W.W. Grainger sources from hundreds of suppliers and is considering the aggregation of inbound shipments to lower costs. Truckload shipping costs $500 per truck along with $100 per pickup. Average annual demand from each supplier is 10,000 units. Each unit costs $50 and Grainger incurs a holding cost of 20 percent. The truck has a capacity of 2,500 units.

a. What is the order size, frequency and the total cost (holding and ordering) for each supplier under their current policy of full truckload shipping? (15 points)

b. What is the optimal order size, frequency, and the total cost (holding and ordering) for each supplier if no aggregation is considered? (15 points)

c. What is the optimal order size, frequency, and the total cost (holding and ordering) for each supplier if four suppliers are aggregated? (30 points)