) Joe Birra need to purchase malt for his micro-brew production. His supplier ch
ID: 370356 • Letter: #
Question
) Joe Birra need to purchase malt for his micro-brew production. His supplier charges $30 per delivery (no matter how much is delivered) and $1 per gallon. Joe’s annual holding cost is 30% of the price per gallon. Joe uses 200 gallons of malt per week.
a. Suppose Joe orders 1000 gallons each time. What is his average inventory? _____ gallons
b. Suppose Joe orders 2000 gallons each time, How many orders does he place with supplier each year? _____ orders
c. How many gallons should Joe order from his supplier with each order to minimize the sum of ordering and holding costs_____ gallons
d. Suppose Joe orders 2750 gallons each time he places an order with the supplier. What is the sum of ordering and holding costs per gallon $ ____/per gallon?
e. Suppose Joe orders the quantity from part © that minimizes the sum of the ordering and holding costs each time he places an order with the supplier, What is the annual cost of the EOQ expressed as a percentage of the annual purchase cost?
f. If Joe’s supplier only accepts orders that are an integer multiple of 1,000 gallons, how much should Joe order to minimize ordering and holding costs per gallon? ______ gallons g. Joe’s supplier offers a 3% discount if Joe is willing to purchase 8000 gallons of more. What would Joe’s total annual cost (purchasing , ordering and holding ) be if he were to take advantage of the discount _____?
Explanation / Answer
Answer to question a :
Annual demand of malt = 200 Gallons/ week x 52 weeks = 10400 Gallons
Order quantity = 1000 Gallons each time
Average inventory = Order Quantity / 2 = 1000/ 2 = 500 Gallons
Answer to question b :
New order quantity = 2000 Gallons
Number of orders in a year = Annual demand / Order quantity = 10400/2000 = 5.2
Answer to question c:
We have to establish Economic Order Quantity ( EOQ ) as per relevant model to minimize ordering and holding cost
Accordingly,
EOQ = Square root ( 2 x Co x D / Ch)
D = Annual demand = 10400 Gallons
Co = Ordering cost = $30
Ch = Annual unit Holding cost = 30% of $1 = $ 0.3
Thus ,
EOQ = Square root ( 2 x 30 x 104000/0.3)
= 1442.22
JOE SHOULD ORDER 1442.22 GALLONS TO MINIMIZE SUM OF ORDERING AND HOLDING COST
Answer to question d :
When order quantity = 2750 Gallons
Annual ordering cost = Ordering cost x Number of orders
= Ordering cost x Annual demand / Order quantity
= 30 x 10400 / 2750
= $ 113.45
Annual holding cost = Annual unit holding cost x Average inventory
= $0.30 x 2750/2
= $412.5
Thus, sum of ordering and holding cost for order qty of 2750 = $113.45+ $412.5= $525.95
Thus, Sum of ordering and holding cost per Gallon = $525.95/ 2750 = $ 0.191
SUM OF ORDERING AND HOLDING COST PER GALLON = $ 0.191
Answer to question e :
For order quantity = EOQ = 1442.22 Gallons,
Annual ordering cost = Ordering cost x Number of orders
= Ordering cost x Annual demand / Order quantity
= 30 x 10400/ 1442.22
= $ 216.33
Annual holding cost = Annual unit holding cost x Average inventory
= $0.3 x 1442.22/2
= $ 216.33
Thus, sum of ordering and holding cost for order qty of 1442.22 = $216.33 + $216.33= $432.66
Annual purchase cost = $1.00/ Gallon x 10400 Gallons = $10400
Thus,
Annual cost of EOQ as percentage of Annual purchase cost = 432.66 /10400 x 100 = 4.16%
ANNUAL COST OF EOQ AS PERCENTAGE OF ANNUAL PURCHASE COST = 4.16%
Answer to question f :
If order quantity should be such that it minimizes total ordering and holding cost and yet is multiple of 1000, then the order quantity should be multiple of 1000 and should be the nearest ones to theoretical EOQ of 1442.22
Options are therefore 1000 Gallons or 200 Gallons
Total annual ordering cost :
For 1000 Gallons = 30 x 10400/1000 = $312
For 2000 Gallons = 30 x 10400 / 2000 = $156
Total annual holding cost :
For 1000 Gallons = 0.3 x 1000/2 = $150
For 2000 Gallons = 0.3 x 2000/ 2 = $300
Total annual ordering cost plus holding cost :
For 1000 Gallons = $312 + $150 = $462
For 2000 Gallons = $156 + $300 = $456
Since total cost is lowest for 2000 Gallons, order quantity should be 2000 Gallons
Answer to question g :
With 3% price discount , the discounted unit price = 97% of $1.00 = $0.97
Thus , Unit annual holding cost = 30% of $0.97 = $291
New order quantity = 8000
Thus,
Annual ordering cost
= Ordering cost x Number of annual orders
= Ordering cost x Annual demand / Order Quantity
= 30 x 10400 / 8000
= $39
Annual holding cost
= Annual unit holding cost x Average inventory
=0.291 x 8000/2
= $1164
Annual purchasing cost = $0.97 x 10400 = $10088
Thus Joe’s total cost
= $10088 + $1164 + $39
= $11291
JOE’S TOTAL ANNUAL COST = $11291
JOE SHOULD ORDER 1442.22 GALLONS TO MINIMIZE SUM OF ORDERING AND HOLDING COST
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.