Rosemary M.S. Falcon’s research while affiliated with University of the Witwatersrand and other places

This paper investigates the implications for coal supply security for the domestic South African market when faced with weaker export demand. A model is proposed of domestic coal trade via a trading hub which links coal production to consumer markets. An application of the theory for equilibrium price discovery at the mine-trader and trader-consumer interfaces is also described. It is found that the profit-maximising trader seeks to sell more volumes to domestic consumers of higher-grade coal to compensate for earnings lost due to lower export volumes. This results in lower prices on higher-grade product. Supply to domestic consumers of lower-grade coal appears to be unaffected by the weaker export market, with the price on lower-grade coal constant.

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.

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 modified version of the Cobb-Douglas production function is proposed for simulating production costs in resource extraction models. The resulting average cost function is U-shaped with a wide bottom, and as such should be more representative of the economies of scale associated with bulk operations. It also possesses a minimum which is obtainable from the characteristics of the operations. The viability of the proposed cost function is demonstrated in a profit maximisation exercise constructed as a problem in optimal control, rendering results consistent with what could be seen in a real-world resource extraction operation with similar constraints.