Exercise 13-3: Goodstone Tires
Inputs
Anticipated demand per week 2,000
Standard deviation 500
Order quantity 10,000
Reorder point 6,000
Replenishment lead time in weeks 2
Unit costs $40
Sales price $80
Inventory holding costs 25%
Cost of understocking $80
Distribution of demand during lead time
Mean demand during lead time 4,000
SD of demand during lead time 707
Outputs
Current safety inventory (tires) 2,000
Cycle service level (CSL) 0.9977
Cost of overstocking, Co$10
Justifying cost of understocking $411
Optimal CSL 0.8889
Optimal safety inventory 863
The manager at Goodstone Tires, a distributor of tires in Illinois, uses a
continuous review policy to manage inventory. The manager currently orders
10,000 tires when the inventory of tires drops to 6,000. Weekly demand for
tires is normally distributed, with a mean of 2,000 and a standard deviation of
500. The replenishment lead time for tires is two weeks. Each tire costs
Goodstone $40, and the company sells each tire for $80. Goodstone incurs
an annual holding cost of 25 percent. How much safety inventory does
Goodstone carry if the cost of understocking is $80 per tire in lost current
and future margin?
CR – 12/3/2020 10:04 AM Page 1 13-3.xlsx – 13.3
Exercise 13-3: Goodstone Tires
Inputs
Anticipated demand per week 2000
Standard deviation 500
Order quantity 10000
Reorder point 6000
Replenishment lead time in weeks 2
Unit costs 40
Sales price 80
Inventory holding costs 0.25
Cost of understocking 80
Distribution of demand during lead time
Mean demand during lead time =C15*C19
SD of demand during lead time =C16*SQRT(C19)
Outputs
Current safety inventory (tires) =C18-C26
Cycle service level =NORMDIST(C18,C26,C27,1)
Cost of overstocking =C22*C20
Justifying cost of understocking =(C32*C33)/(1-C32)
Optimal CSL =C23/(C23+C33)
Optimal safety inventory =NORMSINV(C36)*C27
The manager at Goodstone Tires, a distributor of tires in Illinois, uses a continuous review policy to manage their inventory. The manager currently orders
10,000 tires when the inventory of tires drops to 6,000. Weekly demand for tires is normally distributed with a mean of 2,000 and a standard deviation of 500.
The replenishment lead for tires is two weeks. Each tire costs Goodstone $40 and the company sells each tire for $80. Goodstone incurs a holding cost of 25
percent. How much safety inventory does Goodstone currently carry? At what cost of understocking is the manager’s current inventory policy justified? How
much safety inventory should Goodstone carry if the cost of understocking is $80 per tire in lost current and future margin?