Purchasing Cost¶

Definition¶

The purchasing cost is the amount paid per inventory unit, multiplied by the quantity purchased. If its constant unit price is $c$ and all demand is met at constant rate $D$, the long-run purchasing cost rate is $cD$.

Interpretation¶

Purchasing cost is the money paid for the goods themselves, not the fixed charge per order or the cost of keeping stock. If all demand is met, on average $D$ units are bought per unit of time whatever the batch size, so a constant unit price $c$ gives the rate $cD$ for every EOQ policy.

The lines show cumulative cost at the long-run average purchasing rate, with $D=2$ phones per day: slope $340$ at the price $c_1=170$$170$, slope $320$ at the discounted price $160$. Actual batch payments form a staircase, jumping at purchase times; these straight lines smooth those payments to compare average rates. Batch size determines the payment times and which unit price applies, but not the rate $cD$ at a fixed price.

A constant $cD$ can therefore be left out when choosing the classical EOQ. With quantity discounts the unit price $c(y)$ depends on the batch size $y$, and then $c(y)D$ must be compared together with setup and holding costs.

Key Results¶

• A constant $cD$ can be omitted when finding the classical EOQ, but retained when reporting full costs.
• All-unit price breaks require comparing purchasing cost as well as setup and holding costs.
• Purchasing cost is different from the fixed cost of initiating an order.

Examples¶

• In the figure, time is measured in days. At demand $D=2$ phones per day and unit price $c_1=170$$170$, the smoothed cumulative cost has slope $c_1D=340$ per day.
• A discounted unit price of 160 reduces that rate to 320 when the order qualifies.

Prerequisites¶

• Inventory Policy

Related Concepts¶

• Setup Cost
• EOQ with Price Breaks

Sources¶

• OR Modelling · Week 5

Aliases: purchase cost, procurement cost

Last updated: 27 October 2026 11:52