Question

A distributor of large appliances needs to determine the order quantities and reorder points for the various products it carries. The following data refer to a specific refrigerator in its product line.
Cost to place an order $100 / order
Holding cost 20 percent of product cost per year
Cost of refrigerator $500 / unit
Annual demand 500 units
Standard deviation of
demand during lead time 10 units
Lead time 7 days
Consider an even daily demand and a 365-day year.
a. What is the economic order quantity?
b. If the distributor wants a 97 percent service probability, what reorder point, R, should be used?

Answer 1

Answer:

a. 32 refrigerators

b. 29 refrigerators

Explanation:

a. The computation of the economic order quantity is shown below:

$= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}$

$= \sqrt{\frac{2\times \text{500}\times \text{\ 100}}{{\ 500 \times 20\%}}}$

= 32 refrigerators

b. Now the reorder point is

= Annual demand ÷ total number of days in a year × lead time + (service level × standard deviation for the lead time)

= 500 units ÷ 365 days × 7 days + (1.90 × 10 units)

= 9.59 + 19

= 29 refrigerators