384. Best Worst PWC

For any production line with bottleneck rate , raw processing time , and WIP level , throughput is bounded by three curves (Hopp & Spearman). Real lines fall between these curves.

384.1. Three curves

where is the critical WIP.

384.2. Interpretation

Best case: deterministic line, no variability. Throughput grows linearly until hitting bottleneck rate. Cycle time stays at until WIP exceeds capacity then grows linearly.

Worst case: pathological — all work at one station, batched. Throughput stays at no matter how much WIP. Useless line.

PWC: a “balanced random” baseline. Each station equally loaded with exponential variability. Real production lines should land near PWC if well-managed.

384.3. Critical WIP

The WIP at which best-case throughput reaches and best-case cycle time equals . Above :

• Best case: cycle time grows linearly with , throughput stays at
• PWC: cycle time grows linearly too, throughput approaches asymptotically

384.4. Take-aways

• If your real line’s throughput is well below the PWC curve, you have more variability than even PWC assumes — improve setups, breakdowns, batching
• If real cycle time is well above PWC, same — variability is the culprit
• Critical WIP is the sweet spot for CONWIP (constant WIP) control

384.5. Plot intuition

Throughput
 r_b ┤  best ───────────────────────────────────────────────
     │ /  ╱ PWC asymptote
     │/  ╱
     │  ╱
     │ ╱
     │╱  worst  ──────────────────────────────────────────
 1/T_0
     └─────────────────────────────────────────── WIP w
                W_0

384.6. See also

• Critical WIP
• Factory Physics overview
• VUT — the underlying variability driver
• CONWIP