The Suregrip The Company carries a certain type of tire with the following characteristics:
Average annual sales = 600 tires
Ordering cost = $40 per order
Carrying cost = 25 percent per year
Item cost = $50 per tire
Lead time = 4 days
Standard deviation of daily demand =1 tire
a. Calculate the EOQ.
b. For a Q system of inventory control, calculate the safety stock required for service levels of 85, 90, 95, 97, and 99 percent.
c. Construct a plot of total inventory investment versus service level.
d. What service level would you establish on the basis of the graph in part c? Discuss.
- Calculate the EOQ.
The EOQ is calculated using the following formula:
EOQ = √(2DO/C)
where:
- D = average annual demand = 600 tires
- O = ordering cost = $40 per order
- C = carrying cost = 25% per year
EOQ = √(2 * 600 * 40 / 0.25) = 64 tires
- Calculate the safety stock required for service levels of 85, 90, 95, 97, and 99 percent.
The safety stock is calculated using the following formula:
Zσ = (z/√2) * sqrt(D * L / C)
where:
- Z = the desired service level
- σ = the standard deviation of daily demand = 1 tire
- L = the lead time = 4 days
- C = carrying cost = 25% per year
Safety stock for 85% service level = (1.35/√2) * sqrt(600 * 4 / 0.25) = 2.9 tires
Safety stock for 90% service level = (1.645/√2) * sqrt(600 * 4 / 0.25) = 4.2 tires
Safety stock for 95% service level = (1.96/√2) * sqrt(600 * 4 / 0.25) = 5.5 tires
Safety stock for 97% service level = (2.33/√2) * sqrt(600 * 4 / 0.25) = 6.8 tires
Safety stock for 99% service level = (2.576/√2) * sqrt(600 * 4 / 0.25) = 8.1 tires
- Construct a plot of total inventory investment versus service level.
The total inventory investment is the sum of the safety stock and the average inventory. The average inventory is equal to
the EOQ / 2.
Total inventory investment = (Safety stock + EOQ / 2)
The following graph shows the total inventory investment versus service level:
As the service level increases, the total inventory investment increases. This is because the safety stock increases as the service level increases.
- What service level would you establish on the basis of the graph in part c? Discuss.
The service level that I would establish is 95%. This is because the total inventory investment is relatively low at this service level, and it provides a good balance between customer service and inventory costs.
Increasing the service level to 99% would significantly increase the total inventory investment, and it is not worth the additional cost in my opinion.
I would also consider the following factors when making my decision:
- The cost of stockouts
- The importance of the item to the customer
- The availability of substitute items
I would also consult with the customer to get their input on the desired service level.