Question

Suppose that the annual demand for a component is approximately 63,000 units. The company orders the component from a supplier who has offered the following quantity discount schedule.

Order Quantity Price Per Unit

0-999 $31

1,000-1,999 $29

2,000-3,499 $27

3,500 or more $25

If the​ company's carrying charge is 16% of the​ item's price and the cost per order is ​$170​, determine the order quantity that would minimize the total related inventory costs for this component.

Answer 1

Annual demand D = 63000

Ordering cost S = 170

Carrying charge H = 16% of item price

We Know Economic Order Quantity Q

EOQ with range 2000-3499 is feasible and the remaining are not feasible as they are not with in the range.

Now we Calculate total cost at Q = 2227 and Q = 3500

Total cost = Purchase cost + Annual ordering cost + Annual holding cost = (CD) +(D/Q)S + (Q/2)H

Q = 2227, H=4.32, C = 27

Total = 27*63000 + (63000/2227)*170 + (2227/2)*4.32 = 17,10,619

Q = 3500 , H = 4 , C = 25

Total = 25*63000 + (63000/3500)*170 + (3500/2)*4 = 15,85,060

Total Cost is less at Q = 3500

Q = 3500 is the order quantity which would minimize the total related inventory costs for this component