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?
Answer:
The safety stock = 142 units
The average inventory = 1392 units
The order point = 2542 units
Step-by-step 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