1) The demand during the lead time is normally distributed with a mean of 40 and
ID: 1099679 • Letter: 1
Question
1) The demand during the lead time is normally distributed with a mean of 40 and a standard deviation of 4. If they have calculated a reorder point of 46.60 units, what service level are they assuming?
A) 95 percent
B) 85 percent
C) 90 percent
D) 97.5 percent
E) none of the above
2) A person is using the normal distribution to determine the safety stock for a product. What "z" value would be associated with a 90 percent service level?
A) -0.90
B) 0.90
C) 1.28
D) 0.53
E) none of the above
3) The annual demand for a product has been projected at 2,000 units. This demand is assumed to be constant throughout the year. The ordering cost is $20 per order, and the holding cost is 20 percent of the purchase cost. The purchase cost is $40 per unit. There are 250 working days per year. Whenever an order is placed, it is known that the entire order will arrive on a truck in 6 days. Currently, the company is ordering 500 units each time an order is placed. What level of safety stock would give a reorder point of 60 units?
A) 12 B) 14 C) 22 D) 10 E) 18
4) A person is using the normal distribution to determine the safety stock for a product. The "z" value of 2.33 would be associated with what service level?
A) 98 percent
B) 97.5 percent
C) 95 percent
D) 99 percent
E) none of the above
5) Rose Arena is the production manager for a manufacturing firm that produces buggy whips and other items. The annual demand for a particular buggy whip is 1,600 units. The holding cost is $2 per unit per year. The cost of setting up the production line is $25. There are 200 working days per year. Rose decided to produce 200 units each time she started production of the buggy whips. If it took her 4 days to produce the 200 units, what was her production rate?
A) 60 units/day
B) 100 units/day
C) 40 units/day
D) 80 units/day
E) 50 units/day
Please provide solutions so that I can learn to calculate problems such as these on my own. Thanks.
Explanation / Answer
1) Reorder point = Safety stock + mean
Safety Stock = 46.6 - 40 = 6.6
Safety stock = z*stdev
z = 6.6/4 = 1.65
Thus service level = 95% (Normal Table)
Ans. A) 95 percent
2) C) 1.28 Check the normal table for area under the normal curve to be 0.90
3) Reorder Point = Normal consumption during lead-time + Safety Stock
EOQ = sqrt(2*D*S/H) = sqrt(2*2000*20/8) = 100 units (H = 0.2*40 = 8)
Total orders = annual demand/EOQ = 2000/100 = 20
For 250 days, 20 orders are utilized
1 order is consumed in 250/20 = 12.5 days
Thus consumtion during leadt time of 6 days = (6*100)/12.5 = 48
Re order oint = 60
Safety stock = 60 - 48 = 12 units
Ans) A. 12
4) D) 99% Check the normal table for z = 2.33 and determine the area under the normal curve which is 0.99
5)Annual demand = 1600, Production units for one slot = 200
Time taken for 200 units = 4 days
Production Rate = 200/4 = 50 units/day
Note: The optimum production quantity is given by:
sqrt[ (2*D*Setup cost)/(holding cost * (1 - (d/p))) ]
d = demand rate = annual demand/no of working days in year
p = production rate
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