Southwestern University (SWU) is located in Stephenville, Texas. They have recently hired a new well-known football coach and because of this, they are expecting an increase in their fan base for this sport. Their season ticket sales have gone up, meaning more revenues, however, this also means increase in customer complaints due to traffic problems whenever there’s a game. Dr. Marty Starr, SWU’s president, has asked University Planning Committee to see how they can solve this problem. Based on traffic projections, Dr. Starr would like to have sufficient capacity so that 35,000 cars per hour can be accommodated to travel from the newly-built stadium to the interstate highway. Anticipating this problem, some of the current streets leading from the university to the interstate highway were transformed to one-way streets on a temporary basis, since the problem will only occur after the games. This will be done with police officers directing traffic after each game. Alexander Lee, SWU Planning Committee member did a quick check and stated that 33,000 cars per hour can be accommodated according to the road capacity diagram. With node 1 alone, 33,000 cars per hour can pass through, while nodes 2, 3 and 4 is 35,000 cars per hour and the number of cars that can pass by nodes 5, 6 and 7 is much greater than the former. Therefore, he suggests that based on the current capacity, 33,000 cars per hour can be accommodated. He also suggested that they should recommend to the city manager the widening of some of the streets to increase capacity of an additional 2,000 cars per hour. He recommends the road widening based on which ever Path is cheapest. If the city manager opts not to expand the Paths, traffic problems will still be manageable but a nuisance to SWU football game patrons. It is believed, from past experience that as long as street capacity is within 2,500 cars per hour, the problem will not be too severe. However, the problem grows drastically for each additional 1,000 cars is added in the streets.
II.Define the Problem
What can be done to alleviate the traffic problem that is plaguing Southwestern University (SWU)?
1.To determine whether there is a need for the city manager to expand the Paths. 2.To determine which Paths should be expanded to accommodate the projected 35,000 cars per hour that is expected to travel from the stadium to the highway.
IV.Case Facts and Information
A.Current Street Capacities (in 1,000 cars per hour)
V.Present Alternative Choices to Solving the Problem
ACA #1: Do not recommend to the City Manager the Expansion of certain Paths
Considering that the problem will only persist during the game season, this traffic problem is seasonal and road widening may be too expensive in the part of the local government. The revenues that can be earned by SWU may not be enough to cover for the road expansion of the current roads.
ACA #2: Recommend to the City Manager the Expansion of certain Paths
The group will have to see if Mr. Lee’s road capacity estimates are accurate. If not, the group will have to recommend if:
ACA#2 a) All roads should be widened for maximum easy traffic flow ACA#2 b) Identify only critical roads should be widened for maximum traffic flow VI.Discuss Quantitative methods employed and the solution to the problem
The group will employ maximal-flow technique, to find the most number of cars per hour can flow thru the roads that lead from the SWU stadium to the Interstate Highway.
A.Maximal Flow Computation of Current Capacity
By arbitrarily picking the first path from the top, Path 1 which is comprised of Nodes 1, 2, 5 and 8, 12,000 cars can flow because of nodes 2 to 5. By repeating the steps, Path 2 (Nodes 1, 3, 6 and 8) will result to 6,000 cars; Path 3 (Nodes 1, 4, 6, 7 and 8) will allow the flow of 5,000 cars; Path 4 (Nodes 1, 3, 5 and 8) will produce 4,000 cars and lastly, Path...