Introduction
Southwestern University (SWU) has recently seen an increase in interest in its football program due to the hiring of one of the most notable football coaches on the team. This has increased ticket sales for football games and interest in the football program. Assuming a city will not allow a new road to be built, the traffic situation is expected to be a nuisance but controllable. For this reason, SWU’s President Marty Starr has requested that the University Planning Committee study these traffic difficulties (Su et al., 2021). Mr. Starr came up with the following solutions based on traffic projections: first, a plan that can handle at least 35,000 cars per hour traveling from the stadium to the interstate highway. Secondly, there is a need for an increase in the width of several roads heading from the institution to the interstate. The advice of university planner Alexander Lee indicated the current street capacity to be 33,000 cars per hour. The development of one of the most cost-effective routes from the stadium to Interstate 80 was recommended, allowing an additional 2,000 cars per hour.
Problem Statement
The traffic issue at Southwestern University does not seem to be of significant concern, given that the street’s capacity can accommodate 2,500 cars per hour. In addition, the severity of the situation will increase by one percent for every thousand additional cars on the road (Render et al., 2017). As a result, the University Planning Committee is projecting increasing traffic in the forthcoming football season. The main requirement for both questions in the assignment is that, for the situation to be feasible, incoming cars at any node must be less than the sum of existing cars on that road, leading to the development of solutions.
Objectives of the Case Study
The first objective of this case study is to determine the maximum number of cars traveling from the stadium to the interstate per hour, especially if there is no expansion. In addition, it aims to compare the number of these cars with the 33,000 cars suggested by Dr. Lee. Secondly, the case study is to establish whether an expansion of cars is recommended for an increased capacity of up to 33,000 while determining the streets recommended for such expansion for a total capacity of 35,000 cars per hour.
The Selected Solution
Using the shortest-route problem is a justifiable answer to Southwestern University’s traffic issues. The goal of the shortest-route problem is to discover the shortest distance between two points (Sano & Sianipar, 2021). Finding the shortest path between the network is a typical application of this technique. The problem can be solved using a linear program with 0 and 1 variables or a customized approach provided in Module 8.
Question 1
The stadium to the interstate can accommodate up to 28000 cars per hour. The 33,000 Dr. Lee indicated is the maximum number of cars that pathways 1, 2, 3, and 4 can accommodate. This does not represent the maximum flow or quantity of cars that can move from the stadium to the interstate in an hour. This statistic is not equivalent to 33,000 as Dr. Lee claimed, because he offered an average value based on the assumption that more cars would pass through nodes 5, 6, and 7 than the 35,000 cars that passed through nodes 1, 2, 3, and 4.
Not every outflow can utilize the nodes to their utmost potential, and not every succeeding node has the same capabilities as a preceding node. This is due to Dr. Lee’s advice, which neglected nodes 2, 3, and 4, among others, in favor of focusing exclusively on the number of cars that might leave the stadium via the three routes. Nodes, where the number of cars entering must be less than or equal to the number of cars leaving, are prohibited from becoming congested (Su et al., 2021). In contrast to routes 1-2, which can accommodate 12,000 cars, route 2-5 can accommodate the same number of cars. Therefore, the maximum hourly car speed is 28,000 as shown in the diagram below;
Question 2
I would advise expanding nodes 1-4 and 5-8 to raise the capacity to 33,000 if the cost of doing so were the same for each street. I would switch nodes 1-4, 5-8, and nodes 4-7 to raise capacity to 35,000. Streets 2-5 and 5-8 should be widened to accommodate 33000 cars per hour. This is due to the 33000 cars per hour of traffic that must fit in the 15000 cars from lanes 1-2, and the bottleneck lanes 2-5 and 5-6 as shown in the following table.
To reach a capacity of 33,000, I advise increasing nodes 1 through 4 and 5 through 8 if the cost of doing so were the same for each street. Nodes 1-4, 5 -8, and nodes 4 -7 would be changed to reach a capacity of 35,000. Streets 1-4 must be expanded to make capacity 8 for 35000/hour, in addition to 2-5 and 5-7 in the prior issue as shown in the table below;
Conclusion and Recommendation
The traffic issue is caused by a disparity between the capacity going into and out of the stadium. The 8th iteration of the route is the optimal choice when there are 28,000 cars in total traffic. It is recommended that management consider the possibility of adding additional units to the different clusters. Since the maximum outflow is only 28,000, it is necessary to add at least 5000 more units to make it 33,000. The University Committee should consider the expansion of roads on the path from the stadium to the interstate, especially streets with a potential for high vehicle volumes, to find the best solution to prepare for anticipated traffic from the upcoming football game. Rather than having numerous routes before they can exit in the recommendation, it is preferable to extend the capacity of roads by a minimal amount at a minimal route. The widening of roads will benefit the institution and the community in the long run.
References
Render, B., Stair, R. M., Hanna, M. E., & Hale, T. S. (2017). Quantitative analysis for management.13th Edition. Web.
Sano, V. D., & Sianipar, P. (2021). Algorithm to Find Tourism Place Shortest Route: A Systematic Literature Review.Journal of Theoretical and Applied Information Technology, 99(4). Web.
Su, Y., Huang, L., Liu, H., Chen, S., & Peng, L. (2021). The Effect of Exercise Intervention on Disability and Kinesiophobia in a Retired Athlete with Old Patella Fracture: A Case Report.Frontiers in Psychology, 12. Web.