Question

Ford Motors has an assembly plant located in Chicago area. Ford purchases all tires for the cars assembled in the Chicago plant from Lassa, located in Pittsburgh, PA. Demand for tires at Ford assembly plant is normally distributed with an average of 550 tires per day and a standard deviation of 50 tires per day. Given 365 days a year, Ford purchases 200,750 tires each year from Lassa at a price of $20 per tire. Ford uses a continuous review inventory policy with a reorder point set to achieve a 95% service level.

Ford has two options for transportation of tires: Union Railroads or Steelers Trucking. Details on these options are given in the table below. (Note: Transit lead times has no variability in both options; always 10 days for Union Railroads and always 4 days for Steelers Trucking)

	Union Railroads	Steelers Trucking
Minimum Shipment Size	10,000	2,000
Freight Cost per tire($)	$0.5	$0.75
Transit lead time(days)	10 days	4 days
Fixed Ordering Cost	$1,000	$500

Ford owns the tires while in transit to its plant and annual holding cost during transit or at the Chicago plant is 25 percent of the unit tire cost. Given the information above which transportation option Ford should choose?

Answer 1

Transportation option Ford should choose
	Union Railroads	Steelers Trucking
Tires to be shipped every year	200750	200750
Minimum shipment size	10000	2000
Number of shipments	20	100
Freight cost	$100,375.00	$150,562.50
Fixed ordering cost	$20,000.00	$50,000.00
Annual holding cost	$27,397.26	$10,958.90
Total cost	$147,772.26	$211,521.40
As the cost is lower in Union Railroads, it is advisable to choose Union Railroad as transportation option
Working Note:
Number of shipment = Annual number of tires to be shipped/minimum shipment size
Freight cost = Annual number of tires to be shipped x Freight cost per tire
Fixed ordering cost = Number of shipments x Fixed ordering cost per shipment
Annual holding cost = Minimum shipment size x Transit lead time days/365 x number of shipment x Holding cost
Holding cost = Cost per tire x 25%
= $20 x 25% = $5
	Union Railroads	Steelers Trucking
Number of shipments	200750 / 10000	200750 / 2000
Freight cost	200750 x $0.50	200750 x $0.75
Fixed ordering cost	1000 x 20	500 x 100
Annual holding cost	10000 x 10/365 x 20 x $5	2000 x 4/365 x 100 x $5