Question

In: Operations Management

SY Manufacturers (SYM) is producing T-shirts in three colors: red, blue, and white. The monthly demand...

SY Manufacturers (SYM) is producing T-shirts in three colors: red, blue, and white. The monthly demand for each color is 1,457 units. Each shirt requires 0.75 pound of raw cotton that is imported from the Luft-Geshfet-Textile (LGT) Company in Brazil. The purchasing price per pound is $8.30 (paid only when the cotton arrives at SYM's facilities) and transportation cost by sea is $0.70 per pound. The traveling time from LGT’s facility in Brazil to the SYM facility in the United States is two weeks. The cost of placing a cotton order, by SYM, is $51 and the annual interest rate that SYM is facing is 21 percent of total cost per pound.

a. What is the optimal order quantity of cotton? (Round your answer to the nearest whole number.)

b. How frequently should the company order cotton? (Round your answer to 2 decimal places.)

c. Assuming that the first order is needed on 20-Jan, when should SYM place the order?

  • 6-Jan

  • 20-Jan

  • 3-Feb

d. How many orders will SYM place during the next year? (Round your answer to 2 decimal places.)

  

e. What is the resulting annual holding cost? (Round your answer to the nearest whole number.)

  

f. What is the resulting annual ordering cost?

  

g. If the annual interest cost is only 5 percent, how will it affect the annual number of orders, the optimal batch size, and the average inventory?

Solutions

Expert Solution

Sol:-

Monthly demand = 1457 units
Total monthly demand for all of the three shirts = 1457+1457+1457 = 4371 units
1 shirt = 0.75 pounds
d = 4371×0.75 = 3278.25
D = d×12 = 3278.25×12 = 39339 pounds/year
Cost = $8.30 per/pound
Transpotation cost = $0.70 pound
Total cost = $8.30+ $0.70 = $9
LT = 2 weeks
S = $51
H = 21% of total cost = (21/100)×9 = $ 1.80/unit/year

a):- EOQ =

1457.07 or 1457 pounds

b):- T = Q/d = (1457/3278.25) = 0.44 months

c):- The right answer is 6 january becuase the lead time is 2 weeks (14 days)
6 jan + 14 days = 20 jan.

d):- N = D/Q = 39339/1457 = 2700 times

e):- Annual holding cost =( Q/2)× H = (1457/2)×1.89 = 1376.86 = 1377
f):- Annual ordering cost = (D/Q)×S = (39339/1457)× 51 = 1377
g):- h = 5% of total cost = (5/100)×9 = 0.45 /unit /year.
Batch size (Q) =

= 2986.10 or 2986

Hence batch size will be larger.

keosha answered 2 months ago
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