The problem of efficiently touring a theme park so as to minimize the amount of time spent in queues is an instance of the Traveling Salesman Problem with Time-Dependent Service Times (TSP-TS). In this paper, we present a mixed-integer linear programming formulation of the TSP-TS and describe a branch-and-cut algorithm based on this model. In addition, we develop a lower bound for the TSP-TS and describe two metaheuristic approaches for obtaining good quality solutions: a genetic algorithm and a tabu search algorithm. Using test instances motivated by actual theme park data, we conduct a computational study to compare the effectiveness of our algorithms.

Bouzarth, Elizabeth L., Richard J. Forrester, Kevin R. Hutson, Rahul Isaac, James Midkiff, Danny Rivers, and Leonard J. Testa. A Comparison of Algorithms for Finding an Efficient Theme Park Tour. Journal of Applied Mathematics (2018): e2453185, 14 pages. https://www.hindawi.com/journals/jam/2018/2453185/

Copyright © 2018 Elizabeth L. Bouzarth et al.
This is an Open Access article distributed under the Creative Commons Attribution License, https://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Open access publication of this article was made possible with grant support from Waidner-Spahr Library distributed through the Dickinson College Research & Development Committee.

Richard Forrester is a professor of Mathematics and Data Analytics at Dickinson College.

Co-author James Midkiff, Dickinson College Class of 2017.

This published version is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit Hindawi's Website. https://www.hindawi.com/journals/jam/2018/2453185/