether a mining project will be applied or not Çetin, 2007a, 2007b;Dehghani et al., 2014;Mohutsiwa and Musingwini, 2015;Nourali and Osanloo, 2019;Rademeyer et al., 2019). Business managers need cost data that are trustworthy, objective, and obtainable on time to take precautions against various risks they may face and to develop strategies to minimize the risks (Uygun, 2014a(Uygun, , 2014bAjak et al., 2018;Groeneveld et al., 2019;Mai et al., 2019). ...
In Turkey, for mining enterprises to realize their activities and conduct mining production, they are obliged to pay operating license fees annually. This obligation starts from the date of operating license application, about 1–1.5 years before the enterprises obtain a production permit. In recent years, an increase in the operating license fees has occurred as a result of the amendments made in the mining legislation. These increases made in the fees might become revenue loss in the forthcoming years despite creating an increase in the revenues of the state. In Turkey, according to Law No.7164 came into force in 2019, mineral groups, operating license areas and periods are considered in the calculation of operating license fee. In this direction, these factors in the fee calculation were used in the calculations by means of the answers given by enterprises through SurveyMonkey program. These fees paid to start from the mining operating license application to obtaining an operation permit are included in the investment cost. These costs were proportioned to the investment costs of the enterprises. Fees paid after obtaining an operation permit are operating costs. And, these fees were proportioned to the operating costs of the enterprises. Also, operating license fees per hectare were calculated. All these data were compared for the legislation periods 2005–2015, 2016–2019, 2020 and after in Turkey. An increase of 98% on average on US basis in 2021 compared to 2020 due to the license period being considered in the new calculation formula. Although the rate of increase decreases every year, increases close to this rate will emerge. Mining enterprises should be responsible for the calculation method and conditions of operating license fee that is valid on the date when operating licenses are obtained. And, they should annually pay operating license fees according to this method. Considering that enterprises pay high fees for other land uses too, the increasing license fees should be demanded from enterprises in the direction that they will not create mining cost risk and that the state will charge the optimum fee. If there will not be discounts in the other fees required from enterprises, in line with the expectation of the mining sector, the operating license fee calculation methods in the previous legislation periods can be applied. This fee may not be taken before the operation permit. Or, even if the current operating license fee formula is applied, changes can be made in the critera used in the formula. Within the scope, if permit area is used instead of license area in the calculation, operating license fees will be calculated ∼50–55% deducted.
... Srivastava (2013), in turn, points out to the role of ordinary kriging as an improvement to inverse-distance methods in modelling hard coal deposits. Rademeyer and team (Rademeyer et al., 2019) presented a model which optimizes the NPV from mining activities, taking into account, among others, the changes in available reserves, concluding that mining projects are more sensitive to externalities (capital investment part, investor sentiment, and government policy) than on factors of production such as input cost. ...
In the research we examined the influence of a few geostatistical models (interpolators and kriging models) on the resource base and economic efficiency measures, on the example of coking coal deposits. The research was carried out in scenario-based mode, with 4 alternative analytic models prepared.
The assessment criteria for fitted variability models based on deviations of selected technical and economic indicators and parameters, such as: volume of reserves, price of coking coal, production cost, EBITDA, NPV, IRR, mining height, coal yield, total waste volume, mine lifetime were examined. The variability of seam structural parameters and coking coal quality parameters was modelled with use of interpolators based on finite element method (FEM), inverse distance weighting method (Inverse), as well as triangulation coupled with extrapolation (Planar). Also model C was built separately, where ordinary kriging was used to assess empirical variograms and theoretical models of quality and quantity parameters. A dedicated discount model was used for generating the resultant economic and financial indicators. Monte Carlo simulation (bootstrap method) was applied with empirical copulas as binding functions.
It was demonstrated in the course of the research that the selection of geostatistical model is of significant importance for the assessment of geological, technical and economic potential of the analysed deposit. It was shown that for the mean size of resource base, in the order of 44.6 million Mg (Ref. Model), the differences in estimated volume of reserves may reach 18%. For relatively insignificant differences in operating costs and coal price distributions, the highest differences in totalled EBITDA amounted to some 2.054 billion PLN (18%). NPV differences were calculated at maximum of 16%, whereas the IRR deviations reached 9%. Depending on the interpolator used, the mining height may differ relatively by maximum of 18%, mean waste volume by 17%, mean coal yield by 7%, while mine lifetime by maximum of 10%. Relative differences may reach a few dozen percent (in certain cases of other technical and economic parameters). Based on this data, we formed the conclusion that these differences are significant.
Also the assessment of Spearman's rank correlation coefficients may provide insufficient information about correlation structure, what had been verified with use of empirical copulas.
For mining to be conducted in Turkey, at least one (mining engineer) permanent supervisor is required to be employed in enterprises. From the perspective of mining investors –as a cost item-share of supervisor salaries in the annual mining operating costs is a matter of question. Because, personnel salaries constitute an important part of mining operating costs. Mining investors desire this share not to be high in the total costs. This share makes mining enterprises economically vulnerable in the face of unexpected costs. In Turkey, since land use costs and taxes that mining enterprises pay are high, investors are led towards the methods which they will be able to make an easier cost controlling with. One of these emerges with the deduction from the salaries of employees and mining engineer supervisors and, even, with the practice of dismissing them. With the effect of these factors, can not be fully collecting the supervisor salaries from licensee is one of the biggest problems in the practice in the permanent supervisor system in Turkey. Over SurveyMonkey program, 33% of supervisors stated that they receive their salaries with a delay, and 53% receive their salaries lower than the minimum salary tariff determined in Official Gazette. For supervisors to receive their salaries without delay and over the minimum salary tariff determined according to Official Gazette, in what kind of payment system should the salaries be given? In this study, it was analysed how much of a share the salaries of supervisors working in different mineral groups and (open-pit/underground) operating methods constitute in mining operating costs. The ratio of a supervisor salary to annual operating costs for all mineral groups is 2.8% on average. If other mining engineers who are not supervisors in the operation are included as well, the ratio of salaries of all mining engineers to annual operating costs is 4.7% on average. If all of the supervisors received their salaries over the minimum tariff, this rate would have been 6.4%. When considering an estimated employee salary over the minimum wage, the ratio of the total salaries of all mining engineers and employees in the enterprise to operating costs is 22.7%. These rates, in which the other engineers salaries in the mining operation are excluded, show that the total salaries of the personnel working in a mining operation have a high share in the operating costs. In the presence of this high share, to ensure salary assurance of supervisors and for them to receive a salary at least over the minimum tariff, it will be beneficial to launch a Permanent Supervisor Fund where will be followed up in the control of the state, and where their salaries will be made by the employer. In which payment system should the supervisor salaries be given so that supervisors can receive their salaries without delay and above the minimum tariff? It is wondered whether the supervisor salaries are higher than the minimum salary tariff determined according to Official Gazette in Turkey. The Fund will not only economically contribute to supervisors but also to investors, the bank -with whom the contract is made-, government, mining administration.
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