Question

Question 21 2.86 p Use the following to answer questions 20-21: Given the following inventory system: average daily demand is 75 units with a standard deviation of units, review period is 10 days, lead time is 2 days and the required service probability is 97.5% (z=1.96). Which of the following is the order quantity (currently, inventory on hand is 50 units)? 1 o 172 866 869 904 954 1 Management Le Marketing 14th...zip TB (100) (3).zip Practice Questi...pdf

Answer 1

For periodic review model:

d = daily demand = 75 units

T = Review period or fixed order interval = 10 days

L = Lead Time = 2 days

σd = S.D of daily demand = 8 units per day

Inventory on hand = H = 50

Probability of not stocking out = 97.5%

The target level or restocking level is given as follows:

R = mean demand during lead time and review period + Safety stock during lead time and review period – On hand Inventory

R = d(L + T) + zσT+L – H

mean demand during lead time and review period = d(L + T) = 75*(10 + 2) = 900 units

Safety stock for (L+T =) 12 days has to maintain since there is variation in daily demand with 97.5% not-stocking out probability.

SS = z*σT+L = z*σd√(L + T)

z-score for the 97.5% probability is 1.96 from normal distribution table.

SS = 1.96 x (8)√(2 + 10) = 54.32units

Safety stock = 54.32 units

R = d(L + T) + zσT+L – H

R = 900 + 54.32 – 50 = 904.31

R ~ 904 units

ANS: Target order quantity = 904 units