Overage Cost¶

Definition¶

The overage cost in the newsvendor model is the net loss on one unit ordered but not sold at its regular price:

h=c-s>0,

where $c$ is its unit cost and $s$ its salvage value. Total expected overage cost at order quantity $y$ is $h\mathbb{E}[(y-D)^+]$ $D)^{+}]$ .

Interpretation¶

The overage cost is what one unsold unit costs in the end: it was bought for $c$ and brings back only the salvage value $s$ , so the net loss is $c-s$ $s$ . It is the price of ordering one unit too many.

A vertical money scale with the selling price 5, purchase cost 3.50 and salvage value 1.50; the gaps between them are the underage cost 1.50 and the overage cost 2.

The money scale shows the newspaper data: the purchase cost $c=3.50$ and the salvage value $s=1.50$ are $h=2$ apart, the lower gap. The upper gap, from $c$ to the selling price $p=5$ $5$ , is the underage cost $b=1.50$ $1.50$ ; together they span $p-s=3.50$ $3.50$ , the denominator of the critical ratio $\beta=1.5/3.5=3/7$ $3/7$ .

Each unsold unit loses $h=c-s$ $s$ . A low or negative salvage value $s$ pushes $y^*$ down.

Only leftover units are charged, and the positive part $(y-D)^+$ counts them. A higher salvage value lowers $h$ and raises the optimal order; a negative $s$ , a disposal fee, makes $h$ larger than $c$ . Unlike the EOQ holding cost, which is charged per unit per unit of time, $h$ is charged once per leftover unit of the single period.

Key Results¶

Only leftover units incur overage loss.
Increasing salvage value lowers overage cost.
This is a single-period per-unit loss, whereas EOQ holding cost is charged per unit per unit time.

Examples¶

The illustrated newspaper data give overage cost $h=2$ and underage cost $b=1.5$ $1.5$ , hence critical ratio $\beta=1.5/3.5=3/7$ $3/7$ . These are single-period per-unit losses, rather than EOQ cost rates.

Newspapers costing 3.50 and salvaged for 1.50 have $h=2$ $2$ .
Meals costing 2.20 with zero salvage have $h=2.20$ $2.20$ .

Prerequisites¶

Sources¶

OR Modelling · Week 6

Aliases: overstocking cost, overstock cost Symbols: beta

Last updated: 20 October 2026 03:02