Question

The Gilbreth family drinks a case of Royal Cola every day, 365 days a year. Fortunately, a local distributor offers quantity discounts for large orders as shown in the table below. Considering the cost of gasoline, Mr. Gilbreth estimates it costs him about $5 to go pick up an order of Royal Cola. Mr. Gilbreth also is an investor in the stock market, where he has been earning a 20% average annual return. He considers this opportunity cost to be the only holding cost for the Royal Cola.

Discount Category	Quantity	Purchased Price (per case)
1	1 to 49	$4.00
2	50 to 99	$3.90
3	100 or more	$3.80

Determine the optimal quantity according to the EOQ model with quantity discounts. What is the resulting total variable inventory cost per year?

Answer 1

Annual Demand= 365*1= 365

Ordering cost= $5

let's calculate EOQ in each discount category

1- Holding cost= 20% of $4= 0.8, EOQ= ?2*365*5/0.8= ?4562.5= 67.5

2-  Holding cost= 20% of $3.9= 0.78, EOQ= ?2*365*5/0.78= ?4679.5= 68.4=68

3- Holding cost= 20% of $3.8= 0.76, EOQ= ?2*365*5/0.76= ?4802.6= 69.3=69

Discount category 1 will be discarded because EOQ is greater than the quanity in the bracket. Now calculate Total cost in other two discount category

Category 2- Units to be ordered= 68 case per order

Total cost= 365*3.90+365/68*5+68/2*0.78=1423.5+26.8+26.5=$1476.8

Category 3- Units to be ordered= 100 case per order

Total cost= 365*3.80+365/100*5+100/2*0.76=1387+18.3+38=1443.3

Category 3 should be selected