Alfa Inc. uses a 2-week periodic review for its notebook store inventory. Mean a
ID: 384947 • Letter: A
Question
Alfa Inc. uses a 2-week periodic review for its notebook store inventory. Mean and standard deviation of weekly sales are 16 and 5 respectively. The lead time is 3 days. The mean and standard deviation of lead-time demand are 8 and 3.5 respectively.
1.What is the mean and standard deviation of demand during the review period plus the lead-time period?
2.Assuming that the demand has a normal probability distribution, what is the replenishment level that will provide an expected stockout rate of one per year?
3.If there are 18 notebooks in the inventory, how many notebooks should be ordered?
Explanation / Answer
R = review period = 2 weeks
L = Lead Time = 3 days
dw = average weekly demand = 16 units
W = S.D of weekly demand = 5 units
dL = average lead-time demand = 8 units
L = S.D of lead-time demand = 3.5 units
a.
Mean Demand during review period and lead time = average weekly demand x Review period + average lead-time demand
Mean Demand during review period and lead time = (dw x R) + dL = (16 x 2) + 8 = 40 units
Mean Demand during review period and lead time = 40 units
Standard Deviation of Demand during review period and lead time
= (variance of demand during review period + variance of demand during Lead time)
= (R x (W)2) + (L)2)
= (2 x (5)2) + (3.5)2)
= 62.25
= 7.8898
Standard Deviation of Demand during review period and lead time = 7.8898
b.
Expected Stock out rate = 1 per year = 1/52 weeks = 0.0192
(Assuming the store is open for 52 weeks per year)
Cycle service level = 1 – stock out rate = 1 – 0.0192 = 0.9807
z-score for 98% service level = 2.07, from stand normal cumulative probability distribution table
The replenishment level is determine as follows:
M = demand during lead time and review period + Safety stock
M = 40 + z*(SD of Demand during review period and lead time)
M = 40 + 2.07(7.8898)
M = 56.33
Replenishment level = 56 units (approx)
c.
Inventory on hand = H = 18
Order quantity = replenishment level – inventory = M – H = 56 – 18 = 38
Order quantity = 38 units
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.