🎓 Lesson 1 D1

Getting Started with Production Cost Modeling

Production cost modeling is a way to estimate how much money it will take to mine and blast rock, so engineers can plan the most efficient and affordable operation.

🎯 Learning Objectives

✓ Calculate total unit production cost per tonne for a given blast design and equipment fleet
✓ Analyze the sensitivity of cost components (e.g., drilling vs. explosives) using break-even and contribution margin principles
✓ Apply cost-per-tonne benchmarks to evaluate blast efficiency and identify cost drivers
✓ Explain how burden, spacing, and powder factor influence both fragmentation quality and cost structure
✓ Design a simplified cost model spreadsheet incorporating labor, fuel, consumables, and depreciation

📖 Why This Matters

Every dollar spent on blasting affects profitability, safety, and downstream processing — yet many mines treat blasting as a fixed 'cost center' rather than an optimized value driver. A 5% reduction in unit blast cost can improve net operating income by $2M–$5M annually in mid-sized open-pit operations. This lesson equips you to move beyond guesswork and build defensible, auditable cost models that directly inform blast design, equipment selection, and contract negotiation.

📘 Core Principles

Production cost modeling rests on three foundational pillars: (1) Activity-based costing — assigning expenses to discrete operations (e.g., drill meterage, kg of ANFO, truck-hour); (2) Resource utilization logic — linking equipment productivity (e.g., m/hr for drills, t/h for shovels) to blast geometry and fragment size distribution; and (3) Cost hierarchy — distinguishing fixed (depreciation, supervision), semi-variable (maintenance, labor shifts), and variable costs (fuel, explosives, bits). Critically, cost is not independent of technical performance: poor fragmentation increases loading time, haul cycle times, and crusher wear — inflating *total* cost far beyond the blast itself. Thus, optimal cost modeling requires coupling blast physics with operational economics.

📐 Unit Production Cost (UPC)

The Unit Production Cost (UPC) expresses total operational cost per tonne of blasted material. It serves as the primary KPI for evaluating blast economy and comparing alternatives. UPC integrates upstream (drilling, explosives) and downstream (loading, hauling, crushing) impacts via weighted activity rates.

Unit Production Cost (UPC)

UPC = (C_drill + C_explosives + C_loading + C_hauling + C_crushing) / T_blasted

Total cost per tonne of blasted material, enabling cross-design and cross-mine economic comparison.

Variables:

Symbol	Name	Unit	Description
C_drill	Drilling cost	USD	Total cost of drilling all blastholes (includes bit wear, fuel, labor, depreciation)
C_explosives	Explosives cost	USD	Cost of all explosives and accessories (primers, detonators, packaging)
C_loading	Loading cost	USD	Shovel/excavator cost including operator, fuel, maintenance, and tire depreciation
C_hauling	Hauling cost	USD	Truck fleet cost per round (fuel, tires, maintenance, operator, depreciation)
C_crushing	Crushing cost	USD	Primary crusher energy, liner wear, and maintenance attributable to blast product size distribution
T_blasted	Tonnage blasted	tonnes	Total bank cubic tonnes (bct) of material fragmented in the round

Typical Ranges:

Hard-rock open-pit (copper/gold): $7.20 – $11.80/t

Soft-rock quarry (limestone): $3.10 – $5.40/t

Large-scale iron ore (low-cost fleet): $2.50 – $4.30/t

💡 Worked Example

Problem: A copper mine blasts 12,000 tonnes per round. Drill cost = $85/m; average hole depth = 14 m; 60 holes/round. Explosives cost = $0.62/kg; powder factor = 0.32 kg/t; ANFO density = 0.85 g/cm³. Loading cost = $1.42/t; hauling cost = $1.98/t. Calculate UPC.

1. Step 1: Drill cost = 60 holes × 14 m × $85/m = $71,400

2. Step 2: Explosives mass = 12,000 t × 0.32 kg/t = 3,840 kg → cost = 3,840 × $0.62 = $2,381

3. Step 3: Loading + hauling = 12,000 t × ($1.42 + $1.98) = $40,800

4. Step 4: Total cost = $71,400 + $2,381 + $40,800 = $114,581

5. Step 5: UPC = $114,581 ÷ 12,000 t = $9.55/t

Answer: The result is $9.55/t, which falls within the safe range of $7.20–$11.80/t for hard-rock open-pit copper operations (per SME 2022 Benchmarking Report).

🏗️ Real-World Application

At Newmont’s Boddington Mine (Western Australia), engineers revised their blast design to increase burden from 4.2 m to 4.8 m while maintaining fragmentation quality (P80 < 450 mm). This reduced hole count by 14%, cutting drilling cost by $0.83/t. Though explosives cost rose $0.11/t, total UPC decreased $0.69/t — saving $3.1M/year across 4.5M t blasted. Crucially, the model included crusher liner wear reduction (validated by 12% lower cone crusher kWh/t), proving that blast cost modeling must extend beyond the blasthole.