Solution:
Average demand = 100 units per day, with a standard deviation of 12 units
Average lead time = 12 days with a standard deviation of 2 days
250 days per year
unit cost = $25 , desired service level = 95% , Ordering cost = $50 , Inventory carrying cost = 20%
Lets say
Average demand = Ad
Average lead time = At
Unit cost = U
Desired service level = Dl
Ordering cost = O
Inventory carrying cost = Icc
Standard deviation =S
Thus,
S of demand at Dl = [tex]12 * 12^{\wedge} 2[/tex] = 205 units
SS = 1.65 multiply with 205 = 339 units
Total units in a day = 250 multiply with 100 = 25000
EOQ = [tex]$(2 * 25000 \text { units per year } * 50 \text { per order }) /(25 \text { per unit* } 0.2)$[/tex] = 708 units
here 25 and 0.2 is unit cost and invetory cost
TAC
annual ordering cost
O = [tex]50 * 25000 / 708[/tex] = 1765.5
Annual inventory cost
Icc = [tex]25^{*} 0.2^{*}(708 \text { units } / 2)[/tex] = 1770
Annual product cost = Pc
25 multiply with 25000 = 625000
total = O +Icc+Pc
625000+1770+1765.5 = 628535.5
If the service level increases from 95% to 99%, cost will dec per unit
