Question

Michigan State Figurine Inc. (MSF) sells crystal figurines to Spartan fans. MSF buys the figurines from a manufacturer for $34 per unit. They send orders electronically to the manufacturer, costing $62 per order and they experience an average lead time of nine 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 $10 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.) write down the formula

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

e. What is the annual inventory carrying cost?

Answer 1

Average daily demand (d) = 2 units

Number of days per year = 250

Annual demand (D) = d × number of days per year = 2 × 250 = 500 units

Ordering cost (S) = $62

Carrying cost (H) = 20% of cost = 20% of $34 = $6.80

Without the discount the economic order quantity (Q*) =

√(2DS/H)

= √[(2 X 500 X 62) /6.80) ]

= √(62000/6.80)

= √9117.647058

= 95 units

b) Annual ordering cost with Q* = (D/Q*) S = (500/95) 62 = $326.32

Annual holding cost with Q* = (Q*/2) H = (95/2) 6.80 = $323

Purchase cost = D × cost per unit = 500 × 34 = $17000

Total annual cost with Q* = Annual holding cost + Annual ordering cost + purchase cost

= $323 + $326.32 + $17000

= $17649.32

The minimum quantity needed to avail the discout is 250 units. So with order quantity (Q) = 250 units the cost per unit = $10 and carrying cost (H) = 20% of $10 = $2

Annual ordering cost with Q = (D/Q) S = (500/250) 62 = $124

Annual holding cost with Q = (Q/2) H = (250/2) 2 = $250

Purchase cost = D × cost per unit = 500 × 10 = $5000

Total annual cost with Q = Annual holding cost + Annual ordering cost + purchase cost

= $250 + $124 + $5000

= $5374

Since the total cost with order quantity of 250 units is lowest they should order 250 units each time

b) Number of orders per year = D/Q = 500/250 = 2

e) Annual inventory carrying cost = (Q/2) H = (250/2) 2 = 125 × 2 = $250