Question

Suppose Big Box Office Supply (BBOS) purchases 100,000 office chairs every year. Ordering costs are $95.00 per order and carrying costs are $5.75 per chair. What is BBOS’s total inventory cost per year, including both carrying costs and ordering costs, if BBOS orders the EOQ of office chairs? Enter your answer rounded to two decimal places.

Answer 1

Solution:

Economic order quantity is calculated using the following formula:

= ( 2AO / C ) ^{( ½ )}

Where A = Annual usage units

O = Ordering cost per order

C = Annual carrying cost of one unit

In the given question as per the data given:

A = Annual usage units = 100,000

O = Ordering cost per order = $ 95.00

C = Annual Inventory carrying cost of one unit = $ 5.75

Thus Optimal order quantity = ( ( 2* 100,000 * $ 95 ) / 5.75 ) ^{( ½ )}  

= ( 19,000,000 / 5.75 ) ^{( ½ )}

= ( 3,304,347.8261 ) ^{( ½ )}

= 1,817.7865 ( when rounded off to four decimal places )

= 1,817.79 ( when rounded off to two decimal places )

= 1,818 orders ( when rounded off to the nearest integer )

Note : The square root of 3,304,347.8261 is calculated using the following formula in excel

=SQRT(Number) = SQRT(3,304,347.8261) = 1,817.7865

Statement showing total annual Inventory Cost at the Economic order quantity of 1818 units :

Sl.No.	Particulars	Amount
1	Ordering Cost ( ( 100000 / 1818 ) * 95) = $ 5225.5226 (No. of orders * ordering cost per order ) No. of Orders = Purchase units / EOQ = 100000/1818	$ 5,225.52
2	Carrying cost of average inventory Here Average inventory = 1818 Thus Carrying cost =[ (Average inventory * Inventory carrying cost per unit ) ]/ 2 =[(1818 * 5.75) / 2] = $ 5226.7500	$ 5,226.75
	Total annual Inventory cost of Economic order quantity	$ 10,452.27