Question

In: Operations Management

Daily demand for a product is 90 units, with a standard deviation of 20 units. The...

Daily demand for a product is 90 units, with a standard deviation of 20 units. The review period is 10 days and the lead time is 8 days. At the time of review there are 70 units in stock.

If 99 percent service probability is desired, how many units should be ordered? (Use Excel's NORMSINV() function to find the correct critical value for the given ?-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

Ordered quantity

units

Expert Solution

Z value for 99 percent of service probability = NORMSINV ( 0.99) = 2.326

Given are following data :

Lead time =8 days

Review period = 10 days

Therefore , Protection period = Lead time + review period = 8 + 10 = 18 days

Standard deviation of daily demand = 20 units

Therefore,

Standard deviation of demand during protection period

= Standard deviation of daily demand x Square root ( Protection period)

= 20 x Square root ( 18 )

= 20 x 4.242

= 84.84

Therefore, Safety stock = Z value x Standard deviation of demand during protection period = 2.326 x 84.84 = 197.33 ( 197 rounded to nearest whole number )

Theoretical Reorder point

= average daily demand x Protection period + Safety stock

= 90 x 18 + 197

= 1620 + 197

= 1817

However, number of units in stock at the time of review =70

Therefore , number of units should be ordered

= Reorder point – Number of units in stock

= 1817 – 70

= 1747

ORDERED QUANTITY = 1747 UNITS

keosha answered 6 months ago

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