Question

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%

Answer 1

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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