Question

It is your responsibility, as the new head of the automotive section of Nichols Department Store, to ensure that reorder quantities for the various items have been correctly established. You decide to test one item and choose Michelin tires, XW size 185 x 14 BSW.

A perpetual inventory system has been used, so you examine this as well as other records and come up with the following data: Cost per tire $55 each

Holding cost 25 percent of tire cost per year
Demand 1,200 per year
Ordering cost $40 per order
Standard deviation of daily demand 4 tires
Delivery lead time 5 days

Because customers generally do not wait for tires but go elsewhere, you decide on a service probability of 90 percent. Assume the demand occurs 365 days per year.

a. Determine the order quantity. (Round your answer to the nearest whole number.) Order quantity tires
b. Determine the reorder point. (Round your answer to the nearest whole number.) Reorder point tires

Answer 1

a. 84 units

b. 27.81

Step-by-step explanation:

The computation is shown below:

a. For economic order quantity

`= \sqrt{\frac{2* \text{Annual demand}* \text{Ordering cost}}{\text{Carrying cost}}}`

`= \sqrt{\frac{2* \text{1,200}* \text{\$40}}{\text{\$13.75}}}`

= 84 units

The carrying cost or holding cost is calculated below:

= $55 × 25%

= $13.75

b. The reorder point is

= Demand × lead time + probability × standard deviation × square root of lead time

where, Demand equal to

= Expected demand ÷ total number of days in a year

= 1,200 ÷ 365 days

= 3.28

So, the reorder point would be

= 3.28 × 5 + 1.28 × 4 × sqrt(5)

= 16.4 + 11.41

= 27.81

The 1.28 is a service level of 90% probability