Dynamic Optimization of Open-pit Cutoff Grade by the Maximum Principle

摘要

This paper puts forward a methodology for the optimization of open-pit cutoff grade, which is based on the maximum principle. After a brief introduction to the analytical framework of constrained optimization by the maximum principle, a mathematical model for selecting an optimum cutoff grade function is constructed, this aims at the maximization of total present value of an open pit mine. By this method, the optimum cutoff grade series of a mine can be explicitly expressed as a function of residual mine life, and the function can be obtained by either numerical or analytical solution. Through the solution of the constrained optimum problem, we can also get the information on the shadow price of the mine's ore reserve. This information may be very useful in the decision making of pit extension. In the final part of the paper, a calculation example is given.