Holding Cost¶

Definition¶

A holding cost charges for inventory kept in stock. In the continuous-time EOQ model, $h$ is the cost per unit held per unit of time. With average inventory $\bar I$ , the average holding cost rate is $h\bar I$ . In the discrete-time models, $h_i$ charges each unit carried from period $i$ to $i+1$ $1$ .

Interpretation¶

Holding cost is the price of keeping goods in stock: space, tied-up money, spoilage. Charged per unit and per unit of time, it penalizes large and early orders and pushes batch sizes down.

One cycle of a sawtooth stock level as a shaded triangle from y down to 0, with the average stock y/2 drawn as a horizontal line.

The triangle is one cycle of the sawtooth: stock falls from $y$ to $0$ in time $t_0$ . Its area $\tfrac{1}{2}yt_0$ adds up stock multiplied by time, and $h$ turns it into the holding cost of one cycle, the same as holding the average stock $y/2$ , the dashed line, all the time.

The average stock in the sawtooth is $y/2$ (dashed line), so the holding cost rate is $hy/2$ . Raise $h$ to see $y^*$ fall.

A common slip is to charge $hy$ per unit time in the classical EOQ model, as if the whole batch stayed in stock. The time unit of $h$ must match that of the demand rate: in the snack-bar Examples, $3$ per kilogram per week becomes $3/7$ per kilogram per day.

Key Results¶

The shaded triangle has area $yt_0/2$ . Multiplying by $h$ gives the holding cost of one cycle, $hyt_0/2$ ; dividing by the cycle length $t_0$ gives the cost rate $hy/2$ . Thus classical EOQ average inventory is $y/2$ .
With planned shortages, the full-cycle average positive stock is $s^2/(2y)$ , not $s/2$ .
Discrete-time exercises charge end-of-period stock.

Examples¶

The snack bar converts 3 per kilogram per week to $3/7$ per kilogram per day.
The pencil example charges $1/1000=0.001$ per pencil per day.

Prerequisites¶

Inventory Policy

Sources¶

OR Modelling · Week 5

Aliases: carrying cost, inventory holding cost

Last updated: 20 October 2026 03:02