It is an interesting question.
EOQ model starts from that the minimum point of the total cost (Inventory holding + Ordering cost). At the minimum point, the Inventory holding cost equals to the Ordering cost.
(of cause you can use calculus to find the minimum point but the answer will be the same)
$\frac{Q}{2}h = \frac{\lambda}{Q}K$
The problem starts from here. $\frac{Q}{2}$ is the average inventory level over the year. Therefore, The unit should be Item. However, $\frac{\lambda}{Q}$ is the number of orders per year . Therefore if the $\lambda$ is Item per Year, Q has to be Item/order.
If we accept $Q$ has the unit Item/order, The average Inventory level $\frac{Q}{2}$ should have the unit, Item/order, but it should be Item for average Inventory level.
the $Q$ in $\frac{Q}{2}$ and $Q$ in $\frac{\lambda}{Q}$ are different in the unit.
- The average inventory can be calculated by dividing the highest point in the sawtooth shape cycle by 2. The highest point is the highest inventory level, so the unit should be Item.
How do we find the highest point? We know the highest point in the inventory level is the $Q$, order quantity, (Item per order)
They are indeed the same number (but in different units) so that we can solve the equation.
- The Average Inventory level per order, $\frac{Q}{2}$ (unit: Item/order) is the Annual average Inventory level $\frac{Q}{2}$ (unit: Item)
But when we calculate Annual inventory holding cost, we use 'annual average inventory level', not 'average inventory level per order'.
Not sure it is what you are looking for. Expecting discussions