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

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

<ul>
<li><p>The average annual number of batches ordered is $\dfrac{3600}{Q}$ so the average annual cost of ordering is $£\dfrac{72000}{Q}$</p></li>
<li><p>The average number of items held in inventory is $\dfrac Q2$ worth $£\dfrac{3Q}{2}$ at a holding cost of $£\dfrac{3Q}{8}$ </p></li>
<li><p>So the combined ordering and holding cost is  $£\dfrac{72000}{Q}+£\dfrac{3Q}{8}$</p></li>
<li><p>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</p></li>
<li><p>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</p></li>
</ul>

CC BY-SA 4.0
2018-05-05T20:32:46.570Z
2018-05-06T14:59:50.230Z
2018-05-06T14:59:50.230Z
Henry
<p>This is very simple, however, I have the following setup</p>

<p><em>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.</em></p>

<p>What I want to do is calculate the <strong>EOQ</strong></p>

<p>$$
EOQ = \sqrt{\frac{2DS}{H}}
$$</p>

<p>Where </p>

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

<p>I figured that I would have</p>

<p>$$
H = 0.25 \times 3 = 0.75
$$</p>

<p>I'm sceptical about this result though. </p>

CC BY-SA 4.0
2018-05-05T20:33:26.597Z
This seems to give $EOQ \approx 438$. Do you think this looks too large or too small?
Henry
CC BY-SA 4.0
2018-05-06T14:58:48.143Z
Note that for the formula to be correct, $H$ must be holding cost _per unit per year_.
Adam Bailey
<cost>
EOQ - how to calculate holding cost
wsx399
# EOQ - how to calculate holding cost

(Asked by: username_0 on 2018-05-05)

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.

**Tags:** cost
> **Comments:**
> **username_1**: This seems to give $EOQ \approx 438$. Do you think this looks too large or too small?  
> **username_2**: Note that for the formula to be correct, $H$ must be holding cost _per unit per year_.  

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## 1 answers

### Answer by username_1 on 2018-05-05. Score: 2 | Accepted 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


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