Question

With a fixed cost of $100 per order, Nathan decided it was vital to get his money's worth. His monthly demand for energy drinks was 10,000 bottles and holding cost was estimated at 20% of unit cost. The mail-order company offered him a couple of possibilities — he could pay $4.00 per bottle for orders of up to 10,000 bottles. After that threshold, he would pay only $3.98 per bottle, and if he ordered 20,000 or more bottles in a order, he would pay only $3.96 per bottle.

A. What is the best order quantity for Nathan to use?

B. What is the best total cost that Nathan can incur?

Answer 1

a) Best order quantity = 10000 (See table below) (Lowest cost)

b) Quantity of 10000 has the lowest cost of = Holding cost + order cost + product cost = (10000/2) *0.796+(120000/10000)*100+(120000*3.98) = $482780

Annual demand, D = Months * Monthly demand =	120000
Order cost, S	100
Quantity	1 to 10000	10000 to below 20000	20000 or more
Cost, C	4.00	3.98	3.96
Holding cost, H = 20%	0.80	0.796	0.792
EOQ = sqrt(2DS/H),	5477.23	5490.97	5504.82
Considered Order quantity - Q for calculation	5477.00	10000.00	20000
	Considered Q = 5477 as EOQ is within range	Consider Q = 10000, for discount	Consider Q = 20000, for discount
Order size	1 to 10000	10000 to below 20000	20000 or more
Product cost = D (120000) * Respective cost for order quantity	480000.00	477600.00	475200.00
Holding cost = (Q/2) * Holding cost	2190.80	3980.00	7920.00
Ordering cost = (D/EOQ) * S	2190.98	1200.00	600.00
Total cost	484381.78	482780.00	483720.00