Part 1: The problem Fun facts about Fe:
4th most common element in earth’s crust (about 5%) after Oxygen, Silicon and Aluminum
Has been mined for about 5,000 years
Exists mostly as oxides
Hematite (Fe2O3) and Magnetite (Fe3O4)
Refined back into metal by removing the oxygen in a furnace
Infrastructure Diggers
Crushers and screening
Rail transport to shed
Ship loading by barge
All these activities have variability
No closed form solution
This is the motivation for using simulation modelling
Grade Variability Mine blocks have only estimates of grade from drill
cores
Mine plan is order of digging
After crushing, an assay to determine actual grades
What tonnes and grade will ultimately be exported – this is the devil in the problem
The economic facts Cost of production is $35 to $75 per tonne, depending
on the operation
High grade is considered to be ~63% Fe (or 90% hematite, rest is silica, alumina)
Lower grade material can be beneficiated (OBP) at extra cost (wash the sand off)
Grade penalties apply for deviation from agreed grade
Shipping delays may incur demurrage charges
The Problem To work out in advance what ore can be produced
Time frame of one year or more
How many tonnes of ore
And at what grade
Part 2: The solution We employ a discrete event model that uses built-in
distributions to account for local variability – processing rates, travel times, down times, weather delays, etc.
The model consists of many objects, with each piece of equipment represented as an object
The model has over 1,000 input variables
The model Model built in a simulation language called SLX
Operates on daily plan
Plan created by LP formulation of problem
Model took 4 smart guys 1 year to construct
Optimisation Problem Goal of the optimisation – supply export tonnes
(169,000) within grade limits
Types of constraints – time, tonnes, grade
Three ship lookahead (one month)
Local optimisation for building feed piles
Global optimisation for building ship consignments
Implemented with AIMMS
Multi-level grade control LP optimisation to select ore
Local level: ROM piles – crusher – stockpiles
Local level: stockpiles – rail – shed
Local level: shed + rail direct load to ship
Global level: from mine blocks to ship
Review Daily plan by LP solve takes seconds
Variability of shipped ore grade minimised
No loss of total exported tonnes
Detailed modelling allows prediction of tonnes and grade given changes in actual ore body or external market conditions