Question # 1 French Wind manufactures the blades for wind turbines from a glass
ID: 1094914 • Letter: Q
Question
Question # 1 French Wind manufactures the blades for wind turbines from a glass fiber reinforced plastic. The suppliers of the glass fiber and reinforced plastic send the raw materials to French Wind in cases, where one case of glass fiber requires two cases of reinforced plastic. Glass fiber is being consumed at steady rate of 2000 cases per year and has a cost per case of $1500. Reinforced plastic on the other hand has a unit cost of $300 per case. French wind has a 35% annual holding cost rate on all their inventory. The setup/order cost for glass fiber is $200 while for reinforced plastic there is a $650 order cost. Over the duration of a year French Wind is open for 340 days. Find the following:
a) What is the EOQ for fiber glass and reinforced plastic?
b) What is the periodic interval that orders have to be made for both raw materials (in days)? Do you think they could share delivery trucks?
c) What is the optimum annual cost for fiber glass and reinforced plastic?
d) An error was made in on the lot size for fiber glass and reinforced plastic. The new lot sizes are 55 cases for fiber glass and 315 case for reinforced plastic. Calculate the annual cost for both fiber glass and reinforced plastic.
e) Mathematically compare the actual to optimal cost you got in parts (c) and (d). Explain from the perspective of sensitivity to changes in Q?
Explanation / Answer
A)Fiber glass
Annula demand= 2000
S= 200
H= 35%*1500
EOQ for Fiber glass = sqrt(2*2000*200/(35%*1500))= 39 cases
Reinforced Plastic
Annula demand= 2000*2= 4000
S= 650
H= 35%*300
EOQ for Reinforced Plastic = sqrt(2*4000*650/(35%*300))= 223 cases
b)Period interval for Fiber glass =340/ (2000/39)= 6.63 days
Period interval for Reinforced Plastic =340/ (2*2000/223)= 18.96 days or 19 days
No, they will not be able to share delivery trucks
c) Annual cost for Fiber glass = 2000*1500 + 2000*200/39 + 35%*1500*39/2=$ 3,020,493.91
Annual cost for Reinforced Plastic = 4000*300 + 4000*650/223 + 35%*300*223/2= $1,223,366.69
d) Annual cost for Fiber glass = 2000*1500 + 2000*200/55 + 35%*1500*55/2=$ 3,021,710.23
Annual cost for Reinforced Plastic = 4000*300 + 4000*650/315 + 35%*300*315/2= $ 1,224,791.47
e) Fiber Glass, change in Q = (55-39)/39= 41.03%
change in Total cost = (3,021,710.23 - 3,020,493.91 )/ 3,020,493.91 = 0.040%
41.03% change in Q caused 0.04% increase in annual cost
Reinforced Plastic, change in Q = (315-223)/223= 41.26%
change in Total cost = ($ 1,224,791.47 - 1,223,366.69)/ 1,223,366.69 = 0.12%
41.26% change in Q caused 0.12% increase in annual cost