TopOil, a refiner in Indiana, serves three customers near Nashville, Tennessee, and maintains consignment inventory (owned by TopOil) at each location. Currently, TopOil uses TL transportation to deliver separately to each customer. Each truck costs $800 plus $250 per stop.

Thus, delivering to each customer separately costs $1,050 per truck.

TopOil is considering aggregating deliveries to Nashville on a single truck. Demand at the large customer is 60 tons a year, demand at the medium customer is 24 tons per year, and demand at the small customer is 8 tons per year. Product cost for TopOil is $10,000 per ton, and it uses an annual holding cost of 25 percent. Truck capacity is 12 tons.

a. What is the annual transportation and holding cost if TopOil ships a full truckload to each customer when they are running out of stock? How many days of inventory is carried at each customer under this policy?

b. What is the optimal delivery policy to each customer if TopOil ships separately to each of them? What is the annual transportation and holding cost? How many days of inventory is carried at each customer under this policy?

c. What is the optimal delivery policy to each customer if TopOil aggregates shipments to each of the three customers on every truck that goes to Nashville? What is the annual transportation and holding cost? How many days of inventory are carried at each customer under this policy?

d. Can you come up with a tailored policy that has lower costs than the policies in

(b) or (c)? What are the costs and inventories for your suggested policy?