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:
1. Cost to place an order $100
2. Holding cost 20 percent of product cost per year
3. Cost of refrigerator $500 each
4. Annual demand 500 refrigerators
5. Standard deviation during lead time 10 refrigerators
6. Lead time 7 days
Consider an even daily demand and a 365-day year.
Required:
a) What is the economic order quantity?
b) If the distributor wants a 97 percent service probability, what reorder point, R, should be used?

Question

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Chrisnando Chrisnando · Answer 1 · 2020-05-10T03:05:30+02:00

Answer:

a) 32 refrigerators

b) 28.39 approximately 29 refrigerators

Explanation:

Given:

Cost of order, S = $100

H = 20% of 500 = 100

Cost of refrigerator = $500

Annual demand, D = 500

S.d = 10

Lead time, L = 7 days.

a) To find the economic order quantity, Q_opt, let's use the formula:

[tex] Q_opt = \sqrt{\frac{2*D*S}{H}}[/tex]

[tex] = \sqrt{\frac{2*500*100}{100}} = 32[/tex]

The economic order quantity is 32 refrigerators.

b) The reorder point, R, is calculated as:

R = (d' * L) + ( z * s.d)

Where d' is daily demand which is calculated by dividing annual demand by 365 days.

d' = 500/365 = 1.37

At 97% service probability.

Using the excel function, NORMSINV(0.97) = 1.88.

Therefore z = 1.88

Solving for R, we have:

R = (1.37 * 7) + (1.88 * 10)

= 28.39

≈ 29

If the distributor wants a 97% service probability, the reorder point, R, should be 29 refrigerators