Mine Planning and Equipment Selection -The Australasian Institute of Mining and Metallurgy (the AusIMM) (2010)

PRODUCTION CAPACITY OPTIMISATION IN THE PRESENCE OF GR ADE UNCERTAINTY

Coefficients  N   M cbt 

number of grade realisations discounted cost of mining bench b in pushback c in period t 

 P cbsgt 

discounted net revenue (revenue minus processing cost) of processing grade group g of grade realisation s within pushback c/bench b in period t  discounted cost of stockpiling grade group g of grade realisation s within pushback c/bench b in period t 

 X cbsgt  Y cbsgt     MC   PC  Ocbsg G cbsg Qcb  S csg  Bct max 

discounted net revenue (revenue minus processing cost and reclaiming cost) of reclaiming from the stockpile and processing grade group g of grade realisation s within pushback c/ bench b in period t  discounted cost of purchasing an additional unit of mining capacity discounted cost of purchasing an additional unit of processing capacity ore tonnage in grade group g of grade realisation s within pushback c in bench b average available grade in grade group g of grade realisation s of pushback c in bench b total tonnage of pushback c in bench b total recovered product in grade group g of grade realisation s of pushback c in bench b maximum number of benches to be completed within pushback c in period t 

Objective function The objective of the optimisation model is to maximise the average net present value (NPV) reported  by each of the grade realisations (Equation 1). This incorporates an average of the discounted net revenue from material that is directly processed ( P cbsgt ) and processed from the stockpile (Y cbsgt ), as  well as costs from material added to a stockpile ( X cbsgt ), for each grade realisation. Mining cost ( M cbt ) and capital costs associated with mining ( MC ) and processing capacity ( PC ) purchased, are common to all grade realisations and are thus do not need to be averaged. Maximise: 1 N

/ Mcbt mcbt  - MCmc - PC mc ;c,b,s,/g,t  Pp + Yy - Xx E - c,b,t 

(1)

Constraints Equations 2 and 3 relate to the capacity of mining and processing in each period, respectively. These capacities are established from the outset and are assumed to be constant over the life of the operation. Each additional unit of capacity incurs a capital establishment cost, reflected in the objective function.

/ Qcb mcbt  # mc

6t

 

(2)

c,b

/ Ocbsg ^ pcbsgt + ycbsgt h # pc

6s, t

 

c,b, g

(3)

Equation 4 enforces a constraint on the maximum number of benches completed within a pushback in each period. max / mcbt  # Bct 

6c, t

 

b

(4)

It is important that material flow equilibrium is achieved throughout the optimisation from period to period. The amount of material processed directly and added to the stockpile from a panel progresses at the same rate as the mining of the panel (Equation 5). Material not directly processed or stockpiled is assumed to be sent to a universal waste dump. Secondly, material cannot be removed from the stockpile until it has been placed there (Equation 6).  pcbsgt + xcbsgt - mcbt   # 0

6c,b, s, g,t 

MINE PLANNING AND EQUIPMENT SELECTIO N �MPES� CONFERENCE / FREMANTLE, WA, 1 � 3 DECEMBER 2010

(5)

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