Answer:
a)
Annual demand = 75000 = D
S = ordering cost/set up cost = $53
d = daily demand = 75000/250 = 300
h = holding cost per unit per year = $25
p = Daily production rate = 320
optimal size of the production run =EPQ = sqrt((2*D*S)/(h*(1-(d/p))))
= sqrt((2*75000*53)/(25*(1-(300/320))))
= 2255.659549 = 2255.66 (Rounded to 2 decimal places)
b)
maximum inventory = EPQ*(1 - (d/p))
= 2255.66*(1 - (300/320))
= 140.97875
Avergae inventory = 140.97875/2 = 70.49
c)
Number of production runs = Annual demand/EPQ = 75000/2255.66 = 33.25
d)
Holding cost with EPQ = 2255.66 = 70.49*25 = 1762.25
With EPQ = 500, maximum inventory = 500*(1 - (300/320)) = 31.25
Holding cost with EPQ = 500, holding cost (31.25/2)*25 = 390.625
Savings = 1762.25 - 390.625 = 1371.625
