Question

Michigan State Figurine Inc. (MSF) sells crystal figurines to Spartan fans. MSF buys the figurines from a manufacturer for $11 per unit. They send orders electronically to the manufacturer, costing $23 per order and they experience an average lead time of six days for each order to arrive from the manufacturer. Their inventory carrying cost is 20 percent. The average daily demand for the figurines is three units per day. They are open for business 250 days a year. 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. (Do not round intermediate calculations. Round your answer to the nearest whole number.) b. How many orders will they place in a year? (Use your rounded answer from Part a. Round your answer to 2 decimal places.) c. What is the average inventory? (Use your rounded answer from Part a. Round your answer to 1 decimal place.) d. What is the annual ordering cost? (Use your rounded answer from Part b. Round your answer to 2 decimal places.) e. What is the annual inventory carrying cost? (Use your rounded answer from Part a. Round your answer to 2 decimal places.)

Answer 1

Given values:

Cost of figurines (C) = $11 per unit

Ordering cost (Co) = $23 per order

Lead time (L) = 6 days

Inventory carrying cost (Cc) = 20% of cost = 20% of $11 = $2.2

Daily demand (d) = 3 units

Number of working days = 250

Annual demand (D) = Daily demand x Number of working days = 3 units x 250

Annual demand (D) = 750 units

Solution:

(a) Order Quantity (Q):

Q = SQRT [(2 x D x Co) / Cc]

Q = SQRT [(2 x 750 x $23) / $2.2]

Q = 125.23 or 125 (Rounding off to the nearest whole number)

Order quantity (Q) = 125 units

(b) Number of orders in a year:

Number of orders = (Annual demand / Order quantity)

Number of orders = (750 / 125)

Number of orders = 6 orders per year

(c) Average inventory:

Average inventory = (Order quantity / 2)

Average inventory = (125 / 2)

Average inventory = 62.5 units

(d) Annual ordering cost:

​​​​​​​Annual ordering cost = (Annual demand / Order quantity) x Ordering cost

Annual ordering cost = (750 / 125) x $23

Annual ordering cost = $138

(e) Annual inventory carrying cost:

​​​​​​​Annual inventory carrying cost = (Order quantity / 2) x Inventory carrying cost

Annual inventory carrying cost = (125 / 2) x $2.2

Annual inventory carrying cost = $137.5