Question

In: Statistics and Probability

The VP for Fite's Footballs has asked you to perform an audit of inventory levels for...

The VP for Fite's Footballs has asked you to perform an audit of inventory levels for a different region. The inventory manager was recently terminated and you need to determine the appropriate safety stock for each item. Management has set the service level at 85%. Given the data below, what would the FILL RATE be for the following item?

Price	$100
Annual Demand	156,000 units
Cost per Order	$200
Cost to hold the item per year	25%
Economic order quantity	1580
Lead Time	3 weeks
Standard Deviation of Forecasted Demand During Lead Time	200

choose the correct answer:

Fill Rate = 98.2%

Fill Rate = 98.4%

Fill Rate = 98.6%

Fill Rate = 99.0%

Fill Rate = 99.3%

Expert Solution

Answer:

Here some data is missing in the above queston i can Assume the data to solve this problem to find fill rate.

Price= P= $100

Annual Demand = D=156,000 units

Cost per Order = Co= $200

Holding cost = Ch = 25% *100 = $ 25

Economic order quantity = Q= 1580

Lead Time = 3 weeks

Standard Deviation of Forecasted Demand During Lead Time = σL = 200

CSL = 85% which gives value of Z as -

Z = NORMSINV (85%) = 1.036

Safety stock = SS = Z*σL = 1.036 * 200 = 207.2

Expected shortage = ESC = - SS [1 - NORMDIST(SS /σL,0,1,1)] + σL * NORMDIST(SS /σL,0,1,0)

=-207.2[1-NORMDIST(1.036,0,1,1)] + 200 *NORMDIST(1.036,0,1,0)

=-207.2 *0.150 + 200*0.233

= -31.08 + 46.6

=15.52

Fill rate = fr = (Q - ESC) / Q

= (1580-15.52)/1580

=0.990

Fill rate = fr = 99.0 %

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orchestra answered 1 year ago

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