383. Factory Physics
A framework (Hopp & Spearman, Factory Physics 1996) that applies queueing theory + Little’s Law + variability analysis to manufacturing. Replaces folk wisdom with quantitative laws.
383.1. The three core insights
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Three buffers absorb variability — capacity, inventory, time. You always pay one (or all) of these.
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VUT equation: queue time = Variability × Utilization × Time. Reducing any of the three reduces flow time.
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Best/Worst/Practical-worst-case performance curves: bound any manufacturing line’s behavior given basic parameters.
383.2. Foundational quantities (a single station)
- : bottleneck rate — the maximum sustainable throughput (per hour)
- : raw processing time — sum of mean processing times across stages
- : WIP level — work-in-process inventory
- : critical WIP — minimum WIP to achieve throughput
See Critical WIP.
383.3. Little’s Law applied
For a production line at steady state:
(See Little’s Law.)
Given any two, the third is determined. Manufacturing trade-offs come down to managing these three quantities.
383.4. Best, worst, practical-worst-case
For any line:
- Best-case TH:
- Worst-case TH:
- Practical-worst-case TH:
Real lines lie between best (perfectly deterministic) and worst (max variability). PWC gives a “balanced random” baseline. See Best/Worst/PWC.
383.5. Levers for improvement
- Reduce variability: smaller setups (SMED), reliable equipment (TPM), uniform service times
- Match capacity: balance line (avoid bottleneck migration)
- Right-size WIP: just above critical WIP — see CONWIP
- Pull system control: kanban / CONWIP / drum-buffer-rope
- Eliminate non-value-added activities (lean / Toyota Production System)
383.6. Compared to traditional cost accounting
Traditional manufacturing cost allocation overhead-rates “fully” — pretends each unit absorbs the same overhead. Factory physics shows this is misleading:
- Loading near produces enormous queue and cycle-time penalty
- Marginal unit at high utilization costs much more (time, capital tied up) than marginal unit at low utilization
- Capacity has nonlinear value — overcapacity is good!