Finding K shortest looping paths with waiting time in a time–window network

• Published in: Applied mathematical modelling Vol. 30; no. 5; pp. 458 - 465
• Main Authors: Yang, Hsu-Hao, Chen, Yen-Liang
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.05.2006; Elsevier Science
• Subjects: Applied sciences; Exact sciences and technology; Operational research. Management science; Shortest looping path; Time–window; Time–window; Shortest looping path; Time window; Algorithm complexity; Shortest path; Time-window; Polynomial method; Time complexity; Waiting time; Polynomial time
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2005.05.005

A time-constrained shortest path problem is a shortest path problem including time constraints that are commonly modeled by the form of time windows. Finding K shortest paths are suitable for the problem associated with constraints that are difficult to define or optimize simultaneously. Depending on the types of constraints, these K paths are generally classified into either simple paths or looping paths. In the presence of time–window constraints, waiting time occurs but is largely ignored. Given a network with such constraints, the contribution of this paper is to develop a polynomial time algorithm that finds the first K shortest looping paths including waiting time. The time complexity of the algorithm is O( rK 2| V 1| 3), where r is the number of different windows of a node and | V 1| is the number of nodes in the original network.