A company stocks an SKU with a weekly demand of 600 units and a lead time of 4 weeks. There are 52 weeks in a year. Management will tolerate 1 stock out per year. If sigma for the lead time is 100 and the order quantity is 2500 units, what is:

A company stocks an SKU with a weekly demand of 600 units and a lead time of 4 weeks. There are 52 weeks in a year. Management will tolerate 1 stock out per year. If sigma for the lead time is 100 and the order quantity is 2500 units, what is:  the safety stock, the average inventory, and the order point?

The safety stock = 142 units

The average inventory = 1392 units

The order point = 2542 units

Explanation:

Given that:

the weekly demand = 600 units

lead time = 4 weeks

sigma for the lead time (i.e the standard deviation ) = 100 units

Order quantity = 2500 units

The objective is to calculate :

the safety stock, the average inventory, and the order point?

To start with the number of order per year.

The number of order per year = Annual demand/Order quantity

The number of order per year =  (Weekly demand × 52)/ Order quantity

The number of order per year =  (600 × 52)/2500

The number of order per year =  31200/2500

The number of order per year = 12.48 times /year

Also, the service level for the safety factor = (Number of order per year - 1)/ number of order per year

the service level for the safety factor = ( 12.48 - 1)/12.48

the service level for the safety factor = 11.48/12.48

the service level for the safety factor = 0.9199

the service level for the safety factor = 91.99%

∴ the safety factor at 91.99% service level = (safety factor at (90% +94%))÷2

the safety factor at 91.99% service level = (1.28 +1.56) ÷2

the safety factor at 91.99% service level = 2.84 ÷2

the safety factor at 91.99% service level = 1.42

Now,

the safety stock = 100 × safety factor at 91.99% service level

the safety stock = 100 × 1.42

the safety stock = 142 units

The order point = safety factor +  demand during lead time

where;

The demand during lead time = weekly demand × 4

The demand during lead time = 600  × 4

The demand during lead time = 2400 units

The order point = safety factor +  demand during lead time

The order point = 142 +  2400

The order point = 2542 units

Finally,

The average inventory = (order quantity ÷ 2) + safety stock

The average inventory = (2500 ÷ 2) + 142

The average inventory =1250 +142

The average inventory = 1392 units

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