SM Inc. (SMI) is manufacturing caps in four colors: black, red, white, and blue.
ID: 420442 • Letter: S
Question
SM Inc. (SMI) is manufacturing caps in four 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 the Sheena Textile Company in Mumbai. 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 an order, by SMI, is $100 and the annual opportunity cost of capital is 25 percent.
What is the optimal order quantity?
How frequently should SMI order?
Assuming that the first order is need by May 31, when should SMI place the order?
How many orders will SMI place during the next quarter?
What are the resulting annual ordering cost and holding cost?
Explanation / Answer
Monthly demand of caps = 0.5 / unit x 4000 units = 2000 Pound
Annual demand of caps = D = 2000 pound/ month x 12 months = 24,000 pounds
Cost of 1 pound = Purchase price / pound + Transportation cost / Pound = $3.50 + $0.30 = $3.80
Since . weight of each cap = 0.5 pound
Cost per cap = $0.5 x 3.80 = $1.90
Annual cost of capital = 25%
Therefore annual unit holding cost per cap = Ch = 25% of $1.90 = $0.475
Ordering cost of SMI = Co = $100
Optimal order quantity ( EOQ )
= Square root ( 2 x Co x D / Ch )
= Square root ( 2 x 100 x 24000 / 0.475 )
= 3178.87 ( 3179 rounded to nearest whole number )
Daily demand of caps = 24000/365
Frequency of ordering caps
= Optimal order quantity / Daily demand of caps
= 3179 / ( 24000 / 365 )
= ( 3179 x 365 ) / 24000
= 48.35 days
OPTIMAL ORDER QUANTITY = 3179 CAPS
FREQUENCY AT WHICH SMI SHOULD ORDER = 48.35 DAYS
It is given that Lead time = L = 2 weeks ( 14 days )
Order needed on = May 31
Therefore, SMI should place order on = May 31 – 14 = May 17
SMI SHOULD PLACE ORDER ON MAY 17
Number of quarters in a year = 4
Therefore ,
Number of orders should SMI place during next quarter
= Annual demand / ( 4 x Optimal order quantity )
= 24000 / ( 4 x 3179 )
= 1.88
NUMBER OF ORDERS SMI SHOULD PLACE DURING NEXT QUARTER = 1.88
Annual ordering cost
= Ordering cost x Number of orders
= Ordering cost x Annual demand / Optimal order quantity
= Co x D/EOQ
= (100 X 24000 ) /3179
= $ 754.95
Annual inventory holding cost
= Annual unit inventory holding cost x average inventory
= Ch x Optimal order quantity / 2
= $0.475 x 3179/2
= $755
Annual ordering plus holding cost
= $754.95 + $755
= $1509.95
ANNUAL ORDERING AND HOLDING COST = $1509.95
OPTIMAL ORDER QUANTITY = 3179 CAPS
FREQUENCY AT WHICH SMI SHOULD ORDER = 48.35 DAYS
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