SuperPart, an auto parts distributor, has a large warehouse in the Chicago region and is deciding on a policy for the use of TL or LTL transportation for inbound shipping. TL shipping costs $800 per truck plus $100 per pickup. Thus, a truck used to pick up from three suppliers costs 800 + (3 * 100) = $1,100. A truck can carry up to 2,000 units. SuperPart incurs a fixed cost of $100 for each order placed with a supplier. Thus, an order with three distinct suppliers incurs an ordering cost of $300. Each unit costs $50, and SuperPart uses a holding cost of 20 percent. Assume that product from each supplier has an annual demand of 3,000 units. SuperPart has thousands of suppliers and the company must decide on the number of suppliers to group per truck if using TL.

What is the optimal order size and annual cost if TL shipping is used but two suppliers are grouped together per truck?

What is the optimal number of suppliers that should be grouped together? What is optimal order size and annual cost per product in this case? What is the time between orders?