Question

Michigan State Figurine Inc. (MSF) sells crystal figurines to Spartan fans. MSF buys the figurines from a manufacturer for $13 per unit. They send orders electronically to the manufacturer, costing $24 per order and they experience an average lead time of eight days for each order to arrive from the manufacturer. Their inventory carrying cost is 20 percent. The average daily demand for the figurines is two units per day. They are open for business 250 days a year. The supplier decides to offer a volume discount. They will sell the crystal figurines at $7 per unit for orders of 250 units or more. Answer the following questions:

a. How many units should the firm order each time? Assume there is no uncertainty at all about the demand or the lead time. (Round your answer to the nearest whole number.)

b. How many orders will they place in a year?

c. What is the average inventory?

d. What is the annual ordering cost?

e. What is the annual inventory carrying cost?

Michigan State Figurine Inc. (MSF) sells crystal figurines to Spartan fans. MSF buys the figurines from a manufacturer for $13 per unit. They send orders electronically to the manufacturer, costing $24 per order and they experience an average lead time of eight days for each order to arrive from the manufacturer. Their inventory carrying cost is 20 percent. The average daily demand for the figurines is two units per day. They are open for business 250 days a year. The supplier decides to offer a volume discount. They will sell the crystal figurines at $7 per unit for orders of 250 units or more. Answer the following questions:

Answer 1

Daily demand d = 2

Annual demand D = 2*250 = 500 units

Ordering cost S = 24

Cost C = $13

Carrying cost H =20% = 0.2*13 = $2.6

a) Optimal order Quantity Q

Q = 96 UNTIS

But we are getting more discount if we buy 250 units or more. So we calculate total cost at Q = 96 units and Q = 250 units

At Q = 250 units, H = 0.2*7 = $1.4

Total cost = Purchase cost + Annual holding cost + Annual ordering cost = CD + (Q/2)H + (D/Q)S

At Q = 96 units

Total cost = (13*500) +(96/2)*2.6 + (500/96)*24 = 6749.8

At Q = 250 units

Total cost = (7*500) +(250/2)*1.4 + (500/250)*24 = 3723

Total cost is less at order quantity Q = 250

So they shoukd order 250 units each time

b)

No of orders per year = D/Q = 500/250 = 2 orders

c) Average inventory = Q/2 = 250/2 = 125

d) Annual ordering cost = (D/Q)*S = (500/250)*24 = 48

e) Annual inventory carrying cost = (Q/2)H = (125/2)*1.4 = 175