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?
Question #2
In the table below is a production schedule for a manufacturer. You have been hired on to figure out the optimal 6 month production schedule using the Wagner-Whitin Algorithm. Explain the rationale behind the answer you found and what is the most dominant variable in your calculations?
|
Period (t)
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Demand (Dt)
|
1000
|
300
|
500
|
200
|
800
|
1000
|
|
Unit Cost (ct)
|
21
|
21
|
21
|
21
|
21
|
21
|
|
Setup Cost (At)
|
326
|
326
|
326
|
326
|
326
|
326
|
|
Holding Cost (ht)
|
54
|
54
|
54
|
54
|
54
|
54
|
Question #3
The manager of a Cummings engine manufacturing facility has collected some historical data on the monthly demand of hemi-diesel engines (See table 1)
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Table 1
|
|
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Period
|
Monthly Demand
|
|
January
|
240
|
|
February
|
150
|
|
March
|
350
|
|
April
|
297
|
|
May
|
497
|
|
June
|
566
|
|
July
|
200
|
|
August
|
450
|
|
September
|
300
|
|
October
|
240
|
|
November
|
300
|
|
December
|
350
|
The unit cost of an engine is $3000 and there is a 30% interest rate associated with the holding cost. It takes 6 weeks for a replenishment order to be placed. Every time the facility has to setup to make these engines the manager estimates a setup cost of around $250,000. The cost of backorders is about $150,000 per year and the manager is worried about this figure. Demand seems to be normally distributed and the manager would like to determine the following:
1) What is the annual demand of engines?
2) What is the economic order quantity?
3) What is the average demand of engines over the six week period for replenishment?
4) What is the standard deviation of the sample in table 1 (use the STDEV.S function in excel)
5) Determine the critical fractile of backorder cost. Use the following formula to determine this G(r* )= b/(b+h)
6) What the z score of this critical fractile (Hint use the NORMSINV function
7) What is the reorder point?