Purpose - Finding an optimal path is an essential component for the design and operation of smart transportation or logistics network. Many applications in navigation system assume that travel time of each link is fixed and same. However, in practice, the travel time of each link changes over time. In this paper, we introduce a new transportation problem to find a latest departing time and delivery path between the two nodes, while not violating the appointed time at the destination node. Research design, data, and methodology - To solve the problem, we suggest a mathematical model based on network optimization theory and a backward search method to find an optimal solution. Results - First, we introduce a dynamic transportation problem which is different with traditional shortest path or minimum cost path. Second, we propose an algorithm solution based on backward search to solve the problem in a large-sized network. Conclusions - We proposed a new transportation problem which is different with traditional shortest path or minimum cost path. We analyzed the problem under the conditions that travel time is changing, and proposed an algorithm to solve them. Extending our models for visiting two or more destinations is one of the further research topics.
Abbasi, S., & Ebrahimnejad, S. (2011). Finding the Shortest Path in Dynamic Network using Labeling Algorithm. International Journal of Business and Social Science, 2(20), 239-243.
Ahuja, R. K., Magnanti, T. L.., & Orlin, J. B. (1993).Network Flows: Theory, Algorithms, and Applications. Englewood Cliffs, New Jersey: Prentice Hall.
Amrapali, D., Kale, K. V., & Yogesh, G. (2015). Network Analysis for Finding Shortest Pathin Hospital Information System. IJARCSSE, 5(7), 618-623.
Brian, D. (2004). Introduction Algorithms for Minimum-Cost Paths in Time-Dependent Networks with Waiting Policies. Networks, 44(1), 41-46.
Dijkstra, E. W. (1959). A Note on Two Problems in Connection with Graphs. Numerische Mathematic, 1, 269-271.
Dewen, S., Meixia, T., Wu, H., Fang, X., & Xu, H. (2014). Multiple Constrained Dynamic Path Optimization based on Improved Ant Colony Algorithm. IJUNESST, 7(6), 117-130.
Dreyfus, S. E. (1969). AnAppraisal of Some Shortest Path Algorithms. Operations Research, 17(3), 395–412.
El-Sherbeny, N. A. (2014). The Algorithm of the Time-Dependent Shortest Path Problem with Time Windows. Applied Mathematics, 5, 2764-2770.
Horst, W. H., Stefan, R., & Stevanus, A. T. (2006). Algorithms for Time-Dependent Bicriteria Shortest Path Problems. Discrete Optimization, 3, 238–254.
Jiang, J., & Wub, L. (2014). Dynamic Navigation Algorithm Considering Network Disruptions. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, XL-4, 111-115.
Low, S.P., & Gao, L. (2011). The Application of the Just-in-Time Philosophy in the Chinese Construction Industry. Journal of Construction in Developing Country, 16(1), 91-111.
Maurizio, B., Alberto C., Federico, L., & Alessandro, L. (2014). A Multi-Objective Time-Dependent Route Planner: a Real World Application to Milano city. Transportation Research Procedia, 3, 460- 469.
Nejad, M., Mashayekhy, L., Chinnam, R., & Phillips, A. ( 2 0 1 6 ) . Hierarchical Time-DependentShortestPathAlgorithms for Vehicle Routing under ITS. IIE Transactions, 48(2), 158-169.
Orda, A., & Rom, R. (1990). Shortest-path and Minimum Delay Algorithms in Networks with Time-dependent Edge-length. Journal of the ACM, 37(3), 607–625.
Sherali, H. D., Ozbay, K., & Subramanian, S. (1998). The Time-Dependent Shortest Pair of Disjoint Paths Problem:Complexity, models, and algorithms. Networks, 31(4), 259–272.
Shuai, Z., & Chao, M. (2012), Model and Heuristics for the Heterogeneous Fixed Fleet Vehicle Routing Problem with Pick-Up and Delivery. Journal of Distribution Science, 10(12), 19-24.
Song, J. G., & Kim, T. R. (2012).The Performance Formation Model of Service Quality Factors for Courier Service. Journal of Distribution Science, 10(4), 37-45.
Yajun, Y., Hong, G., Jeffrey, X., & Jianzhong, L. (2014). Finding the Cost Optimal Path with Time Constraint over Time Dependent Graphs. The Proceedings of the VLDB Endowment (PVLDB), 7(9), 673-684.