Question 8 George Mason’s bookstore currently stores inventory of notebooks at b
ID: 361566 • Letter: Q
Question
Question 8 George Mason’s bookstore currently stores inventory of notebooks at both the Arlington and Fairfax campuses. They use a continuous replenishment policy for each assuming annual demand at each campus is independent and normally distributed with a mean of 5,878 and a standard deviation of 593. If they pool the inventory into a single location (or virtually pool it), what will be the reduction in total inventory (a positive number). Assume a safety factor z of 1.5. (Hint: calculate the current ROP for each warehouse, then calculate the new ROP for the combined warehouse using the pooling principle. See the example in the slides. Assume leadtime = 1 and doesn't change) Round your answer to the nearest integer.
Explanation / Answer
In the given problem,
Lead time = L = 4 days
Review interval = P = 4 days
We define ,
Protection Period = T = L + P = 4 + 4 days = 8 days
Determination of safety stock :
Standard deviation of daily demand = 20
Therefore , Standard deviation of demand during protection period , Sd
= Standard deviation of daily demand x Square root ( Protection period )
= 20 x Square root ( 8)
= 20 x 2.828
= 56.56
Corresponding Z value for Cycle service level of 95% ( i.e. In stock probability of 0.95)
= NORMSINV ( 0.95)
= 1.6448
Therefore required safety stock
= Z x Sd
= 1.6448 x 56.56
= 93.02 ( 93 by rounding to nearest whole number)
Determination of Order Upto level :
Order upto level
= Average demand during protection period + Safety stock
= Average daily demand x T + Safety stock
= 60 x 8 + 93
= 480 + 93
= 573
Determination of Average Inventory:
Breaking up the Order upto level quantity ,
The Safety stock remains constant throughout the year
The regular production order varies between Average demand during protection period and zero
Therefore,
Average Inventory
= Average demand during protection period /2 + Safety stock
= 480/2 + 93
= 240 + 93
= 333
Product E
Safety inventory
93
Order Upto level
480
Average inventory
333
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