The Prompt Corporation purchases product from two suppliers, A and B. Supplier A is located in Austin, TX, and supplier B in Carthage, TN. Supplier A supplies component a and supplier B supplies component b. These components are used to make gizmos of two types, 1 and 2. Gizmo 1 is made in Helena, MT (Plant 1) and Gizmo 2 is made in Duluth, MN (Plant 2). Manufacturing plants make gizmos according to daily demand and one Gizmo 1 requires 1 unit of component a and one Gizmo 2 requires 1 unit of component b.

Demand per day for Gizmo 1 is distributed normally with a mean of 195 and a standard deviation of 100. Demand per day for Gizmo 2 is distributed normally with a mean of 330 and a standard deviation of 250. Prompt Corporation follows a fixed order quantity inventory policy (i.e., fixed Q). Here is a brief sketch of the supply chain system of Prompt Corporation:

Currently, loads are shipped full truckload from suppliers directly to plants. These trucks have a capacity of 500 units. Transit time between Supplier A and Plant 1 is 4 days while the transit time between Supplier B and Plant 2 is 2 days. The costs of trucks per truckload shipped are $2,250 to Plant 1 and $1,500 to Plant 2. Holding cost per component per day is $0.8. Assume the Prompt Corporation aims 90% service level, 1 year has 360 days and there are 30 days per month.

(a) Provide the annual total supply chain costs for this system. Please note that total supply chain costs equal to annual holding cost plus annual transportation costs. Annual holding cost is a function of pipeline stock, cycle stock, and safety stock. [15 points]

(b) Prompt has realized that it can obtain larger trucks with a capacity of 1,000 units for a cost of $4,000 to Plant 1 and $2,500 to Plant 2 with the same transit times for each route. If Prompt has these trucks, should all shipments be full truck load or less-than-full truckload? What will be the associated annual total supply chain costs to use these trucks with the appropriate level of loads on these trucks? Are the costs lower than part (a)? Explain why or why not? [20 points]