A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph

Bo Xu (), Xiaodong Ji and Zhengrong Cheng
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Bo Xu: Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
Xiaodong Ji: School of Management, Shanghai University of Engineering Science, Shanghai 201620, China
Zhengrong Cheng: School of Business Information, Shanghai Business School, Shanghai 201499, China

Mathematics, 2025, vol. 13, issue 1, 1-18

Abstract: The Dynamic Interval (DI) graph models the updating uncertainty of the arc cost in the graph, which shows great application prospects in unstable-road transportation planning and management. This paper studies the Real-time Shortest Path (RTSP) problems in the DI graph. First, the RTSP problem is defined in mathematical equations. Second, three models for RTSP are proposed, which are the Dynamic Robust Shortest Path (DRSP) model, the Dynamic Greedy Robust Shortest Path (DGRSP) model and the Dynamic Mean Shortest Path (DMSP) model. Then, three solution methods are designed. Finally, a numerical study is conducted to compare the efficiency of the models and corresponding solution methods. It shows that the DGRSP model and DMSP model generally present better results than the others. In the real road network test, they have the minimum average-regret-ratio of DGSP 7.8% and DMSP 7.1%; while in the generated network test, they both have a minimum average-regret-ratio of 0.5%.

Keywords: dynamic interval graph; real-time shortest path; nested Dijkstra algorithm; dynamic vehicle routing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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