XYZ Auto Company distributes car filters. The lead-time to obtain the filters is
ID: 363510 • Letter: X
Question
XYZ Auto Company distributes car filters. The lead-time to obtain the filters is 1 month. The lead-time demand is normally distributed with an average of 500 items per month and a standard deviation of 70 units. Order cost is $12 per order, and holding cost is $0.30 per filter per year. The estimated cost of a stockout is $10 per stockout. Calculate 1. The EOQ 2. The economic optimum probability of stockout and the corresponding service level. 3. The optimum reorder level. The annual inventory cost. 4. Note: The area under the standardized normal distribution curve from minus infinitive to Z is 0.9965 (99.65%) for a Z value of 2.7.Explanation / Answer
L = Average lead time = 1 month
D = Monthly demand = Lead time demand / L = 500 / 1 = 500
SLT = Std. dev of lead time demand = 70
CO = Ordering cost per order = $12
CH = Holding cost per item per month = $0.30 / 12 = $0.025
CB = Stockout cost = $10
EOQ = Q* = (2.D.CO.(CH+CB)/CH.CB)1/2 = sqrt(2*500*12*(10+0.025)/(10*0.025)) = 693.7 or 694
Optimum probability of stockout per order cycle = (CH x Q*) / (CB x D) = (0.025 x 694) / (10 x 500) = 0.0035
So, Service level = 1 - 0.0035 = 0.9965 (correspending Z is 2.7)
Safety Stock (SS) = Z x SLT = 2.7 x 70 = 189
Optimum reorder level = Average lead time demand + SS = 500 + 189 = 689
b* = optimal units in backorder when placing an order = CH x Q* / (CH + CB) = 0.025*694/(0.025+10) = 1.73
Annual Inventory Cost = Cycle stock inventory cost = Safety stock inventory cost
Cycle stock inventory cost per month = (Q* - b*)2 x CH / 2Q* = ((694 - 1.73)^2)*0.025/(2*694) = $8.63
Safety stock inventory cost per month = SS x CH = 189 x 0.025 = $4.73
Total inventory cost per year = ($8.63 + $4.73) x 12 = $160.32
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