Question

2. Assume that the following quantity discount schedule is appropriate. If annual demand is 120 units, ordering costs are $20 per order, and the annual holding cost rate is 25%, what order quantity would you recommend?

Order size Discount (%) Unit cost ($)

0 - 49 0 30.00

50 - 99 5 28.50

100 or more 20 27.00

Answer 1

D = 120

S = 20

Holding cost -

Upto 49 unit = 30*25% = 7.5

From 50 to 99 unit = 28.50*25% = 7.125

From 100 onwards - 27*25% = 6.75

So,

EOQ with Price 30 per unit = (2DS/Holding cost)^(1/2) = (2*120*20/7.5)^(1/2) = 25.298 = 25 units

EOQ with Price 28.50 = (2*120*20/7.125)^(1/2) = 25.95 = 26 units

EOQ with price 27 = (2*120*20/6.75)^(1/2) = 26.67 = 27 units

Out of above mentioned three EOQ, only EOQ with price 30 is feasible as it falls within the quantity range 0 to 49.

Now, we will check the Total Cost with EOQ, 50 & 100 order quantity.

Total Cost at EOQ = (QH/2) + (DS/Q) + P*D

Total Cost at EOQ = (25*7.5/2) + (120*20/25) + (30*120) = 3789.75

Total Cost at 50 order quantity = (50*7.125/2) + (120*20/50) + (28.50*120) = 3646.13

Total Cost at 100 order quantity = (100*6.75/2) + (120*20/100) + (27*120) = 3601.50

Since, the total cost with 100 quantity is least, hence optimal order quantity should be 100 units.