a. According to the formulae of Economic order quantity
D= 51*52= 2652
S= 4
H= 48
Putting these values in formulae we get Q = 21 (approx.)
Hence Economic order quantity is 21 units.
b. Total number of orders in a year = (Total Demand/ EOQ) = (2652/ 21) = 126 (approx.)
Ordering cost = Total number or orders in a year * Cost to place an order = 126* 4 = $ 504
Holding cost = Avg. Inventory * Holding cost per unit per year
= (Order quantity/2) * Holding cost per unit per year
= (21/ 2) * 48
= $ 504
This also verifies EOQ model as Ordering cost = Holding cost.
Annual Holding cost and Ordering cost = 504 + 504 = $ 1008
c. Safety stock = z* Std. Dev. of Lead Time* Average Demand
= 2.33* 0 * 51 = 0
As safety stock is zero, the Same formula for Holding cost and Ordering cost are formula is unchanged from part b of this question.
Now first, let's calculate Annual ordering and holding costs when ordering 250.
Holding cost = (250/2)*48 = $ 6000
Ordering cost = (2652/250)*4 = $ 42 (approx.)
Total cost @ 250 order size = $ 6042
Now, let's calculate Annual ordering and holding costs when ordering 25.
Holding cost = (25/2)*48 = $ 600
Ordering cost = (2652/25)*4 = $ 420 (approx.)
Total cost @ 25 order size = $ 1020
Money saved when order size is reduced to 25 from 250 = 6042-1020 = $ 5022
PS - In case Safety stock is not zero, Average inventory level = (Safety stock + Order quantity/2) for holding cost calculation.
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