# Production ramps, inventory and allocation

Canonical: https://semiaifoundry.com/learn/atlas/production-ramp-allocation/
Revision: 2026-10-07
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Data-center physical systems · Atlas v1.3.0

# Production ramps, inventory and allocation

Tracks time-dependent output and distinguishes qualified supply from a customer’s accessible share.

[Explore in Atlas](https://semiaifoundry.com/ai-atlas/#production-ramp-allocation)Manufacturing supply to commissioned hall; time-dependent model

Learning objectiveModel ramps and allocation without treating future capacity as immediate inventory.

## The mechanism

A capacity announcement describes a plan or installed capability, while output ramps as equipment, process performance and qualification mature. Inventory can buffer delays, but repeated visits and queued work make factory cycle time longer than processing time. A finished product may then be reserved, contracted or allocated to a different customer. TSMC’s annual report describes customer-linked capacity planning without revealing private allocation shares. Physical output and access require separate accounting: completed equipment can exist without being allocated to the workload in question. Increasing a nominal monthly capacity input must not instantly create finished inventory before its lead time and qualification gates have elapsed.

1.  Represent the announced or installed capability separately from actual starts and completed units.
2.  Delay output by processing and waiting time, with qualification as its own release gate.
3.  Update inventory as compatible inputs arrive and finished products consume them.
4.  Allocate qualified output using explicit scenario rules rather than guessing confidential customer shares.
5.  Compare the time-dependent delivered result with the intended deployment schedule and identify the current bottleneck.

## Science and assumptions

### Inventory conservation

$$
I(t+1)=I(t)+A(t)-C(t)
$$

Next inventory equals current inventory plus arrivals minus consumption during the same interval.

A and C explicitly name the original arrivals and consumption functions; they are counts per interval, not unintegrated rates.

Symbols and units

I(t)

Inventory at the beginning of discrete interval t

same compatible item units

I(t+1)

Inventory at the end of that interval

same compatible item units

A(t)

Arrivals during interval t

same compatible item units

C(t)

Consumption during interval t

same compatible item units

t

Discrete interval index

integer index

Every term counts the same compatible item over the same time step.

Assumptions No hidden scrap or rework; those flows must be explicitly added when modeled.

## Engineering example

Synthetic three-week lead time means extra starts in week one cannot become completed supply until week four at the earliest. A customer allocated half that output receives only that half, even if total factory output is larger.

## Distinctions and tradeoffs

Capex is not production volume, and supplier capacity does not identify a customer’s allocated share.

Inventory improves resilience to some delays but consumes resources and can become mismatched when designs change; conservative ramps reduce overcommitment.

Hardware availability for a training program depends on arrival dates and allocation, not merely on a supplier’s eventual nameplate capacity.

## Specifications and interfaces

Three time concepts

Processing, waiting and qualification delay

All can affect first usable output without representing the same work.

Supply versus access

Qualified production and allocated units

Physical existence does not establish availability to a particular buyer.

### Interfaces

Capacity plan and incoming inventory Input

Time-varying starts, lead times and screening assumptions

Allocated qualified supply Output

Finished units released to a defined destination and date

## Check your understanding

### Why can a capacity increase fail to improve next week’s deliveries?

1.  Lead time, qualification or another input can delay output
2.  Capacity and inventory are always identical
3.  All reservations disappear when a tool arrives

Answer and reasoning

Lead time, qualification or another input can delay output

A change in possible starts takes time to propagate and may encounter another required input or release gate.

## Evidence and scope

Allocation fractions and delays are synthetic. TSMC source material supports planning roles, not confidential queues, customer shares or current unit-per-month estimates.

Trace compatible component rates, a bounded qualification/ramp scenario and package backlog; this is not a detailed fab queue or operator-allocation simulator.

## Sources

-   [TSMC 2025 Annual Report](https://investor.tsmc.com/sites/ir/annual-report/2025/2025%20TSMC%20Annual%20Report.E.pdf)

[Published lesson data](https://semiaifoundry.com/ai-atlas/lesson-data/production-ramp-allocation-3d4ff12263731960.json) · [Atlas releases and licensing](https://semiaifoundry.com/ai-atlas/licenses.html)

## Continue exploring

### Foundations

-   [Compatible supply and converging bottlenecks](https://semiaifoundry.com/learn/atlas/compatible-supply-capacity/)

### Related lessons

-   [Facility phases and geographical evidence](https://semiaifoundry.com/learn/atlas/capacity-phase-geography/)
-   [Cluster scheduler and resource allocation](https://semiaifoundry.com/learn/atlas/scheduler/)