Relation between order quantity and average cycle stock

Question

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?

Answer 1

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

• what your order strategy should be based on managerial implications
• how far off you are with the current situation.

This is also handled in the book of Silver, Pyke & Peterson :Inventory Management and Production Planning and Scheduling (1998)