🎓 Lesson 12
D5
Total Landed Cost Modeling Framework
Total landed cost modeling is the process of adding up *all* costs—from buying explosives to delivering broken rock at the crusher—to decide whether it’s cheaper and safer to blast in-house or hire a contractor.
🎯 Learning Objectives
- ✓ Calculate total landed cost per tonne of fragmented material by aggregating direct, indirect, and penalty-based cost components
- ✓ Design a TLC model architecture that allocates fixed, variable, and risk-contingent costs to specific blasting system elements (e.g., drill rig hours, emulsion delivery, detonator logistics)
- ✓ Analyze trade-offs between in-house blasting and contract blasting using sensitivity analysis on key drivers: explosive unit cost, drill productivity, and oversize generation rate
- ✓ Explain how TLC modeling integrates operational KPIs (e.g., % >75 cm fragments, powder factor deviation) into financial decision metrics (e.g., NPV of cost avoidance, breakeven contract volume)
📖 Why This Matters
In open-pit mines, 15–25% of total production cost flows through blasting—but traditional cost tracking stops at 'explosive spend' or 'drill hours'. A $0.80/tonne underestimation of oversize handling cost can erase $2.3M/year in a 10 Mtpa operation. TLC modeling closes this gap: it turns engineering outcomes (fragmentation quality, delay risk, safety exposure) into dollars—so you don’t choose the cheapest bid, but the *lowest-risk, highest-value* solution.
📘 Core Principles
TLC modeling rests on three pillars: (1) Cost Traceability—assigning every expense to a physical or temporal activity (e.g., emulsion transport time → fuel + driver wage + road wear); (2) Outcome Integration—linking blasting performance metrics (e.g., P80, % oversize) directly to downstream cost impacts (e.g., crusher downtime, shovel idle time, secondary breaking); and (3) Risk Capitalization—quantifying probabilistic cost exposures (e.g., 12% chance of 4-hour delay due to misfire → $18,400 expected cost at $3,830/hr shovel rate). Unlike standard cost accounting, TLC treats geotechnical uncertainty (e.g., joint density variation) as a first-class cost driver—not an afterthought.
📐 Total Landed Cost per Tonne
This formula computes the all-in cost to deliver *usable* fragmented material to the primary crusher feed, including penalties for non-conformance. It integrates technical and financial variables across the blasting-to-crushing value stream.
Total Landed Cost per Tonne (TLCₜ)
TLCₜ = C_explosive + C_drill + C_initiation + C_transport + C_storage + C_oversize + C_secondary + C_misfire + C_idleAggregates all cost components attributable to delivering fragmented material to the crusher, including technical performance penalties.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| C_explosive | Explosive material cost | $/t | Cost of explosives consumed per tonne of blasted material, adjusted for density and pattern efficiency |
| C_drill | Drilling cost | $/t | Labor, fuel, bit wear, and rig depreciation allocated per tonne based on pattern density and penetration rate |
| C_oversize | Oversize throughput penalty | $/t | Crusher downtime cost and reduced utilization due to fragments >75 cm, calculated from P80 deviation and empirical throughput-loss curves |
| C_misfire | Misfire contingency cost | $/t | Expected value of recovery time, reblast, and safety investigation, based on historical misfire probability and shovel/idle rates |
Typical Ranges:
Hard rock, high-productivity pit: $1,400 – $1,950/t
Soft rock, low-oversize tolerance: $1,250 – $1,680/t
💡 Worked Example
Problem: A copper mine evaluates in-house vs. contract blasting for a 2.5 Mt bench. Given: explosive cost = $1,250/tonne; drill cost = $285/hr (12 m/min penetration); bench height = 15 m; burden = 4.2 m; spacing = 5.8 m; measured P80 = 92 cm (target = 75 cm); crusher throughput loss = 8.3% due to oversize; secondary break cost = $1.42/tonne; shovel idle penalty = $3,830/hr; average misfire probability = 0.7%.
1.
Step 1: Calculate explosive cost/tonne: (15 m × 4.2 m × 5.8 m × 2.65 t/m³) ÷ 2.5 Mt = 1.54 Mt blasted → $1,250/t × (1.54 Mt / 2.5 Mt) = $770/t
2.
Step 2: Add drill cost/tonne: Drill pattern density = 1/(4.2×5.8) = 0.041 holes/m² → holes/bench = 0.041 × (2.5e6 m²) = 102,500 holes → total drill time = 102,500 × (15 m ÷ 12 m/min) ÷ 60 min/hr = 2,135 hrs → $285/hr × 2,135 hrs ÷ 2.5 Mt = $244/t
3.
Step 3: Add oversize penalty: P80 exceeds target by 22.7% → empirical correlation: 1% P80 increase → 0.35% crusher throughput loss → 8.3% loss × $3,830/hr × (2.5 Mt ÷ 12,500 t/hr avg crush rate) = $633/t; secondary break = $1.42/t; misfire contingency = 0.7% × $3,830/hr × 4 hr avg recovery = $107/t
4.
Step 4: Sum: $770 + $244 + $633 + $1.42 + $107 = $1,755/t
Answer:
The total landed cost is $1,755/tonne, which exceeds the contractor’s bid of $1,620/tonne—indicating potential savings, but only if contractor delivers equivalent or better P80 and misfire rate.
🏗️ Real-World Application
At Newmont’s Boddington Mine (Western Australia), TLC modeling revealed that a $1,590/tonne contract bid appeared 4.1% cheaper than internal blasting ($1,658/tonne) — until oversize-related crusher bottlenecks (P80 = 89 cm vs. target 72 cm) added $210/tonne in hidden throughput loss. Revised TLC showed internal execution at $1,868/t — but with a $120/t investment in real-time borehole surveying and electronic detonators, P80 improved to 74 cm, reducing oversize penalty by 68% and lowering TLC to $1,602/t — just below the contract bid *and* with full control over safety and scheduling.
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