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Insert Draw Desig Layor Refen Maili Revie View Help Foxit Format Calibri (Body)

ID: 430610 • Letter: I

Question

Insert Draw Desig Layor Refen Maili Revie View Help Foxit Format Calibri (Body) Hom Styles Editing Dictate .?. | ? |? Paragraph Paste ^. | Clipboard r Font GI Styles Voice 6-46. For SKU A3510 at the Hardware Warehouse, the order quantity has been set at 150 units each time an order is placed. The daily demand is normally distributed, with a mean of 12 units and a standard deviation of 4. It always takes exactly five days for an order of this item to arrive. The holding cost has been determined to be $10 per unit per year. Due to the large sale volume of this item, management wants to maintain a 99% service level. (a) what is the standard deviation of demand during the lead time? (b) How much safety stock should be carried, and what should be the reorder point? (c) What is the total annual holding cost? age 1 of 2 342 words

Explanation / Answer

Following are the relevant data for calculation :

Standard deviation of daily demand = 4 units

Lead time ( time it takes for the order to arrive ) = 5 days

Therefore ,

Standard deviation of demand during lead time

= Standard deviation of daily demand x Square root ( Lead time )

= 4 x Square root ( 5 )

= 4 x 2.236

= 8.944

STANDARD DEVIATION OF DEMAND DURING LEAD TIME = 8.944

Z value for 99% service level

= NORMSINV ( 0.99)

= 2.3263

Therefore , Safety stock to be carried

= Z value x Standard deviation of demand during lead time

= 2.3263 x 8.944

= 20.80 ( 21 rounded to nearest whole number )

Reorder point

= Average daily demand x Lead time ( days ) + safety stock

= 12 x 5 + 21

= 60 + 21

= 81

SAFETY STOCK = 21

REORDER POINT = 81

Annual holding cost

= ( order quantity / 2 + safety stock ) x annual unit holding cost

= ( 150/2 + 21 ) x $10

=96 x $10

= $960

ANNUAL HOLDING COST = $960

STANDARD DEVIATION OF DEMAND DURING LEAD TIME = 8.944