# EOQ - how to calculate holding cost

This is very simple, however, I have the following setup

Suppose that the company ABC has a product that shows a constant annual demand rate of 3600 items. One item costs £3. Ordering cost is £20 per order and holding cost is 25% of the value of inventory.

What I want to do is calculate the EOQ

$$EOQ = \sqrt{\frac{2DS}{H}}$$

Where

• D = annual demand (here this is 3600)
• S = setup cost (here that's £20)
• H = holding cost
• P = Cost per unit (which is £3 here)

I figured that I would have

$$H = 0.25 \times 3 = 0.75$$

I'm sceptical about this result though.

• This seems to give $EOQ \approx 438$. Do you think this looks too large or too small? – Henry May 5 '18 at 20:33
• Note that for the formula to be correct, $H$ must be holding cost per unit per year. – Adam Bailey May 6 '18 at 14:58

## 1 Answer

So your EOQ expression is suggesting that the optimal order size is for about $438$ items each time.

You can check the result if you wish. Suppose you order in batches of $Q$:

• The average annual number of batches ordered is $\dfrac{3600}{Q}$ so the average annual cost of ordering is $£\dfrac{72000}{Q}$

• The average number of items held in inventory is $\dfrac Q2$ worth $£\dfrac{3Q}{2}$ at a holding cost of $£\dfrac{3Q}{8}$

• So the combined ordering and holding cost is $£\dfrac{72000}{Q}+£\dfrac{3Q}{8}$

• For $Q=437$ this gives about $£328.6347$; for $Q=438$ this gives about $£328.6336$; for $Q=439$ this gives about $£328.6341$. This suggests that $438$ may indeed be the best order size

• You can check the calculus: the derivative of $\dfrac{72000}{Q}+\dfrac{3Q}{8}$ is $\dfrac{3}{8} - \dfrac{72000}{Q^2}$ which is a increasing function of $Q$ and is zero when $Q^2=192000$ i.e. $Q \approx 438.178$, and this would minimise the combined cost