Business & Operations
Factory Physics CONWIP: Critical WIP (W0), Best-Case & Practical Worst-Case Throughput
Benchmark manufacturing line performance under Constant Work-In-Process (CONWIP) cap w using Hopp & Spearman Critical WIP W0 = rb * T0, Best-Case MIN(w/T0, rb), and Practical Worst-Case throughput (w / (w + W0 - 1)) * rb.
Benchmark your factory floor against Hopp & Spearman's Factory Physics laws!
In Wallace Hopp and Mark Spearman's Factory Physics framework, every production line is anchored by two physical constants: bottleneck rate rb (jobs/hr of the slowest station) and raw process time T0 (hours to walk a single job through an empty line with zero queueing)! Their product defines Critical WIP W0 = rb * T0—the exact WIP cap where a zero-variability balanced line achieves 100% bottleneck throughput rb at minimum possible cycle time T0!
Real factories suffer arrival and process variability! Hopp and Spearman's Practical Worst Case (PWC—balanced exponential stations under a CONWIP cap of w cards) gives exact expected throughput TH_PWC(w) = (w / (w + W0 - 1)) * rb and cycle time CT_PWC(w) = T0 + ((w - 1) / rb)! Notice the sobering insight at Critical WIP (w = W0 = 20 for rb = 4 jobs/hr, T0 = 5 hr): a real stochastic line only reaches 20 / 39 = 51.3% of bottleneck capacity (2.051 jobs/hr), while raising CONWIP to w = 60 lifts throughput to 3.038 jobs/hr!
| CONWIP Cap w (rb=4/hr, T0=5 hr -> W0=20) | Best-Case Throughput | Practical Worst-Case TH_PWC | PWC Cycle Time CT_PWC |
|---|---|---|---|
| Under-WIPped (w = 10 < W0) | 10 / 5 = 2.000 jobs/hr | (10 / 29) * 4 = 1.379 jobs/hr | 5 + (9 / 4) = 7.25 hr |
| At Critical WIP (w = 20 = W0) | 4.000 jobs/hr (100% rb!) | (20 / 39) * 4 = 2.051 jobs/hr | 5 + (19 / 4) = 9.75 hr |
| Buffered Line (w = 60 = 3*W0) | 4.000 jobs/hr (Capped at rb) | (60 / 79) * 4 = 3.038 jobs/hr | 5 + (59 / 4) = 19.75 hr |
Critical WIP W0 = rb * T0 & Best-Case Throughput MIN(w / T0, rb)
Computes Critical WIP W0 = B2 * B3; Best-Case throughput is MIN(B4 / B3, B2).
=IF(OR(B2 <= 0, B3 <= 0), "Invalid Line Parameters", ROUND(B2 * B3, 2))Practical Worst-Case (PWC) CONWIP Throughput TH_PWC = (w / (w + W0 - 1)) * rb
Evaluates Hopp & Spearman's stochastic benchmark throughput for CONWIP cap w >= 1.
=IF(OR(B2 <= 0, B3 <= 0, B4 < 1), "Invalid Line Parameters", ROUND((B4 / (B4 + (B2 * B3) - 1)) * B2, 3))Try the example
Use the original values or change them to test your understanding.