Exercise set
Mine Planning, Production Scheduling, and Georesource Risk Exercises
Worked mining engineering exercises for mine planning and georesource risk covering cutoff grade, block value, stockpile balance, truck fleet capacity, crusher utilization, critical path, blending grade, NPV, Monte Carlo risk, reconciliation variance, and replanning triggers.
These exercises practise first-pass calculations used in mine planning, production scheduling, and georesource risk review. They connect cutoff grade, block routing, stockpile balance, haulage capacity, crusher utilization, critical path, blending, discounted cash flow, uncertainty scenarios, reconciliation variance, and replanning triggers.
Assume simplified nominal values unless an exercise states otherwise. Real mine plans require a current georesource model, survey control, grade-control evidence, geotechnical constraints, dewatering and ventilation readiness, equipment availability, processing response, environmental obligations, closure constraints, and documented authority for schedule changes.
How to Use These Exercises
For each problem:
- define the planning horizon, material class, operating constraint, and decision boundary;
- keep tonnes, grades, recovery, time, capacity, cost, and probability on explicit bases;
- distinguish a target from a physically executable schedule;
- identify which field record, dispatch record, survey, assay, or plant result would validate the calculation;
- state whether the result should trigger routing, rescheduling, contingency, or model update.
The most common mistake is optimizing a schedule from average assumptions while hiding the constraints that make it executable: access, water, ventilation, slope stability, haulage, plant feed limits, stockpile state, maintenance, and environmental controls.
Use the exercises as planning gates: change routing, hold a pushback, reserve stockpile capacity, adjust fleet assumptions, protect a crusher bottleneck, revise a blend, add contingency, or trigger replanning when model uncertainty, operating records, plant response, or reconciliation data contradict the schedule.
Exercise 1: Break-Even Cutoff Grade
A copper mine uses a simplified routing rule. Net variable cost is 32\ \text{USD/t ore}. Copper price is 8500\ \text{USD/t Cu}, metallurgical recovery is 88\%, and payable fraction is 96\%.
Estimate the break-even copper grade by mass, ignoring sustaining capital and fixed cost.
Solution
Break-even grade:
where C is cost per tonne of ore, P is metal price, R is recovery, and f_p is payable fraction.
Convert to percent:
Engineering Comment
This is a simplified economic screen. Real cutoff policy may include mining cost by material class, processing bottlenecks, dilution, ore loss, stockpile option value, recovery by domain, deleterious elements, royalties, fixed cost, and environmental handling constraints.
Exercise 2: Block Routing Value
A planned block contains 25{,}000\ \text{t} of ore at 0.65\% copper. Use the same price, recovery, payable fraction, and variable cost from Exercise 1.
Estimate payable copper, revenue, cost, and simplified margin.
Solution
Contained copper:
Payable recovered copper:
Revenue:
Variable cost:
Simplified margin:
Engineering Comment
The block appears economic under the simplified assumptions. Routing should still check grade-control confidence, ore type, hardness, moisture, clay, recovery by domain, haul distance, stockpile destination, and whether the plant can accept the material in the planned period.
Exercise 3: Stockpile Balance During a Campaign
During a ten-day campaign, the mine sends 15{,}500\ \text{t/day} of ore toward the plant area. The plant can process 14{,}000\ \text{t/day}. Assume the difference reports to a controlled stockpile.
Estimate daily and campaign stockpile change.
Solution
Daily stockpile increase:
Ten-day stockpile increase:
Engineering Comment
The stockpile buffers the plant, but it also creates rehandle cost, sampling uncertainty, moisture changes, segregation, runoff exposure, and possible oxidation. The plan should state the stockpile capacity and reclaim rule before the campaign begins.
Exercise 4: Truck Fleet Production Capacity
A haulage plan uses 14 trucks. Each truck carries 180\ \text{t} per trip. Average cycle time is 42\ \text{min}. Availability is 82\% and utilization during scheduled time is 88\%. The shift plan provides 20 scheduled operating hours per day.
Estimate daily truck production capacity and compare it with a target of 52{,}000\ \text{t/day}.
Solution
Trips per truck per scheduled hour:
Effective hourly capacity:
Daily capacity:
Shortfall:
Engineering Comment
The nominal fleet is essentially at target with no practical margin. Weather, queues, ramp restrictions, refuelling, operator breaks, maintenance delay, road condition, or dispatch inefficiency can push the plan below target.
Exercise 5: Crusher Utilization and Queue Risk
Truck arrivals to a crusher average 24\ \text{trucks/h}. The crusher can serve 30\ \text{trucks/h} under normal conditions.
