Question

Michigan State Figurine Inc. (MSF) sells crystal figurines to Spartan fans. MSF buys the figurines from a manufacturer for $21 per unit. They send orders electronically to the manufacturer, costing $35 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 four 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 500 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?

Answer 1

Given are following data :

Ordering cost = Co = $35

Annual demand = D = 4 units/ day x 250 = 1000

Annual inventory carrying cost for order quantity < 500 = Ch1 = 20 percent of $21 = $4.2

Annual inventory carrying cost for order quantity > = 500 = Ch2 = 20 percent of $ 7 per unit = $1.4

Economic Order quantity for quantity < 500

= Square root ( 2 x Co x D / Ch1 )

= Square root ( 2 x 35 x 1000/ 4.2 )

= 129.09 ( 129 rounded to nearest whole number )

Economic Order quantity for quantity > = 500

= Square root ( 2 x Co x D / Ch2 )

= Square root ( 2 x 35 x 1000 /1.4)

= 223.60 ( 224 rounded to nearest whole number )

However 224 is not the solution since it is supposed to correspond to order quantity > = 500 which is not possible .

Therefore , correct order quantity = 129

1. The firm should order 129 units each time
2. Number of orders to be placed in a year

= annual demand / Order quantity

= 1000/129

= 7.75

1. Average inventory = Correct order quantity/ 2 = 129 / 2 = 64.50
2. Annual ordering cost

= Ordering cost x Number of orders

= $ 271.25

1. Annual inventory carrying cost

= annual unit inventory carrying cost x average inventory

= Ch1 x 64.50

= $270.90