Setup load: the fast cycle still falls short

A 60 second run time suggests a station covers 40 units an hour, but setups between batches eat its time. Type the batch and the occupied times, and the real capacity and the break even batch appear.

Capacity after every setup

The station returns 34.3 units/hour, below demand of 40.0, with 1,800 seconds of setup per 40 units and 60 seconds of run work per unit.

Capacity, units/hour

Production batch, units

Entered batch40Equal capacity60

Units: The view runs from 1 to 100 units; the comparison checks every whole batch from 1 to 1,000

Count the workstation time occupied by one setup and every unit in the repeated batch

Production batch, units

Demand, units/hour

Run time, seconds/unit

Setup time, seconds/batch

Setup times, seconds

Where the spare time begins

First whole batch above demand: 61 units
Whole batch equal to demand: 60 units
Run-only capacity, units/hour: 60.0
Required load, percent: 116.7
Cycle spent on setup, percent: 42.9

An equal capacity leaves zero spare time in this repeated-cycle ledger

Entered batch and crossing neighbourhood

Entered batch and crossing neighbourhood
Batch, units	Capacity, units/hour	Reading
40	34.3	Below demand
59	39.8	Below demand
60	40.0	Equal to demand
61	40.2	Above demand

The cycle figure left out a clock

A 60-second run time gives 60 units per hour while the workstation is producing. The production order repeats a different clock: one setup, then the run work for the whole batch. Every repetition pays that setup again. A capacity figure built from run time alone gives those occupied seconds no place in the denominator.

At the opening batch of 40, the station runs for 2400 seconds and spends another 1800 on setup. It therefore releases 40 units in 4200 seconds, equivalent to 34.3 per hour. The order calls for 40.0 per hour. The nominal rate is above demand while the repeated-cycle rate is below it, using the same station and the same run time.

Spreading the setup over more units raises capacity toward the run-only rate. The curve cannot go above that rate. If demand already equals or exceeds the run-only rate, a positive setup cannot be diluted enough by any finite batch. With no setup, batch size has no effect on capacity at all.

A transfer lot is a different quantity. Moving completed units onward in smaller groups can open overlap between stations while the process batch continues under the same setup. This ledger charges a new setup only when a new process batch begins. The distinction decides which clock changes when someone writes a smaller lot on the sheet.

The calculation and its basis

One occupied cycle

Let Q be batch units, S setup seconds, p run seconds per unit, and D hourly demand. Capacity divides units by all occupied time: $C(Q)=\frac{3600Q}{S+Qp}$ . Required load is the fraction of available time the demand would occupy: $u=\frac{D(S+Qp)}{3600Q}$ .

The strict crossing

$Q>\frac{DS}{3600-Dp}\quad(3600-Dp>0)$ . The first whole quantity strictly above the quotient has spare capacity. Equality receives its own reading, and a nonpositive denominator means no finite batch is strictly above demand.

The opening ledger

Run work: $40\times60=2400$ seconds; cycle time: $1800+2400=4200$ seconds.
Capacity: $\frac{3600\times40}{4200}=34.285714285714285$ units/hour, displayed as 34.3; load: $\frac{40\times4200}{3600\times40}=1.1666666666666667$ , displayed as 116.7%.
Crossing: $\frac{40\times1800}{3600-40\times60}=60$ units; 60 ties at 40.0 units/hour, and 61 first exceeds demand at 40.21978021978022, displayed as 40.2.

Source basis

Gerard Cachon and Christian Terwiesch derive setup-adjusted batch capacity in Matching Supply with Demand: An Introduction to Operations Management, fourth edition, 2018, chapter 5. Wallace Hopp and Mark Spearman distinguish process batches from transfer batches and describe their capacity effect in Factory Physics, third edition, 2008, section 9.4.2.

Scale: Whole batches checked from 1 to 1,000; continuous guide between them, exact integer comparison
Basis: One sequential workstation, one occupied setup per process batch, identical run time per unit
Assumptions: Repeated identical cycles, constant demand, all completed units counted on the same basis
Model version: 1.0.0

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This counts repeated setup and run time; it does not choose a batch size or estimate waiting, scrap, or delivery dates.

Setup load record