Question 18 A large hospital uses a certain intravenous solution that it maintai
ID: 3074721 • Letter: Q
Question
Question 18
A large hospital uses a certain intravenous solution that it maintains in inventory. Assume the hospital uses reorder point method to control the inventory of this item. Pertinent data about this item are as follows:
------------------------------------------------------------
Forecast of demanda = 1,000 units per week
Forecast errora, std. dev. =100 units per week
Lead time = 4 weeks
Carrying cost = 25 % per year
Purchase price, delivered = $52 per unit
Replenishment order cost = $20 per order
Stockout cost = $10 per unit
In-stock Probability during the lead time =90%
a Normally distributed
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Due to possible rounding effect, please pick the closest number in the following options.
Question 19
If the hospital orders 400 units each time, what’s the total annual costs (holding cost + ordering cost + stock-out cost) excluding purchasing costs?
Question 19 options:
10000
21008
31008
42016
Use the following information to answer questions 17-20.
A large hospital uses a certain intravenous solution that it maintains in inventory. Assume the hospital uses reorder point method to control the inventory of this item. Pertinent data about this item are as follows:
------------------------------------------------------------
Forecast of demanda = 1,000 units per week
Forecast errora, std. dev. =100 units per week
Lead time = 4 weeks
Carrying cost = 25 % per year
Purchase price, delivered = $52 per unit
Replenishment order cost = $20 per order
Stockout cost = $10 per unit
In-stock Probability during the lead time =90%
a Normally distributed
------------------------------------------------------------
Due to possible rounding effect, please pick the closest number in the following options.
Question 20
If the lead time is normally distributed with a mean of 4 weeks and a standard deviation of 0.5 weeks, what’s the reorder point?
Question 20 options:
4689
4129
5188
6000
10000
21008
31008
42016
Explanation / Answer
17.
Weekly demand forecast, d = 1000
StDev of the weekly forecast, = 100
Average lead time, L = 4 weeks
Service level = 0.90 so Z = NORMSINV(0.90) = 1.28
ROP = d * L + Z * * L = 1000*4 + 1.28*100*SQRT(4) = 4,256
18.
Normal loss function, L(Z) corresponding to 90% serivce level = 0.048
Expected shortage per cycle (ESC) = L(Z) * * L = 0.0473*100*SQRT(4) = 9.6
Annual shotage = ESC x no. of cycles annually = 9.6 x (52000/400) = 1248
19.
Shortage cost = Annual shortage x shortage cost per unit = 1248 x $10 = $12,480
Order quantity, Q = 400
Holding cost per unit per annum, H = $52 * 25% = $13
Annual demand, D = 1000 x 52 = 52,000
Ordering cost, S = $20
Cycle stock holding cost = Q * H/ 2 = 400*13/2 = $2,600
Ordering cost = (D/Q) * S = (52000 / 400) * 20 = $2,600
Safety stock cost = Safey stock * H = 1.28*100*SQRT(4) * 13 = $3,328
Total cost = $2,600 + $2,600 + $12,480 + $3,328 = $21,008
20.
L = 4
L = 0.5
The following formula for ROP will apply.
ROP = d * L + Z * (2.L + d2.L2)= 1000*4 + 1.28*SQRT((100^2)*4 + (1000*0.5)^2) =4,689
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