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A company is planning to purchase 90,800 units of a particular item in the year ahead. The item is purchased in boxes each containing 10 units of the item, at a price of $200 per box. A safety inventory of 250 boxes is kept.
The cost of holding an item in inventory for a year (including insurance, interest and space costs) is 15% of the purchase price. The cost of placing and receiving orders is to be estimated from cost data collected relating to similar orders, where costs of $5,910 were incurred on 30 orders. It should be assumed that ordering costs change in proportion to the number of orders placed. 2% should be added to the above ordering costs to allow for inflation. Assume that usage of the item will be even over the year.
Workings:
To avoid confusion this question is best tackled by working in boxes not units.
Co = 5910/30 x 1.02 = 200.94
Ch = 0.15 x 200 = $30 per box
D = 90,800/10 = 9,080 boxes
EOQ = ?(2×200.94) x 9,080/30) = 349 boxes
No. of orders per year = 9,080/349 = 26
26 orders per annum is equivalent to placing an order every 2 weeks (52 weeks / 26 orders).
I have only one question, in Co, how did we get 1.02?
Multiplying by 1.02 is the same as adding 2% (for inflation).
If you prefer, then Co (without inflation) is 5910/30 = $197.
Because of inflation add on 2% x 197 which is $3.94
Which gives Co = 197 + 3.94 = $200.94
Thank you sir for the clarification.
You are welcome 🙂
Thanks a lot for your guide. But this solution make more complication on question. You solved in a right way.
The order quantity which minimises total costs is 3,487
This will mean ordering the item every 2 weeks
I have only one question, in Co, how did we get 3,487?
We order in boxes and there are 10 in each box.