Cappy R Us is manufacturing caps in 4 colors: Black, Red, White, and Blue. The m

Question

Cappy R Us is manufacturing caps in 4 colors: Black, Red, White, and Blue.

The monthly demand for each color is 4,000 units. Each cap requires .5 pound of raw cotton that is imported from Colombia. The purchase price per pound is $3.50 and transportation cost by sea is $0.30 per pound. The lead time is 2 weeks with negligible variability. The cost of placing on order, by Cappy R Us is $100, and the annual opportunity cost of capital is 25%.

A. What is the optimal order quantity?

B. How frequently should Cappy R Us order?

C. Assuming that the first order is needed by May 31, when should Cappy R Us place the order?

D. How many orders will Cappy R Us place during the next quarter?

E. What are the resulting annual ordering cost and holding cost?

Explanation / Answer

one unit requires 0.5 pound of cotton.

Cost of one unit = 0.5*3.5+0.3*0.5 = $1.9

Annual demand = 4000*12*4 = 48000*4 = 192000

a)

Optimal order quantity is

EOQ = sqrt((2*192000*100)/0.25*1.9) = 8991.224 = 8992(rounding off)

b)

Number of orders in a year = 192000/8992 = 21.352 = 22 (rounding off)

Frequency of orders = 12/22 = 0.545

The order is placed for every 0.545 months

c) The order should be placed on 17th May as lead time is 2 weeks

d) Cappy R Us places order every 0.545 months. It would place six orders in the current quarter.

Quantity required for 6 months = 6*4000 *4= 24000*4 = 96000

To meet the demand , 11 orders need to placed in total. Therefore , five orders would be placed in next quarter

e)

Holding cost = (8992/2)*.25 = $1124

Annual ordering cost = 22*100 = $2200

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