A mathematical optimisation approach to modelling the economics of a coal mine

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 mathematical model of coal production is developed and described. Aspects covered include mineral exploration, reserve determination, capacity build-up, overburden removal, extraction and beneficiation.•The aim of this research is to develop the economic framework used to investigate aspects of coal mining and ultimately coal supply.•A formulation for determining the availability of reserves is described, whereby coal markets and mine costs are linked to indicate coal supply.•The proposed model is solved computationally as a constrained optimisation problem in which the net present value of future cash owns from coal mining project is maximised subject to constraints arising from the physical limitations inherent to mining operations.•The results suggest that the capital investment decision has greater bearing on the profitability of the project whereas production volumes are largely kept stable.