Question

2. Audie Murphy Apparel (AMA) produces patriotic shirts in three colors: red, blue, and white. The monthly demand for each color is 3,000 units. Each shirt requires 1/2 pound of raw cotton. The cotton costs AMA $2.70 per pound. The transportation time from the supplier to AMA is 2 weeks. It costs AMA $100 to place each order and the annual holding cost percentage for AMA is 20 percent of the cost per pound.

a. What is the optimal order quantity of cotton? Round intermediate calculations to 2 decimal places (e.g., $18.61) and your answer to the nearest whole number.

Optimal order quantity _____ pounds

b. How many orders will AMA place during the next year? Round intermediate calculations to 2 decimal places (e.g., $18.61) and your answer to 2 decimal places (e.g., 108.37 times).

Number of orders ______

c. How frequently should the company order cotton? This is sometimes called the time between orders (TBO). Round intermediate calculations to 2 decimal places (e.g., $18.61) and your answer to 2 decimal places (e.g., once every 4.13 months).

Company orders once every ______months

d. Assuming that the first order is needed on April 1, when should AMA place the order?

a. March 15th

b. April 1st

c. April 15th

e. What is the annual holding cost when the optimal quantity (part a) is ordered? Round intermediate calculations to 2 decimal places (e.g., $18.61) and your answer to the nearest whole number.

Annual holding cost________per year

f. What is the resulting annual ordering cost when the optimal quantity (part a) is ordered? Round intermediate calculations to 2 decimal places (e.g., $18.61) and your answer to the nearest whole number.

Annual ordering cost ______

g. If the annual holding cost percentage was only 5 percent, how would it affect the annual number of orders, the optimal order size, and the average inventory?

If the holding cost is lower, then the batch size would be	larger/smaller	-
Thus, the average inventory would be	larger/smaller	and
the number of orders would be	larger/smaller	-

Answer 1

2.

Monthly demand of shirts = 3000*3 = 9000

Monthly demand of cotton = 9000*(1/2) = 4500 pounds

Annual demand of cotton D = 4500*12 = 54000

Ordering cost S = 100

Price per pound of cotton P = 2.70

Holding cost H = 0.20*2.70 = 0.54

Lead time L = 2 weeks or ½ month

a)

Optimal order quantity Q = sqrt(2DS/H) = sqrt(2*54000*100/0.54) = 4472.13 or 4472 pounds

b)

Number of orders placed = 54000/4472.13 = 12.07 or 12 orders

c)

The company should order cotton every 4472.13/4500 = 0.99 months

d)

Lead time is 2 weeks so the order should be placed 2 weeks prior to the requirement. That is 15th March.

e)

Annual holding cost AHC = HQ/2 = 0.54*4472.13/2 = 1207.47 or $1207 per year

f)

Annual ordering cost AOC = DS/Q = 54000*100/4472.13 = 1207.47 or $1207 per year

g)

The relationship between order quantity and the holding cost is inverted. This means as the holding cost increases by X times, the order quantity is reduces by sqrt(X) times, keeping everything constant.

If the holding cost is reduce to 5% then the order quantity will increase. 5% is 0.25 times the previous 20%. This means the order quantity will increase by inverse of sqrt(0.25) = 0.5 times. That is 1/0.5 = 2 times.

If the holding cost is lower, then the batch size would be larger

Thus the average inventory would be larger

The number of orders would be smaller