Estimate utilization. Then check utilization if wet ore reduces service capacity to 25\ \text{trucks/h}.
Solution
Normal utilization:
Wet-ore utilization:
Engineering Comment
At 96\% utilization, small variability can create long queues and lost truck hours. The schedule should include wet-ore handling rules, alternate dump options, crusher cleanout access, stockpile flexibility, and dispatch response before the bottleneck forms.
Exercise 6: Critical Path for Access Release
Before a pushback can start, the plan requires:
- dewater sump: 5 days;
- rehabilitate ramp after sump access: 8 days;
- install temporary power: 6 days, independent of sump work;
- move shovel after ramp and power are ready: 2 days.
Estimate earliest pushback start.
Solution
Sump and ramp path:
Power path:
The shovel move waits for both ramp and power:
Engineering Comment
The critical path is sump access plus ramp rehabilitation plus shovel move. If the schedule assumes mining starts earlier, it is missing a physical readiness constraint.
Exercise 7: Blended Feed Grade
A daily plant blend uses:
- 4000\ \text{t} from stockpile A at 0.90\% copper;
- 6000\ \text{t} from stockpile B at 0.55\% copper;
- 5000\ \text{t} of direct ore at 1.20\% copper.
Estimate blended copper grade.
Solution
Contained copper:
Total feed:
Blended grade:
Engineering Comment
The arithmetic blend may still fail operationally if hardness, clay, moisture, oxidation, deleterious elements, or recovery differ between sources. Mine-to-mill planning should blend process response, not grade alone.
Exercise 8: Simplified NPV of a Pushback
A pushback requires 18\ \text{million} of stripping and access cost at time zero. It is expected to generate net cash flow of 8\ \text{million/year} for four years. Use discount rate 10\%.
Estimate simplified net present value.
Solution
Present value of the four annual cash flows:
Net present value:
Engineering Comment
The simplified pushback is positive, but the decision depends on schedule confidence, grade uncertainty, recovery, cost escalation, water or slope constraints, permitting, tailings capacity, and whether the cash flows are independent of other mine stages.
Exercise 9: Probability of Negative Value from Scenario Results
A planning team runs 100 georesource and operating scenarios for the pushback in Exercise 8. In 18 scenarios, estimated NPV is below zero. The scenario mean is 7.2\ \text{million USD} and the standard deviation is 5.5\ \text{million USD}.
Estimate the empirical probability of negative NPV and a simple mean-to-zero margin in standard deviations.
Solution
Empirical probability:
Mean-to-zero margin:
Engineering Comment
The project has positive mean value but material downside risk. The review should identify which inputs drive the negative scenarios: grade, recovery, strip ratio, water inflow, slope delay, equipment availability, price, or processing constraint.
Exercise 10: Reconciliation Variance and Replanning Trigger
A monthly plan expected 100{,}000\ \text{t} of ore at 0.85\% copper. Actual reconciled production was 96{,}000\ \text{t} at 0.78\% copper. A replanning trigger is defined as contained-metal variance worse than 8\%.
Estimate contained-metal variance. Then rank the grade-control failure mode with S=8, O=5, and D=4. After tighter sampling and dispatch checks, occurrence is estimated at O=3 and detection at D=2.
Solution
Planned contained copper:
Actual contained copper:
Variance:
Percentage variance:
Initial risk priority number:
Revised risk priority number:
Engineering Comment
The variance exceeds the replanning trigger. The response should not only update the schedule; it should check the georesource model, grade-control sampling, dilution, ore loss, survey boundaries, stockpile accounting, plant assays, and whether routing rules are still valid.
Review Checklist
When reviewing a mine planning or georesource-risk calculation, ask:
- Is the decision boundary explicit: routing, cutoff, stockpile, fleet size, plant feed, pushback release, contingency, or replanning?
- Does the plan distinguish economic value from physical executability under access, water, ventilation, slope, maintenance, and environmental constraints?
- Are tonnes, grade, recovery, dilution, ore loss, moisture, hardness, deleterious elements, and plant response on consistent bases?
- Are fleet, crusher, stockpile, and plant capacities tested under variability rather than only average throughput?
- Does the schedule identify critical-path readiness items and the owner of each release constraint?
- Are uncertainty scenarios tied to specific drivers that can be monitored or mitigated?
- Do reconciliation results trigger model review, grade-control action, dispatch correction, and schedule change when the variance exceeds the threshold?
Good mine planning connects the block model to executable work. A schedule is credible only when geology, equipment, infrastructure, plant limits, operating records, and risk triggers describe the same mine reality.