3. A computer manufacturer ships partially assembled computers (hereafter called units from an assembly plant in Thailand to a distribution center in Oregon. We want to determine if shipping in 40ft containers by the ocean or airline containers by air carriers is more economical. Shipment by ocean costs $11,000 per container, and a 40ft container can hold 5,000 units. The handling cost is $2000 per 40ft container. The journey by sea takes 20 days on average. Shipment by air costs $20,000 per container, and an airline container can hold 1,400 units. The handling cost is $1000 per airline container. On average, the journey by air takes two days (door to door). The forecasted demand is 120,000 units for the next year, which is also the planned production quantity. No safety stock is kept at the assembly plant, and a shipment is sent to the distribution center when a container is filled. A safety stock of 1,000 units is owned at the distribution center. A unit costs $600 at the assembly plant and $800 at the distribution center. The inventory holding cost rate is estimated at 20% of the yearly value. The space cost is evaluated as $30 / unit*year at the assembly plant and $40 /unit*year at the distribution center.

(a) What are the annual inventory holding costs at the assembly plant (including the space and holding cost in this calculation)?

(b) What are the annual inventory holding costs at the distribution center (including the space and holding cost in this calculation)?

(c) What are the annual in-transit inventory costs for each mode?

(d) What are the annual transportation costs for each mode (don't forget to consider the shipment handling cost when calculating these costs)?

(e) What are the total annual cost equations for each mode of transportation?

(f) Assume that the shipper will always ship full loads. Determine the most economical transportation service to use in this case.

(g) Now assume that the shipper may use less than full loads. Determine the most economical transportation service to use in this case.