Electrical Engineering and Applied Computing

Volume 90 of the series Lecture Notes in Electrical Engineering pp 391-403


The Determination of a Dynamic Cut-Off Grade for the Mining Industry

  • P. V. JohnsonAffiliated withSchool of Mathematics, University of Manchester Email author 
  • , G. W. EvattAffiliated withSchool of Mathematics, University of Manchester
  • , P. W. DuckAffiliated withSchool of Mathematics, University of Manchester
  • , S. D. HowellAffiliated withManchester Business School, University of Manchester

* Final gross prices may vary according to local VAT.

Get Access


Prior to extraction from a mine, a pit is usually divided up into 3-D ‘blocks’ which contain varying levels of estimated ore-grades. From these, the order (or ‘pathway’) of extraction is decided, and this order of extraction can remain unchanged for several years. However, because commodity prices are uncertain, once each block is extracted from the mine, the company must decide in real-time whether the ore grade is high enough to warrant processing the block further in readiness for sale, or simply to waste the block. This paper first shows how the optimal cut-off ore grade—the level below which a block should be wasted—is not simply a function of the current commodity price and the ore grade, but also a function of the ore-grades of subsequent blocks, the costs of processing, and the bounds on the rates of processing and extraction. Secondly, the paper applies a stochastic price uncertainty, and shows how to derive an efficient mathematical algorithm to calculate and operate a dynamic optimal cut-off grade criterion throughout the extraction process, allowing the mine operator to respond to future market movements. The model is applied to a real mine composed of some 60,000 blocks, and shows that an extra 10% of value can be created by implementing such an optimal regime.


Real-options Mining Stochastic control Reserve valuations Cut-off grade