Question

R and N Investment Corp. has an annual demand of 1,500, ordering costs of $15/order, and inventory carrying costs of 25% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost? When we use the quantity discount model, what are the two basics elements to take into consideration? Why?

Quantity	1 to 499	500 to 999	1,000 to 1,499	1,500 and up
Price	$15.00 per unit	$14.50 per unit	$14.00 per unit	$13.75 per unit

Answer 1

data given :

annual demand (D) = 1500

ordering cost per order / set up cost (S) = $15 per order

inventory carrying cost = 25% of item price

R and N Investment Corp. would pay $13.75 per unit by ordering 1500 units at a time.

EOQ = √(2 D S) / I

EOQ = √(2 x 1500 x 15) / (13.75 x 25%)

EOQ = √45000 / 3.4375

EOQ = 114.4155 or 114 units

we should order EOQ on which ordering cost and inventory carrying cost will BE MINMUM OR EQUAL.

company is not ordering EOQ in range 2,3 and 4 so ordering cost and inventory carrying cost will not equal.

particular	range 1	range 2	range 3	range 4
minimum quantity	1	500	1000	1500
unit price	$15	$14.50	$14	$13.75
results:
quantity (EOQ = √(2 D S) / I) (i)	109.5445	111.4172	113.3893	114.4155
order quantity (ii)	1	500	1000	1500
EOQ (i or ii which ever is higher)	109.5445	500	1000	1500
ordering cost per order / set up cost (annual demand x ordering cost per order /order quantity) (a)	$205.39 = 1500 x 15 / 109.5445	$45 = 1500 x 15 / 500	$22.5 = 1500 x 15 / 1000	$15 = 1500 x 15 / 1500
inventory carrying cost (EOQ x unit price x inventory carrrying cost in % / 2) (b)	$205.39 = 109.5445 x 15 x 25% / 2	$906.25 = 500 x 14.5 x 25% / 2	$1750 = 1000 x 14 x 25% / 2	$2578.125 = 1500 x 13.75 x 25% / 2
unit cost (c)	$22500 = 1500 x $15	$21750 = 1500 x $14.50	$21000 = 1500 x $14	$20625 = 1500 x $13.75
total cost (a+b+c)	$22910.78	$22701.25	$22772.5	$23218.125

so we should order that quantity of EOQ on which ordering cost and inventory carrying cost will minimum or equal.

EOQ = 109.5445 units or 110 units (round off)

inventory carrying cost and ordering cost are two element which is considered to for quantity discount model because we have to order the quantity on which ordering cost and inventory carrying cost will minimum or equal. on there costs we have to invest very high amount for maintenece,carrying and placing order when we order quantity and our try to reduce these cost to minimum.

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