scholarly journals A Comparison of Algorithms for Finding an Efficient Theme Park Tour

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Elizabeth L. Bouzarth ◽  
Richard J. Forrester ◽  
Kevin R. Hutson ◽  
Rahul Isaac ◽  
James Midkiff ◽  
...  
Keyword(s):  
Mixed Integer Linear Programming ◽  
Search Algorithm ◽  
Computational Study ◽  
Branch And Cut ◽  
Time Dependent ◽  
Mixed Integer ◽  
Theme Park ◽  
Linear Programming Formulation ◽  
The Traveling Salesman Problem ◽  
Integer Linear Programming Formulation

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.

scholarly journals A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Yujian Song ◽  
Ming Xue ◽  
Changhua Hua ◽  
Wanli Wang
Keyword(s):  
Column Generation ◽  
Mixed Integer Linear Programming ◽  
Parallel Machines ◽  
Set Partitioning ◽  
Mixed Integer ◽  
Order Acceptance ◽  
Generation Algorithm ◽  
Order Acceptance And Scheduling ◽  
Linear Programming Formulation ◽  
Integer Linear Programming Formulation

In this paper, we investigate the resource-constrained order acceptance and scheduling on unrelated parallel machines that arise in make-to-order systems. The objective of this problem is to simultaneously select a subset of orders to be processed and schedule the accepted orders on unrelated machines in such a way that the resources are not overutilized at any time. We first propose two formulations for the problem: mixed integer linear programming formulation and set partitioning. In view of the complexity of the problem, we then develop a column generation approach based on the set partitioning formulation. In the proposed column generation approach, a differential evolution algorithm is designed to solve subproblems efficiently. Extensive numerical experiments on different-sized instances are conducted, and the results demonstrate that the proposed column generation algorithm reports optimal or near-optimal solutions that are evidently better than the solutions obtained by solving the mixed integer linear programming formulation.

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