Prof. Dennis Berino
April 3, 2012
Southwestern University Traffic Problems
Bullen, Nino Joseph
Donato, Anna Rica
Southwestern University is experiencing an increased interest in its football program since it hired a big-name coach. As such, there have been increased sales in their season tickets. This increase in sales has also increased the traffic problem of the town which is also projected to get worst once the new stadium is build. To solve the problem, the Marty Starr the University’s president has asked the University Planning Committee to solve the problem. Based on the traffic projections that the University has made, it was concluded by Dr. Starr that the roads leading to the interstate highway from the stadium should have a sufficient capacity of 35,000 cars per hour. In order to solve the problem, the Planning Committee is looking at widening some of the current streets from the stadium to the interstate highway to increase its current capacity.
The main problem of the case is: How to maximize the traffic flow in order to accommodate 35,000 cars per hour from the stadium to the interstate highway?
The sub-problems that needs to answered are:
1. What is the maximum number of cars that may actually travel from the stadium to the interstate per hour? Why is this number not equal to 33,000, as Dr. Lee suggested? 2. If the cost for expanding a street were the same for each street, which street(s) would you recommend expanding to increase the capacity to 33,000? Which streets would you recommend expanding to get the total capacity of the system to 35,000 per hour?
The group aims to identify the best traffic flow that can accommodate 35,000 cars per hour from the stadium to the interstate highway.
IV. Case Facts and Information
Due to the projected increase of sales of Southwestern University, it is projected that the streets from the stadium to the interstate highways should have a sufficient capacity of 35,000 cars per hour. The current street capacity from the stadium to the interstate highway is shown in the diagram below: [pic]
The diagram indicates the number of cars (in 1,000s) per hour that a street can accommodate. The diagram shows the following number of cars:
|Node |Number of Cars | |1 |33,000 (15+12+8) | |2, 3, 4 |35,000 (12+8+6+5+4) | |5,6,7 |41,000 (16+7+5+5+8) |
At present, it was noted that the current capacity of the cars that may leave the stadium is only 33,000 cars per hour. It was also stated that if the street capacity is within 2,500 cars per hour then the traffic problem is not too severe. However, every 1,000 cars that is added to the streets, the traffic problem grows dramatically.
V. Alternative Approaches
There are various paths that cars can choose to lead them to the interstate highway from the stadium. The following are the possible paths:
VI. Quantitative Methods
Given that the case involves finding the maximum amount of cars that a street can accommodate from the stadium to the interstate highway, the maximum flow network model was used to analyze the problem.
The table below shows the inputed data in QM for Windows to solve the problem. [pic]
Given the capacities stated in the diagram above, the table below shows that the maximal network flow that the network can accommodate is 28,000 cars per hour from the stadium to the interstate highway. [pic]
Discussion Question 1: If there is no expansion, what is the maximum number of cars that may actually travel from the stadium to the...