Setup Cost¶

Definition¶

A setup cost is a fixed charge incurred whenever an order is placed, regardless of the order quantity. In the EOQ model it is denoted by $K$ . With demand rate $D$ and batch size $y$ , its average rate is

\frac{K}{y/D}=\frac{KD}{y}.

Interpretation¶

A setup cost is paid once per order, whatever its size, so what matters is how often orders are placed. Ordering $y$ units at demand rate $D$ gives one order every $y/D$ time units, the ordering cycle, hence $D/y$ orders per unit time and the setup cost rate $KD/y$ .

Two sawtooth stock patterns over 33 days: small batches with six setups K, and batches twice as large with only three setups.

Both panels cover the same $33$ days at $D=2$ units per day. Batches of $y=11$ last $5.5$ days, so six setups $K$ are paid; batches of $y=22$ last $11$ days and need only three, but each sawtooth starts twice as high, so the average stock doubles.

Each order costs $K$ and there are $D/y$ orders per unit time, so setups cost $KD/y$ . Raise $K$ to make larger batches worthwhile.

The rate $KD/y$ falls as $y$ grows while the holding cost rate rises, and the economic order quantity balances the two. A common slip is to charge $K$ for every unit ordered: a cost proportional to the quantity belongs to the purchasing cost.

Key Results¶

The charge is per order, not per inventory unit.
A period with no order incurs no setup in the dynamic lot-size model.
Increasing $K$ increases the classical optimal order size.

Examples¶

For the illustrated phone shop, $K=605$ per order and $D=2$ per day. The two panels cover the same $33$ days:

Batch size	Number of setups	Setup cost per day
$y=11$ (left)	$6$	$KD/y=1210/11=110$
$y=22$ (right)	$3$	$KD/y=1210/22=55$

Doubling the batch size halves the setup frequency and its cost rate, but doubles average stock.

The snack bar pays 50 per order in addition to a per-kilogram purchase price.

Prerequisites¶

Sources¶

OR Modelling · Week 5

Aliases: fixed ordering cost

Last updated: 20 October 2026 03:02