Question

. Assume that the following quantity discount schedule applies:

Order Size	Discount	Unit Cost
0 to 999	0%	$150
Over 999	$5 per unit	$145

   Annual demand is 5000 units, ordering cost is $ 400 per order, and inventory holding cost is 10% of the cost of goods.

• What is the optimal quantity to order?

What will be the Inventory Cost?

Answer 1

Annual Demand D = 5000 units

Ordering cost = 400

First of all, we will find the EOQ with different price -

For Price 150

Holding Cost H = 150*10% = 15

EOQ = (2DS/H)^(1/2)

EOQ = (2*5000*400/15)^(1/2)

EOQ = 516.39

EOQ = 516 units (Feasible)

For Price 145 -

Holding Cost = 14.50

EOQ = (2*5000*400/14.50)^(1/2)

EOQ = 525.22 = 525 units (Not feasible)

Now we will find the total Coat at EOQ = 516 and Q = 1000. Quantity with least total cost will be optimal.

Total Cost = (D/Q)*S + (Q/2)*H + P*D

Total Cost at EOQ = (5000/516)*400 + (516/2)*15 + 5000*150 = 757746

Total Cost at Q = 1000 = (5000/1000)*400 + (1000/2)*14.50 + 5000*145 = 734250

Since Cost is least with Q = 1000, hence Q = 1000 will be optimal order quantity.

Optimal Order quantity = 1000

Cost of Inventory = Ordering Cost + Holding Cost

Cost of Inventory = (D/Q)*S + (Q/2)*H

Cost of Inventory = (5000/1000)*400 + (1000/2)*14.50

Cost of Inventory = 9250