Question

Book: Operations And Supply Chain Management Jacobs & Chase 14e

Chapter 20 Inventory Management

The I-75 Carpet Discount Store has an annual demand of 10,000 yards of super shag carpet. The annual carrying cost for a yard of carpet is $0.75 and the ordering cost is $150. The carpet manufacturer normally charges the store $8 per yard for the carpet.; however, the manufacturer has offered a discount price of $6.50 per yard if the store will order 5,000 yards. How much should the store order, and what will be the total inventory cost for that order quantity?

Order Size	P
0–4,999	$8.00
5,000 +	$6.50

Answer 1

Annual demand(D) = 10000 yards

ordering cost(S) = $150

Holding cost(H) = $0.75

For this problem we have to first calculate the common Economic order Quantity as the holding cost for all range is the same.So the common EOQ = √ (2DS/H)

= √[(2X10000X150) / 0.75]

= √(3000000/0.75)

= √4000000

= 2000 units

We can order 2000 units at a price of $8.00

Total cost with order quantity(Q) of 2000 units = [(Q/2)/H] + [(D/Q)S] + (Price X D)

= [(2000/2)0.75] + [(10000/2000)150] + (8.00 X 10000)

= $750 + $750 + $80000

= $81500

Because a lower price ranges exist that must be checked against the cost generated by 2000 units at the price of $8.00

The minimum units required to order to obtain a price of $6.50 is 5000 units.So the total cost with an order quantity(Q) of 5000 units = [(Q/2)H] + [(D/Q)S] + (Price X D)

= [(5000/2)0.75] + [(10000/5000)150] + (6.50 X 10000)

= $1875 + $300 + $65000

= $67175

So the store should order 5000 yards as it has the lowest total cost which is $67175

So the total inventory cost = $67175