What Shape Is Your Plant? A V, A, T and I Simulator

Four plant shapes, one engine. Drag any station's capacity and watch that shape's characteristic pathology emerge on its own.

VATI analysis sorts a plant by the shape of its material flow, not by what it makes. A V flow diverges: one raw material, many end products. An A flow converges: many parts, one end item. A T flow converges into common parts and then diverges again into many configurations. An I flow runs in a straight line. Nothing in this simulator is scripted. Every outcome falls out of three rules: convergence fires at the minimum across its legs, divergence lets the priority branch claim first, and a shared buffer is drawn down first come first served.

running self-check...

What you are looking at

One trunk operation converts raw material for both branches. After the divergence point, branch A has the priority claim on the shared buffer. Both branches carry 50 units a day of orders and the trunk makes exactly 100 a day, so on paper this plant is perfectly balanced. Watch what branch A's own capacity does to branch B's customers.

Flow, day 30 of 30

Scroll the diagram sideways to see the whole plant.

Running at capacity Starved, input was short Running full, output queue growing Drum, the slowest resource

Capacity against the 100 a day order book

Bar is the station's capacity. The black tick marks total daily demand of 100 units. Starvation at a non-constraint is normal and cheap. Starvation at the constraint is the expensive kind.

Cumulative shipped against cumulative orders

Both branches book 50 units a day, so a single dashed order line covers both. Under the default greedy policy branch A sits exactly on that line while branch B falls away from it.

Try this

Drag the trunk down to 80. Throughput falls, as it must. Now check who loses the units.
Put the trunk back to 100 and drag branch B down to 40 instead. Branch B's fill rate does not move at all, because 40 a day is already every unit branch A was leaving it. Its problem was never its own capacity.
Change no capacity at all and switch to Pull. Same machines, same people, same trunk rate, and branch B is back at 100 percent.

The lesson

Robbing

The Theory of Constraints literature calls the primary problem in V-plants robbing: the operation immediately after a diverging point takes material meant for its sibling. Once that material has been processed down one branch it cannot come back and run through the other without significant rework.

In the default run branch A claims 60 a day against 50 of orders. Those 10 units a day are the same 300 units seen from three sides: 300 robbed, 300 sitting as branch-A dead stock, 300 of branch-B orders never filled. Note what the fix does not change. The trunk converts 100 units a day under both policies.

What you are looking at

Two legs feed one assembly. Assembly can only fire when both legs have delivered, so it moves at the rate of the slower leg no matter how fast the other one runs. Leg 1 can make 50 a day, leg 2 can make 30, assembly could do 100. Demand is 50 a day. Watch where everything leg 1 makes actually ends up.

Flow, day 30 of 30

Scroll the diagram sideways to see the whole plant.

Running at capacity Starved, input was short Running full, output queue growing Drum, the slowest resource

Capacity against the 50 a day order book

Bar is the station's capacity. The black tick marks daily demand of 50 units. Assembly has capacity to spare and is still the station standing idle.

WIP waiting in front of assembly, by leg

Under a rope the two lines lie on top of each other, because both legs are released at the drum rate.

Try this

Drag leg 1 down from 50 to 30. Leg-1 WIP stops growing and not one unit of output is lost. Making less improved nothing except the balance sheet, which is the whole point.
Drag leg 2 up to 50 instead. Now watch assembly throughput and both legs at once.
Drag assembly down to 25. The station that had capacity to spare is now the constraint, both legs go quiet, and this time the customer really does get less.

The lesson

Synchronisation

The classic A-plant problem is synchronising the converging lines so that each one supplies the final assembly point at the right time. Assembly fires at the minimum across its legs, so a fast leg can never buy back a slow one.

Leg 1 runs at 100 percent utilisation and looks like the best performing resource on the floor while it builds 650 units nobody can assemble. Roping leg 1 to the drum rate removes 620 units of WIP and ships exactly the same 900 units. Assembly, meanwhile, sits at 30 percent utilisation and is starved every single day.

What you are looking at

Two legs converge into a common-parts assembly, then the common parts diverge again into two configurations. The legs run at 65 against a 60 a day assembly, so this shape is carrying an A-plant problem and a V-plant problem at the same time. Config 1 draws from the shared shelf first. Supply of 60 a day exactly equals the combined order book of 30 plus 30, so every part Config 1 over-draws is a part Config 2 was entitled to.

Flow, day 30 of 30

Scroll the diagram sideways to see the whole plant.

