Question 1) Ford and GM carry spare parts for their dealers at a third-party warehouse in the Upper Peninsula (UP) of Michigan. Demand for Ford spare parts is 100 units per month while demand for GM parts is 120 per month. Each spare part costs $100, and both companies have an annual holding cost of 20 percent. Currently, each company uses a separate truck to ship these parts. Each truck has a fixed cost of $500. Answer the following questions (each part has 5 points)

a) What is the optimal order size and frequency for Ford?

b) What is the optimal order size and frequency for GM?

c) What is the cycle inventories for Ford and GM?

d) How many days does cycle inventory add to the average time that Ford spare parts spend in the supply chain? How about GM? (assume 365 days in a year)

e) What is the total annual ordering and holding cost for each company?

A 3rd party logistics (3PL) provider has offered to combine shipments for each of the two companies on a single truck. This will require a fixed transportation cost of $500 per truck and an additional fixed cost of $50 per company included. If the two companies agree to the joint shipment,

f) What are the optimal order frequency and batch size for Ford and GM?

g) What is the annual ordering and holding cost for the two companies combined? h) Should Ford and GM accept the 3rd party's proposal? Why?

i) How do you think Ford and GM should divide the fixed cost per truck among themselves? (Note that there are multiple ways of dividing the cost. Think about a way that both Ford and GM would feel is fair)

j) Now suppose trucks have a maximum capacity of 350 units. If Ford and GM agree to joint shipments, what are the optimal order frequency and batch sizes for Ford and GM?