Joe Birra needs to purchase malt for his micro-brew production. His supplier cha
ID: 371988 • Letter: J
Question
Joe Birra needs to purchase malt for his micro-brew production. His supplier charges $30 per delivery ( no matter how much is delivered) and $1.05 per gallon. Joe's annual holding cost is 25% of the price per gallon. Joe uses 225 gallons of malt per week.
a) suppose Joe orders 750 gallons each time. What is his average inventory.
b) suppose joe orders 1500 gallons each time. How many order does he place with his supplier each year?
c) how many gallons should Joe order from his supplier with each order to minimize the sume of ordering and holding costs?
d) suppose Joe orders 2250 gallons each time he places an order with the supplier. What is the sum of ordering and holding costs per gallon?
Explanation / Answer
Answer to question a:
Order quantity = 750 Gallons
Average inventory = 750 /2 = 375 Gallons
AVERAGE INVENTORY = 375 GALLONS
Answer to question b:
Annual demand = 225 Gallons/ week x 52 weeks = 11700 Gallons
Order Quantity = 1500 Gallons
Hence, number of orders to be placed with supplier each year = 11700 /1500 = 7.8
NUMBER O ORDERS TO BE PLACED WITH SUPPLIER EACH YEAR = 7.8
Answer to question c :
Economic Order Quantity ( EOQ) model will be used to calculate optimal order quantity which minimizes total ordering cost and inventory holding cost .
Accordingly,
EOQ = Square root ( 2 x Co x D/ Ch )
Co = Ordering cost = $30
Ch = Annual unit holding cost = 25% of $1.05 = $ 0.2625
D = Annual demand = 225/ week x 52 weeks = 11700
Therefore ,
EOQ = Square root ( 2 x 30 x 11700/ 0.2625)
= 1635.32
JOE WOULD ORDER 1635.32 GALLONS EACH TIME FROM HIS SUPPLIER
Answer to question d :
Order quantity = 2250 Gallons
Annual ordering cost = Ordering cost x Number of orders = Ordering cost x Annual demand / Order quantity = $30 x 11700/2250 = $156
Annual inventory holding cost = Annual unit inventory holding cost x Average inventory = Ch x Order quantity/ 2 = $0.2625 x 2250/2 = $295.31
Sum of ordering and holding cost per Gallon = $156 + $295.31 = $451.31
Hence sum of ordering and holding cost per Gallon = $451.31 / 2250 = 0.20 ( rounded to 2 decimal places )
SUM OF ORDERING AND HOLDING COST PER GALLON = $0.20
AVERAGE INVENTORY = 375 GALLONS
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