PROTRAC is an auto manufacturer and has four assembly plants in the US. They are located in Ames, Iowa (1), Altoona, Pennsylvania (2), San Diego, California (3), and Phoenix, Arizona (4). The engines used by these plants (only one type of engine called A-2 engine is used) are produced in Japan and Europe, and are shipped to the US via ocean transportation. Engines arrive at harbors in Seattle, Washington (A), Miami, Florida (B), and New York, New York (C).
Production plans for the next month have been set. The demand at each plant (requirements) for A-2 engines are shown in the following table.
The available number of A-2 engines at harbors (or the supply available at ports) in time to be used for next month production are shown below.
Note that the total supply of engines available at ports equals the total number required at plants. PROTRAC must decide how many engines to send from each harbor to each plant. PROTRAC’s goal is to minimize the total cost of transporting the A-2 engines from harbor to plant. The engines are transported by common carriers and charges are on a per engine basis. The relevant costs for transportation are given in the following table.
PROBLEMS
1. Use LP to find the answer to PROTRAC’s question. In other words, determine how many engines to transport from each origin to each destination.
2. What happens if the supply at harbor B is increased to 1,000? Re-run the LP model and provide your answer. Notice that now demand is less than supply.
3. What happens if the supply at harbor B and C are decreased to 600 and 700 respectively. Do you have to change your LP model? Re-run your LP problem and provide your answer. Observe that now demand is more than supply.