Using Geostatistical Ore Block Variances In Production Planning By Integer Programming

This paper outlines the chance constrained binary integer program developed by the author in his doctoral dissertation at Columbia University, New York, 1973. The optimum planning of a mining program involves the determination of a production schedule which maximizes the net present value of the mining property. The actual mining process has an inherent stochastic and discrete nature. In particular, the demand for the mined product and the grade of the mineralized material in the ore are the two most important stochastic mining variables. The decision to mine or not to mine any block of a mining property is a binary integer variable. This paper outlines the formulation of pit production scheduling problem as a chance constrained binary integer program. The deterministic equivalents of these chance constraints are nonlinear in binary variables which have subsequently been linearized. The planned objective is to meet with a stipulated high degree of reliability, all the random demands as they materialize with a random supply of the commodity being marketed as determined by the eventuating random grade values of the exposed ore blocks and the mining system's production constraints such that the discounted total production costs over the entire planning horizon are minimized or the profits maximized. The emerging surface of the mine in each scheduling period is determined by the values taken by the binary decision variable associated with each block of material in each scheduling period.