Many manufacturing resources require setup before processing a different part, tool set or product family. Setup time is usually incurred per batch rather than per individual piece.

If setup time is $S$, run time per part is $t$ and batch size is $Q$, the average resource time allocated per part is

$$t_{avg}=t+\frac{S}{Q}.$$

Suppose a machine needs a 60-minute setup and 2 minutes per part.

For $Q=10$,

$$t_{avg}=2+\frac{60}{10}=8\ \mathrm{min/part}.$$

For $Q=100$,

$$t_{avg}=2+\frac{60}{100}=2.6\ \mathrm{min/part}.$$

Large batches dilute setup time, but they also create more WIP, longer waiting and slower response to changing demand.

Reducing setup time changes this trade-off. If the same setup is reduced from 60 to 10 minutes, a 10-part batch requires only

$$2+\frac{10}{10}=3\ \mathrm{min/part}.$$

Small batches then become much less costly in capacity terms.

Batch size is therefore not purely an inventory choice. It is coupled to changeover design, production flow and process flexibility.