Question

Joe Birra needs to purchase malt for his microbrewery production. His supplier charges $37 per delivery (no matter how much is delivered) and $1.25 per gallon. Joe’s annual holding cost per unit is 35 percent of the price per gallon. Joe uses 250 gallons of malt per week. Assume 52 weeks per year.

Round your answer to 3 digits after the decimal point. Do NOT use comma in your numeric answers.

Suppose Joe orders 1000 gallons each time. His average inventory is _________ gallons.

Suppose Joe orders 1500 gallons each time. He needs to place _______ orders with his supplier each year to meet the demand exactly.

Joe’s annual purchasing cost is $ _________

Joe’s annual inventory holding cost of the malt is $ _____ per gallon.

Joe should order ________ gallons each time to minimize the annual ordering and holding costs. The minimum ordering and holding costs can be expressed as _______ % of the annual purchasing cost.

Suppose Joe orders 2500 gallons each time he places an order. The annual ordering and holding costs will be $ _______ per gallon.

If Joe’s supplier only accepts orders that are integer multiples of 1000 gallons, then Joe should order _________ each time to minimize the annual ordering and holding costs.

Joe’s supplier offers a 3% discount if Joe is willing to purchase 8000 gallons or more. Suppose Joe orders 8000 gallons each time to take advantage of the discount. Joe’s annual inventory holding cost will be $ ________ per gallon, and Joe’s total annual cost (purchasing, ordering, and holding) will be $.________

Answer 1

Order Cost (S) = $37

Price per gallon (p) = $1.25

Annual Holding Cost per unit (H) = 35% of p = 0.35*1.25 = $0.4375

Weekly demand (d) = 250 gallons

Annual Demand (D) = d*52 = 250*52 = 13000

1. Suppose Joe orders 1000 gallons each time. His average inventory is _________ gallons.

Q = 1000 gallons

Average Inventory = Q/2 = 1000/2 = 500 gallons

2. Suppose Joe orders 1500 gallons each time. He needs to place _______ orders with his supplier each year to meet the demand exactly.

Q = 1500

No. of Orders = D/Q = 13000/1500 = 8.67

3. Joe’s annual purchasing cost is $ _________

Annual Purchasing Cost = D*p = 13000*1.25 = $16250

4. Joe’s annual inventory holding cost of the malt is $ _____ per gallon.

Annual Holding Cost per unit (H) = 35% of p = 0.35*1.25 = $0.4375 per gallon

5. Joe should order ________ gallons each time to minimize the annual ordering and holding costs. The minimum ordering and holding costs can be expressed as _______ % of the annual purchasing cost.

EOQ (Q*)

Q* = SQRT(2*S*D/H) = SQRT(2*37*13000/0.4375) = 1482.85 ~ 1483 gallons

Ordering Cost = (D/Q)*S = (13000/1483)*37 = $324.34

Holding Cost = (Q/2)*H = (1483/2)*0.4375 = $324.40

Minimum Ordering and Holding Cost = 324.34 + 324.40 = 648.74

% of annual purchasing cost = 100*Minimum Ordering and Holding Cost/Annual Purchasing Cost = 100*648.74/16250 = 4%

6. Suppose Joe orders 2500 gallons each time he places an order. The annual ordering and holding costs will be $ _______ per gallon.

Ordering Cost = (D/Q)*S = (13000/2500)*37 = $192.4

Holding Cost = (Q/2)*H = (2500/2)*0.4375 = $546.875

The annual ordering and holding costs = 192.4 + 546.875 = $738.875

7. If Joe’s supplier only accepts orders that are integer multiples of 1000 gallons, then Joe should order _________ each time to minimize the annual ordering and holding costs.

EOQ = 1483

Nearest multiple of 1000 to EOQ is 1000 gallons

Feasible EOQ (Q) = 1000 gallons

8. Joe’s supplier offers a 3% discount if Joe is willing to purchase 8000 gallons or more. Suppose Joe orders 8000 gallons each time to take advantage of the discount. Joe’s annual inventory holding cost will be $ ________ per gallon, and Joe’s total annual cost (purchasing, ordering, and holding) will be $.________

Purchasing cost per gallon = 0.97*1.25 = $1.2125 per gallon

H = 0.35*1.2125 = $0.4243 per gallon

Q = 8000 gallons

Ordering Cost = (D/Q)*S = (13000/8000)*37 = $60.125

Holding Cost = (Q/2)*H = (8000/2)*0.4243 = $1697.2

Purchasing Cost = D*p = 13000*1.2125 = $15762.5

Total Annual Cost =Ordering Cost + Holding Cost + Purchasing Cost =  $17519.83