# Relation between order quantity and average cycle stock

Annual demand: $$1000$$ units

Unit cost: $$5$$ dollars

Company replenishes the inventory two times per year.

Average Cycle Stock: $$300$$

I am asked to compare average cycle stock with number of replenishments per year.

My approach:

The formula of average cycle stock is: $$\frac{cQ}{2}$$

So when I applied the given information:

$$\frac{(5)(Q)}{2}=300$$

I found $$Q$$ to be $$120$$. If that is correct, how can it be possible that annual demand is $$1000$$, and company replenishes the inventory two times a year and order quantity to be $$120$$? I mean if we order twice a year, wouldn't our total order quantity be $$240$$? What point do you think I am missing?

• What do you mean by "compare average cycle stock with number of replenishments per year"? Further, why do you multiply by the unit cost to get an average quantity? If you order always $Q$ then your average stock should be $Q/2$. Could you please clarify your goal? Mar 28, 2021 at 21:09
• I want to draw a graph similar to the one on page 6(exchange curve) of this slide. That's what I mean by to compare average cycle stock with number of replenishments. Well, in some sources it is called as average cycle stock, some others call it $value of average inventory. I am trying to draw the exchange curve of replenishment frequency vs inventory value. Formula & graph also can be found on the page 289 of Nahmias, S., Production and Operations Analysis, 6th edition. Mar 29, 2021 at 7:06 • your$Q$is$600$, because your average cycle stock is in pieces. TACS is$\frac{600}{2}*5 = 1500$Mar 29, 2021 at 9:18 • @Steven01123581321 I couldn't understand how Q is 600. And how did you obtain 1500? Mar 29, 2021 at 12:25 • how I read it, is that your average cycle stock is$300$, which would lead to a$Q$of$600$, because$average \space cycle \space stock = \frac{Q}{2} $. If the average cycle stock is$300$, the ACSV = average cycle stock value is$300 \times 5 = 1500$. Then the point on the exchange curve is$(1500, 2 \times order \space cost)\$. Mar 29, 2021 at 12:47

So as a formal answer: your $$Q$$ is $$600$$ as the average cycle stock is in pieces. So
$$average\space cycle\space stock = 300 = \frac{Q}{2} \implies Q = 300 \times 2 = 600$$
The total average cycle stock value in the exchange curve is the sum of all average cycle stocks of all items in your group you are evaluating, expressed in value. So for one item, your average cycle stock value is $$\frac{cQ}{2}$$, which in this example is $$\frac{5\times 600}{2} = 1500$$.
With $$Q = 600$$, the company orders twice a year which is the x-axis in the exchange curve. You can then do this for several items and plot the current situation, together with the exchange curve to see