Question

Suppose that the annual demand for a componet is aproximately 60,000 units. The company ordes the component from a supplier who has offered the following quantity discount shedule.

order Quantity Price per unit

0-999 $30

1,000-1,999 $29

2,000-3,999                                             $28

4,000-or more                                           $27

If the company's carrying charges is 15 percent of the item's price and the cost per order is $150, determine yhe order quantity that would minimize the total related inventory cost for this component.

Answer 1

Demand (D)=	60,000	units
Quantity(Q)	Price(P)
0-999	$ 30
1,000-1,999	$ 29
2,000-3,999	$ 28
4,000-or more	$ 27
Carrying cost	15%
Cost per order	$ 150
Calculating EOQ + Validity of order quantity with context to the above quantity discount schedule
Economic order quantity (EOQ) = square root of [(2 x demand x ordering costs) ÷ carrying costs]
EOQ(@$30 price)	2,000	( valid EOQ 999)
EOQ(@$29 price)	2,034	(Valid EOQ 1999)
EOQ(@$28 price)	2,070	(Valid EOQ 2070)
EOQ(@$27 price)	2,108	(Valid EOQ 4000)
		Total Cost (TC)= Ordering cost +holding cost + Cost of inventory Particulars Demand/Valid quantity*cost per order + (Valid Quantity/2) *carrying cost per unit +Demand*cost per unit Total Cost TC(@$30 price) $         9,009.01 $                                   2,247.75          1,800,000 $ 1,811,257 TC(@$29 price) $         4,502.25 $                                   4,347.83          1,740,000 $ 1,748,850 TC(@$28 price) $         4,347.41 $                                   4,347.41          1,680,000 $ 1,688,695 TC(@$27 price) $         2,250.00 $                                   8,100.00          1,620,000 $ 1,630,350

Hence,  the order quantity that would minimize the total related inventory cost for this component would be 4000 units.