Let us consider an item whose inventory is controlled by a p

Let us consider an item whose inventory is controlled by a periodic review and a base-stock policy. Assume that the review period is 1 day, the replenishment lead-time is 5 days, and the daily demand is a normal distribution function with a mean 100 and standard deviation 30.

1) Calculate the base stock B to assure that the service level is 0.90?
2) Calcuate the average inventory level?
3) Calculate the stock-out periods might you expect per year? (Assume 250 days per year)

Solution

Let the Protection Period ( P ) = Review period + Lead time = 1 + 5 = 6 days

Standard deviation of daily demand = 30

Therefore, standard deviation of demand during Protection Period

= Standard deviation of daily demand x Square root ( Protection period )

= 30 x Square root ( 6 )

= 30 x 2.449

= 73.47

Given,

Service level = 0.90

Corresponding Z value for service level of 0.90 = NORMSINV ( 0.90) = 1.2815

Therefore,

Safety stock = Z value x Standard deviation of demand during protection period

                         = 1.2815 x 73.47

                          = 94.15 ( 94 rounded to nearest whole number )

We presume “Base stock” implies safety stock. Therefore, Base stock = 94 units

The maximum value of cycle inventory = Average daily demand x Protection period = 100 x 6 = 600 units

Minimum value of cycle inventory = 0

Thus , average cycle inventory = ( Maximum + Minimum ) /2 = 600/2 = 300 units

Thus,

Average inventory level = Average cycle inventory + Safety stock = 300 + 94 = 394 units

Since Service level = 0.90, probability of stock out = 1 – 0.90 = 0.10

Thus , Expected stock out period in a year = probability of stock out x Number of days in a year = 0.10 x 250 = 25 days

BASE STOCK = 94 UNITS

AVERAGE INVENTORY LEVEL = 394 UNITS

EXPECTED STOCKOUT PERIOD PER YEAR = 25 DAYS