Question

Annual demand is 12500 units, cost per order is $60 and carrying cost per unit as a    percentage is 8%. The company works 50 weeks a year; the lead-time on all orders placed is 5 weeks.
Assuming constant lead-time demand, and a unit cost of $40 what is the economic order quantity? What is the reorder point.
If lead-time demand shows variability that follows a normal distribution with a mean μ =280 and a standard deviation σ =20, what will the revised reorder point if two stock-outs (shortages) are allowed?
What is the company’s reorder point if the probability of a stock-out on any cycle is restricted to 0.05

Answer 1

EOQ
Details
Annual usgae units	12,500
Cost pr Order	$                                                       60
Carrying cost per unit =8% *$40	$                                                    3.20
EOQ = Sq Root of [(2*Order cost*Annual usage)/(Annual Holding cost per unit]
=Sq Rt ( 2*12500*60)/3.2
EOQ =684.65 units
Annual Usage	12,500
No of Working days in a Year =50 weeks =350 days
Usage /Day =12500/350=	35.71
Lead Time =5 weeks =35 days
Reorder Point =Lead Time days*Daily usage=35*35.71=	1,250.00
So ROP =1250 Units
When stock out is restricted to 0.05, we can take the stock
out probability as 5%. So service Level will be 95%
Z value at 95% coverage=1.65
Std Deviation =20
Safety Stock =Z*Std deviation=1.65*20=33 units
Mean demand =250 units
Reorder Point =Expected Demand During Lead time+Safety Stock
=250+33=283 Units
ROP =283 units.