Berth Allocation Algorithms & Stacker-Reclaimer Sequencing Logic - Mining Engineering Knowledge & Tools Platform

🎯 Learning Objectives

✓ Formulate a berth allocation problem as a mixed-integer linear program (MILP) with time-window and precedence constraints
✓ Design a conflict-free stacker-reclaimer operation schedule for a twin-belt stockyard using time-indexed sequencing logic
✓ Analyze throughput bottlenecks by quantifying berth occupancy ratio and reclaimer utilization factor from operational logs
✓ Apply priority rules (e.g., EDD, SPT) to dynamically reschedule reclaimers under delayed ship arrivals or stockpile quality deviations
✓ Explain how stacker-reclaimer sequencing impacts ore blending consistency and downstream processing stability

📖 Why This Matters

In modern mining logistics, a 12-hour vessel delay at port can cost $350k in demurrage—and 70% of such delays stem not from weather or customs, but from suboptimal berth assignments or uncoordinated stacker-reclaimer movements. When a copper concentrate ship arrives early but its designated stockpile isn’t ready—or when two reclaimers race for the same luffing zone—the entire mine’s production schedule unravels. This lesson bridges algorithmic decision-making with physical equipment constraints to ensure port interfaces operate as synchronized extensions of the mine—not as failure-prone choke points.

📘 Core Principles

Berth allocation is fundamentally a resource-constrained scheduling problem: each berth has fixed length, draft, and crane capacity; each vessel has arrival time, service duration, draft, and cargo type. Optimal allocation balances fairness (minimizing waiting), efficiency (maximizing berth utilization), and safety (enforcing separation distances). Stacker-reclaimer sequencing adds spatial-temporal complexity: stackers move along rails to deposit material in layered cones; reclaimers traverse the same rails to extract material in controlled cuts—requiring collision avoidance zones, minimum turn-around times, and alignment with blending targets. Modern systems use hybrid approaches: MILP for day-ahead planning, combined with rule-based reactive dispatch for real-time exceptions (e.g., rain-induced stockpile caking requiring faster reclamation).

📐 Berth Occupancy Ratio & Reclaimer Utilization Factor

These two KPIs quantify system saturation and guide capacity expansion decisions. Berth Occupancy Ratio (BOR) measures how intensively berths are used; Reclaimer Utilization Factor (RUF) reflects whether reclaimers are under- or over-tasked relative to design throughput. Both must stay below safe thresholds to maintain buffer for disruptions.

💡 Worked Example

Problem: A port has 3 berths (total quay length = 950 m). Over a 7-day period, vessel service time totals 142 hours, with 28 hours of waiting time before berthing. Total available berth-hours = 3 berths × 168 h = 504 h. Meanwhile, 2 reclaimers handled 189,000 t of iron ore; their rated capacity is 1,200 t/h each, operating 24/7.

1. Step 1: Compute BOR = (Service time + Waiting time) / Total available berth-hours = (142 + 28) / 504 = 170 / 504 = 0.337

2. Step 2: Compute total reclaimer capacity-hours = 2 × 1,200 t/h × 168 h = 403,200 t-h

3. Step 3: Compute RUF = Actual tonnage handled / Capacity-hours = 189,000 / 403,200 = 0.469

Answer: BOR = 0.34 (34%) and RUF = 0.47 (47%). Both fall well within safe operational ranges (<0.65 for BOR, <0.75 for RUF), indicating adequate buffer for unplanned delays and blending adjustments.

🏗️ Real-World Application

At Roy Hill’s Port Hedland export facility (Western Australia), a MILP-based berth allocator—integrated with real-time AIS vessel tracking and stockpile moisture sensors—reduced average vessel turnaround time by 22% (from 38 to 29.6 hrs) between 2021–2023. Crucially, its stacker-reclaimer sequencer enforced ‘blending windows’: reclaimers were prohibited from cutting into stockpiles <12 hours old to avoid homogenization loss, while enforcing 15-m minimum separation between adjacent machines on shared rail. This eliminated 100% of near-miss incidents and improved Fe-grade consistency (σ reduced from ±0.82% to ±0.31%).