Question

Joe Birra needs to purchase malt for his microbrewery production. His supplier charges $35 per delivery (no matter how much is delivered) and $1.20 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.

1. Suppose Joe orders 1000 gallons each time. What is his average inventory (in gal)?
2. Suppose Joe orders 1500 gallons each time. How many orders does he place with his supplier each year?
3. How many gallons should Joe order from his supplier with each order to minimize the sum of the ordering and holding costs?
4. Suppose Joe orders 2500 gallons each time he places an order with the supplier. What is the sum of the ordering and holding costs per gallon?
5. Suppose Joe orders the quantity from part (C) 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?
6. If Joe’s supplier only accepts orders that are an integer multiple of 1000 gallons, how much should Joe order to minimize ordering and holding costs per gallon?
7. Joe’s supplier offers a 3 percent discount if Joe is willing to purchase 8000 gallons or more. What would Joe’s total annual cost (purchasing, ordering, and holding) be if he were to take advantage of the discount?

Answer 1

a. Average inventory = 1,000 x .5 = 500

b.  Orders = (250 per week x 52 weeks) / 1500 = 8.67

c. Order size = Sqrt (2 x 35 x 250 x 52) / (120 x .35) = 1,472

d. (250 per week x 52 weeks) / 2500 = 5.2 orders.

Annual order cost = 5.2 x $35 = $182.

Annual holding cost = .5 (2500 x 1.2 x .35) = $525.

Annual order + holding costs = 182 + 525 = $707.

(Annual order + holding costs) / annual demand = cost per gallon.

$707/ 13,000 = 0.0544

e.

(250 per week x 52 weeks) / 1472 = 8.83 orders.

Annual order cost = 8.33 x $35 = $309.10.

Annual holding cost = .5 (1472 x 1.2 x .35) = $309.12.

Annual order + holding costs = 309.10 + 30912 = $618.22.

Annual purchase cost = $1.20 x 13,000 = $15,600.

Annual order + holding costs/annual purchase cost

$618.22 / $15,600 = 3.96%

f.

From part c the EOQ = 1,472.

For 1,000 order quantity, Annual order cost = 13 orders x $35 = $455.

Annual holding cost = .5 (1000 x 1.2 x .35) = $210.

Annual order + holding costs = 455 + 210 = $665.00.

For 2,000 order quantity, Annual order cost = 6.5 orders x $35 = $227.50.

Annual holding cost = .5 (2000 x 1.2 x .35) = $420.

Annual order + holding costs = 227.50 + 420 = $647.50.

An order size of 2,000 has the lowest annual order + holding costs.

g.

For 8,000 order quantity, Annual order cost = (13,000/8,000) orders x $35 = $56.88.

Annual holding cost = .5 (8000 x 1.164 x .35) = $1,629.60.

Annual order + holding costs + purchasing cost = 56.88 + 1,629.60 + 15,132= $16,818.48.

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