🎓 Lesson 3
D2
Identifying Critical Path Nodes & Bottlenecks
Critical path nodes are the most important steps in a mining logistics chain whose delays will directly delay the entire operation, like a traffic jam that stops all trucks from moving.
🎯 Learning Objectives
- ✓ Identify critical path nodes using activity-on-node (AON) network diagrams and float analysis
- ✓ Calculate total system cycle time and pinpoint bottlenecks using throughput–capacity mismatch analysis
- ✓ Apply resource-constrained scheduling to redesign logistics sequences and eliminate float-critical dependencies
- ✓ Explain how blast timing and muck pile consistency affect downstream haul cycle variability and critical path stability
- ✓ Design a mitigation strategy for a validated bottleneck using discrete-event simulation validation
📖 Why This Matters
In open-pit mines, a 5-minute delay at the primary crusher can stall 20 haul trucks per hour—costing $18,000/hour in lost production. Unlike isolated equipment failures, critical path nodes cascade failure across the entire logistics chain. Understanding them transforms reactive maintenance into proactive flow architecture design—and separates world-class 92% fleet utilization operations from industry-average 68%.
📘 Core Principles
Critical path analysis begins with mapping the end-to-end material flow as a directed acyclic graph (DAG), where nodes represent discrete activities (e.g., 'shovel loading', 'truck haul', 'crusher feed') and edges represent precedence and material handover. Float (slack) is calculated as Late Start − Early Start; zero-float nodes define the critical path. Bottlenecks differ: they arise from capacity constraints (throughput < demand) rather than sequence dependency—but when located on the critical path, they become *critical bottlenecks*. Real-world complexity arises from stochasticity: blast fragmentation variability alters shovel loading time, which shifts float distribution dynamically—requiring Monte Carlo–enhanced CPM (Critical Path Method) or integrated DES (Discrete-Event Simulation).
📐 Critical Path Duration & Bottleneck Severity Index
The Critical Path Duration (CPD) is the sum of durations of all zero-float activities. Bottleneck Severity Index (BSI) quantifies capacity shortfall relative to demand: BSI > 1.0 indicates a critical bottleneck. Used to prioritize interventions across multi-stage logistics chains.
Bottleneck Severity Index (BSI)
BSI = D / (C × A)Measures the ratio of demand (D) to effective capacity (C × A), where A is availability. BSI > 1.0 identifies a critical bottleneck.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| D | Demand rate | t/h | Required material throughput at the node |
| C | Rated capacity | t/h | Maximum theoretical throughput under ideal conditions |
| A | Availability | decimal | Fraction of scheduled time the resource is operationally ready (e.g., 0.92 = 92%) |
Typical Ranges:
Primary crusher in large open-pit: 0.85 – 0.95
Shovel fleet (per shovel): 0.80 – 0.90
💡 Worked Example
Problem: A copper mine’s primary crusher processes ore at 8,500 t/h. Daily ROM feed demand averages 9,200 t/h (based on blast schedule & fleet output). Crusher availability is 94%. Calculate BSI and interpret.
1.
Step 1: Compute effective crusher capacity = rated capacity × availability = 8,500 t/h × 0.94 = 7,990 t/h
2.
Step 2: Compute BSI = demand / effective capacity = 9,200 / 7,990 = 1.151
3.
Step 3: Since BSI = 1.151 > 1.0, the crusher is a critical bottleneck—demand exceeds sustainable throughput by 15.1%
Answer:
BSI = 1.15, confirming a critical bottleneck requiring intervention (e.g., pre-screening, surge bin optimization, or shift reallocation).
🏗️ Real-World Application
At Rio Tinto’s Yandi Mine (Pilbara, WA), GPS-tracked haul cycle data revealed 12–18 minute delays at the ROM pad transfer point—not due to equipment failure, but inconsistent muck pile geometry causing variable shovel swing times. This introduced ±4.3 min variance into loading time, converting a previously non-critical node into a floating-point-sensitive critical path segment. Redesigning blast burden/spacing to improve muck uniformity reduced cycle time variance by 68%, eliminating 3.2 hours/day of cascaded delay—equivalent to +1.7 Mt/year throughput.