Lab Transshipment Problem (100 Points)
Problem 1 Transshipment Problem
Courtesy example from Spreadsheet Modeling and Decision Analysis By Cliff Ragsdale)
The Bavarian Motor Company (BMC) manufactures expensive luxury cars in Hamburg, Germany and exports cars to sell in the United States. The exported cars are shipped from Hamburg to ports in Newark, New Jersey, and Jacksonville, Florida. From these ports, the cars are transported by rail or truck to distributors located in Boston, Massachusetts; Columbus, Ohio; Atlanta, Georgia; Richmond, Virginia; and Mobile, Alabama. Figure 1 shows the possible shipping routes available to the company along with the transportation cost for shipping each car along the indicated path.
Currently, 200 cars are available at the port in Newark, NJ and 300 are available in Jacksonville, FL. The numbers of cars needed by the distributors in Boston, Columbus, Atlanta, Richmond, and Mobile are 100, 60, 170, 80, and 70, respectively. BMC wants to determine the least costly way of transporting cars from the ports in Newark and Jacksonville to the cities where are needed.
Problem 2 Maximum Flow Problem
Consider the north-south interstate highway system passing through Cincinnati, Ohio. The north-south vehicle flow reaches a level of 15,000 vehicles per hour at peak times. Due to a summer highway maintenance program, which calls a for the temporary closing of lanes and lower speed limits, a network alternative routes through Cincinnati has been proposed by a transportation planner committee. The alternative routes include other highways as well as city streets.
Because of differences in speed limits and traffic patterns, flow capacities vary, depending on the particular streets and roads used. The proposed network with arc flow capacities is shown in Figure 2.
The direction of flow for each arc is indicated, and the arc capacity is shown next to each arc. Note that most of the streets are one-way. However, a two-way street can be found between nodes 2 and 3 and between node 5 and 6. In both cases, the capacity is the same in each direction.