Question 1. Consider an item whose inventory is controlled by a periodic review,

Question

Question 1. Consider an item whose inventory is controlled by a periodic review, base-stock policy. Suppose the review period is 1 day, the replenishment lead-time is 5 days, and the daily demand is normally distributed with mean 100 and standard deviation 30. Part A. What is the base stock B to assure that the service level is 0.90 Part B. What is the average inventory level? Part C. How many stock-out periods might you expect per year? (Assume 250 days per year) Hint: In Part C, we ask for stock-out cycles and not stock-out quantities. Think of type 1 service level.

Explanation / Answer

Part A)

Review Period = 1 day

Lead time = 5 day

Mean demand for 1 day = 100

So mean demand for 6 day = 100 * 6 = 600

Daily Std deviation = 30

Std deviation for 6 days = sqrt (6) * 30 = 73.48

Service level = 90%

Base stock = mean + z * std deviation = Norminv ( service level, mean, std deviation ) = Norminv( 0.9, 600, 73.48) = 694.17 units

Part B)

Find stock outs units

z = (Base stock - mean ) / std deviation = (694.17 - 600) / 73.48 = 1.28

Lookup L(z) in the Standard Normal Loss Function Table:L(1.28) = 0.0475

This indiates factor of expected loss

Expected backorder = std deviation * L(z) = 73.48 * 0.0475 = 3.49

So average inventory level = Base stock - mean demand + stock outs = 694.17 - 600 + 3.49 = 97.66 ~ 97

Part C)

90% is the servive level indicates that during 90% of review period no backorder is generated and available invetory is used immediately to fulfill demand

So during 10% of review period backorder will be generated.

So stock out is expected during 10% of 250 days in a year i.e. on 25 days.

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