'11.8. A company stocks an SKU with a weekly demand of 225 units and a lead time of 3 weeks. Management will tolerate one stockout per year. If sigma for the lead time is 175 and the order quantity is 800 units, what is the safety stock, the average inventory, and the order point

a. 261  units

b. 661  units

c. 936 units

Explanation:

Safety stock, average inventory, and the order point can be calculated as follows according to their formulas.

DATA

Weekly Demand = 225 units

Lead time = 3 weeks

Annual Demand  = 225 units  x 52 weeks  = 11,700 units

sigma = 175

Order Quantity Q = 800

Solution

No of orders per year = Annual demand/order quantity

No of orders per year= 11700/800

No of orders per year= 14.625  orders

Service level = (no of orders-1)/no of orders

Service level = (14.625-1)/14.625

Service level = 93.16 %

Saftey factor for 93.16 is 1.49

Saftey stock = 1.49 \sigma

Saftey stock = 1.49 * 175

Saftey stock = 260.75 OR 261  units

Average inventory = Q/2 + saftey stock

Average inventory = 800/2 + 261

Average inventory = 400 + 261

Average inventory = 661

Order point = Demand during the lead time + safety stock

Order point= 225 x 3 + 261

Order point= 936 units

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