What This Teaches
Factory Physics, developed by Wallace Hopp and Mark Spearman, is a rigorous science-based framework for understanding manufacturing performance. Where Lean gives you tools and principles, Factory Physics gives you the mathematics behind why those principles work. This simulator uses the Penny Fab model, a classic teaching tool from the textbook, to make those relationships visible and interactive.
The core argument is this: every production system has a performance frontier defined by its physics, not its management. You cannot outperform your bottleneck rate. You cannot escape the penalty of variability. But if you understand where your system sits relative to that frontier, you know exactly how much improvement is theoretically available and what levers to pull to get there.
The Goal of Every Intervention — Move your simulation dot toward the Best Case line on the TH vs WIP and CT vs WIP charts. That gap is your improvement opportunity, measured in real units and real time.
How to Use the Simulator
The factory line shows four stations processing pennies from left to right. Each penny represents one unit of work in process moving through the system.
- Station times — Click any station to adjust how long it takes to process one unit. Making one station slower than the others creates a bottleneck and drops the bottleneck rate, capping the entire line's maximum throughput.
- Spread slider — Automatically creates an uneven line by spreading station times apart while keeping the total constant. A spread of zero gives a perfectly balanced line. Increasing it creates a dominant bottleneck.
- CV slider — Controls process time variability at every station. A coefficient of variation of zero means perfectly consistent output every cycle. A value of 1.0 means high variability. Watch the simulation dot drift toward Worst Case as CV rises.
- WIP Cap slider — Sets the maximum number of units allowed in the system at once. This simulates CONWIP, a pull mechanism that prevents line overload. Set the cap at the Critical WIP value and observe how cycle time stabilizes without sacrificing throughput.
- Run / Pause / Step — Step mode advances one cycle at a time, ideal for classroom walkthroughs of the first few rounds.
- Performance dot — On the TH vs WIP and CT vs WIP charts, the dot shows exactly where your current configuration sits relative to Best Case, Practical Worst Case, and Worst Case. This is the key visual in every round.
- Presets — Load standard configurations from the Hopp and Spearman textbook exercises. Use them as starting points for each classroom round.
The Three Benchmark Lines
The TH vs WIP and CT vs WIP charts show three curves that frame every discussion in Factory Physics.
Best Case
Assumes zero variability and perfect flow. No real factory achieves this. It is the theoretical ceiling and the target for improvement.
Worst Case
A completely chaotic system where work releases randomly with no coordination. This is the floor. No managed system should be here.
Practical Worst Case
Where most real factories actually operate. Better than pure chaos, worse than perfect flow. The gap between your dot and Best Case is your improvement opportunity. Use this line to set honest expectations about what process improvement can deliver.
The Five Laws
- L1: Little's Law (WIP = TH × CT) — Know any two values and you can calculate the third. This holds for any stable system, a factory floor, a hospital, a software team, or a drive-through line. It is not a management philosophy. It is mathematics.
- L2: Bottleneck Rate — Throughput can never exceed the rate of the slowest station. Adding WIP above the bottleneck does not increase throughput. It only increases cycle time and ties up capital.
- L3: Critical WIP (W₀) — The WIP level that achieves maximum throughput at minimum cycle time. Below W₀ the line is starving. Above W₀ it is congested. W₀ is calculated as bottleneck rate times raw process time. Most organizations run well above it.
- L4: Variability Law — Variability always degrades performance. Even at the same WIP level, a higher coefficient of variation pushes cycle time up and throughput down. Reducing variability moves your system toward Best Case without changing capacity or headcount.
- L5: Practical Worst Case — The realistic baseline for an unmanaged system. Use it to set honest expectations about what improvement can deliver, and to show students how much performance is being left on the table.
Suggested Classroom Rounds
| Round | Setup | What to Observe |
|---|
| 1 — Best Case | All stations equal, CV at 0, WIP at Critical WIP | The system achieves maximum throughput at minimum cycle time. Ask students: why can't we just run like this? |
| 2 — Add Variability | Keep WIP at Critical WIP, raise CV to 1.0 | Watch the dot drift toward Practical Worst Case. Throughput drops, cycle time climbs. No capacity changed. Discuss where variability comes from in real operations. |
| 3 — Create a Bottleneck | Raise the Spread slider to create an uneven line | The bottleneck rate drops. Critical WIP recalculates. The throughput ceiling falls. Ask students: where is your real-world bottleneck? |
| 4 — CONWIP Control | Raise WIP above Critical WIP, then enable WIP Cap | Capping WIP at Critical WIP restores cycle time without sacrificing throughput. This is the pull principle, quantified. |
| 5 — Cost Model | Open the Cost Model chart, adjust revenue and holding cost inputs | The profit-maximizing WIP is often below Critical WIP when holding costs are high. Discuss the financial case for lean inventory. |
Reading the Cost Model
The Cost Model chart adds the financial dimension that operational metrics miss. Throughput revenue increases with WIP up to the bottleneck rate, then flattens. WIP holding cost increases linearly forever. The profit curve peaks at the WIP level where marginal throughput gain equals marginal holding cost.
This optimum is almost always below Critical WIP when holding costs are meaningful. It is the quantitative argument for why excess inventory destroys value even when the line appears to be running well.
Glossary of Terms
Bottleneck Rate (rₐ)
The throughput of the slowest station. The absolute ceiling on what the system can ever deliver, regardless of how much WIP you add.
Coefficient of Variation (CV)
Standard deviation divided by the mean. A measure of process time variability. CV of 0 is perfectly consistent. CV of 1.0 is high variability. Higher CV always degrades performance.
Critical WIP (W₀)
The WIP level that achieves maximum throughput at minimum cycle time. Calculated as bottleneck rate times raw process time. Below W₀: starving. Above W₀: congested.
Cycle Time (CT)
The average time a unit spends in the system from release to delivery. Rises steeply when WIP exceeds Critical WIP or variability is high.
Little's Law
WIP = TH × CT. A mathematical identity that holds for any stable system. Know any two values and you can calculate the third.
Practical Worst Case (PWC)
A realistic performance benchmark for an unmanaged system. Better than pure chaos, worse than perfect flow. Most real factories operate near this line.
Raw Process Time (T₀)
The sum of all station process times with no waiting. The minimum possible cycle time if a unit moved through the system with zero queue time.
Throughput (TH)
The rate at which the system delivers completed units. Cannot exceed the bottleneck rate regardless of how much WIP is added.
WIP (Work in Process)
Units currently inside the system from release to delivery. High WIP ties up capital and inflates cycle time without increasing throughput once the bottleneck is saturated.
CONWIP
Constant WIP. A pull control mechanism that caps the number of units in the system. New units enter only when a unit is delivered. Prevents line overload and keeps WIP near Critical WIP.