Running at capacity Starved, input was short Running full, output queue growing Drum, the slowest resource

Capacity against the 60 a day order book

Bar is the station's capacity. The black tick marks total daily demand of 60 units. Both legs sit above the drum, which is exactly why leg WIP runs away while the configure side is fighting over parts.

The shared shelf and what each configuration actually shipped

Shelf level is read at the end of each day, on the left axis. Fill rate is cumulative units shipped divided by cumulative orders, on the right axis.

Try this

Drag Config 1 down from 45 to 30. Watch Config 2's fill rate and the shelf at the same time. Config 1 loses nothing.
Switch to Pull without touching a single capacity, then look at the shelf line. It stops moving.
Drag both legs down to 60. Leg WIP stops running away and the customer sees no difference at all. That is the A-side problem and the V-side problem responding to two completely different fixes.

The lesson

Both failure modes at once

A T-plant is an A-plant feeding a V-plant, so it inherits synchronisation on the converging side and robbing on the diverging side. Practitioners commonly describe it as the trickiest of the four to schedule, and this run shows why.

The theft is invisible in an averages view. The common-parts shelf never ends a day below 60 units and averages 63, which looks healthy on any inventory report, while Config 2 shipped complete on 4 days out of 30.

Careful with the two counters. 450 parts stolen is not 450 missed orders. It is 390 unfilled Config 2 orders plus 60 units of shelf drawn down over the first four days, while the buffer was still cushioning the theft.

What you are looking at

Five stations in a straight line. Station 3 can only do 24 a day, everything else can do 40, and demand is 30 a day. There is no divergence and no convergence here, so the only real question is how much material you release into the front of the line. Push releases at station 1's capacity. Rope releases at the drum rate.

Flow, day 30 of 30

Scroll the diagram sideways to see the whole line.

Running at capacity Starved, input was short Running full, output queue growing Drum, the slowest resource

Capacity against the 30 a day order book

Bar is the station's capacity. The black tick marks daily demand of 30 units. Every station except the drum has protective capacity, and that is not waste.

Queue waiting in front of each station

One panel per station, all five drawn on the same vertical scale, 0 to 600 units, so the spike is honest. Blue marks the drum.

Try this

Stay on Push and drag station 1 down from 40 to 24. You just built a rope with a capacity slider, and the WIP figure proves it.
Drag station 3 up to 40. Where does the drum go next, and what happens to lead time?
Switch to Rope and compare WIP. The identical 720 units ship out, with 512 fewer units of inventory standing in the way.

The lesson

Starve and block

In a straight line the slowest station sets the pace. Everything upstream of it piles up, everything downstream of it starves, and releasing material faster than the drum can convert it buys inventory and nothing else.

Push and Rope ship the identical 720 units. The rope's steady-state WIP settles at 120, which is exactly the critical WIP from Factory Physics: the drum rate of 24 multiplied by the 5-day raw process time. Lead time follows from Little's Law, WIP divided by throughput, and falls from 26.3 days to 5.0.

Sources and model notes

The V, A and T definitions and the named failure modes follow the standard TOC plant-type entries (APICS Dictionary, 13th ed., as cited in Wikipedia's Theory of Constraints article). "I" is commonly described as a later practitioner addition, and is also commonly described as a subset of V rather than a true fourth type.
Lockamy, A. (2008). "Examining supply chain networks using V-A-T material flow analysis." Supply Chain Management: An International Journal, 13(5), 343 to 348. DOI: 10.1108/13598540810894924
Srikanth, M.L., "DBR, Buffer Management, and VATI Flow Classification", chapter 8 of the Theory of Constraints Handbook. Umble, M.M. and Srikanth, M.L., Synchronous Manufacturing (1990). Cox, J.F. III and Spencer, M.S., The Constraints Management Handbook (1998). Goldratt, E.M. and Cox, J., The Goal (North River Press, 1984).
Simulation maths follows Hopp and Spearman, Factory Physics: bottleneck rate sets throughput, Little's Law gives WIP equals throughput times cycle time, and critical WIP equals bottleneck rate times raw process time.
Real plants are hybrids. Every source stresses that a working factory is more likely a V base with a T top than a pure type. Treat the four tabs as lenses, not labels.

This is a deterministic teaching model, not industry data. Thirty daily ticks, integer units, no randomness anywhere, every buffer primed to its steady-state value so day 1 is already running. Each node moves material exactly one step per tick. Numbers here are simulation output from a model defined for this post, not measurements from any plant. Engine ported from the frozen dataset contract v1.0. AI transparency (EU AI Act): this simulator was built with AI assistance under human editorial control; its outputs were verified against the published R reference implementation.