Abstract
Recently, taking more than one means of transportation to work or to deliver goods has become common for citizens in big cities or logistics companies. A transport system that contains various transport means is called a multimodal transport system. In each route, there is carrier: airline, railway or bus company who has contracted to carry passengers with a specific schedule. As each carrier may have other customers, the number of passengers that it can serve is stochastic. Hence, this study formulates a stochastic multimodal transport network (SMTN) to model a multimodal transport system. The transfer time and fee are necessary when changing the means of transportation. This study proposes a complete algorithm to evaluate the reliability of the SMTN that is the probability that the requested number of passengers can be sent successfully from the origin to the destination under time and budget constraints. Since time and budget are the passengers considered most before traveling, the reliability in this study evaluates the SMTN regarding meeting travel demand and passengers’ requirements simultaneously. A case study of a travel agent is presented to demonstrate the solution procedure.






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References
Alexopoulos, C. (1995). A note on state-space decomposition methods for analyzing stochastic flow networks. IEEE Transactions on Reliability, 44(2), 354–357. https://doi.org/10.1109/24.387394.
Bai, G., Tian, Z., & Zuo, M. J. (2016). An improved algorithm for finding all minimal paths in a network. Reliability Engineering & System Safety, 150, 1–10. https://doi.org/10.1016/j.ress.2016.01.011.
Boujelbene, Y., & Derbel, A. (2015). The performance analysis of public transport operators in Tunisia using AHP method. Procedia Computer Science, 73, 498–508. https://doi.org/10.1016/j.procs.2015.12.039.
Djurhuus, S., Hansen, H. S., Aadahl, M., & Glümer, C. (2016). Building a multimodal network and determining individual accessibility by public transportation. Environment and Planning B: Planning and Design, 43(1), 210–227. https://doi.org/10.1177/0265813515602594.
Dock, S., Westrom, R., Lee, K., & Cesme, B. (2017). Advancing urban multimodal transportation system performance management. Transportation Research Record, 2646(1), 17–27. https://doi.org/10.3141/2646-03.
Forghani-elahabad, M., & Mahdavi-Amiri, N. (2016). An improved algorithm for finding all upper boundary points in a stochastic-flow network. Applied Mathematical Modelling, 40(4), 3221–3229. https://doi.org/10.1016/j.apm.2015.10.004.
Hassan, M. R. (2015). Solving a component assignment problem for a stochastic flow network under lead-time constraint. Indian Journal of Science and Technology, 8(35), 1–5. https://doi.org/10.17485/ijst/2015/v8i35/70455.
Huisheng, G., & Jingyu, Z. (2012). An improved algorithm of network reliability based on pathset and Boolean operation. In Symposium on ICT and energy efficiency and workshop on information theory and security (CIICT 2012), 4–5 July 2012 (pp. 189–193). https://doi.org/10.1049/cp.2012.1889.
Ila, M., & Mentzer, J. T. (2008). Global supply chain risk management strategies. International Journal of Physical Distribution & Logistics Management, 38(3), 192–223. https://doi.org/10.1108/09600030810866986.
Jane, C.-C., & Laih, Y.-W. (2012). Evaluating cost and reliability integrated performance of stochastic logistics systems. Naval Research Logistics (NRL), 59(7), 577–586. https://doi.org/10.1002/nav.21507.
Kim, S., Park, M., & Lee, C. (2013). Multimodal freight transportation network design problem for reduction of greenhouse gas emissions. Transportation Research Record, 2340(1), 74–83. https://doi.org/10.3141/2340-09.
Kos, S., Šamija, S., & Brčić, D. (2012). Multimodal transport in the function of the port system containerization development. In International conference on transport science.
Krygsman, S., Dijst, M., & Arentze, T. (2004). Multimodal public transport: An analysis of travel time elements and the interconnectivity ratio. Transport Policy, 11(3), 265–275. https://doi.org/10.1016/j.tranpol.2003.12.001.
Kumar, P. P., Parida, M., & Swami, M. (2013). Performance evaluation of multimodal transportation systems. Procedia - Social and Behavioral Sciences, 104, 795–804. https://doi.org/10.1016/j.sbspro.2013.11.174.
Lin, Y.-K. (2001). A simple algorithm for reliability evaluation of a stochastic-flow network with node failure. Computers & Operations Research, 28(13), 1277–1285. https://doi.org/10.1016/S0305-0548(00)00039-3.
Lin, Y.-K. (2004). Reliability of a stochastic-flow network with unreliable branches & nodes, under budget constraints. IEEE Transactions on Reliability, 53(3), 381–387. https://doi.org/10.1109/TR.2004.833315.
Lin, Y.-K. (2010). System reliability of a stochastic-flow network through two minimal paths under time threshold. International Journal of Production Economics, 124(2), 382–387. https://doi.org/10.1016/j.ijpe.2009.11.033.
Lin, Y.-K., & Chen, S.-G. (2017). A maximal flow method to search for d-MPs in stochastic-flow networks. Journal of Computational Science, 22, 119–125. https://doi.org/10.1016/j.jocs.2017.09.009.
Lin, Y.-K., & Huang, C.-F. (2013). Assessing reliability within error rate and time constraint for a stochastic node-imperfect computer network. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 227(1), 80–85. https://doi.org/10.1177/1748006X12468685.
Lin, Y.-K., & Nguyen, T.-P. (2018). Reliability evaluation of a multistate flight network under time and stopover constraints. Computers & Industrial Engineering, 115, 620–630. https://doi.org/10.1016/j.cie.2017.12.016.
Lin, Y.-K., Yeh, C.-T., & Huang, C.-F. (2013). Reliability evaluation of a stochastic-flow distribution network with delivery spoilage. Computer and Industrial Engineering, 66(2), 352–359. https://doi.org/10.1016/j.cie.2013.06.019.
McCann, P. (2008). Globalization and economic geography: The world is curved, not flat. Cambridge Journal of Regions, Economy and Society, 1(3), 351–370. https://doi.org/10.1093/cjres/rsn002.
Mishra, S., Welch, T. F., & Jha, M. K. (2012). Performance indicators for public transit connectivity in multi-modal transportation networks. Transportation Research Part A: Policy and Practice, 46(7), 1066–1085. https://doi.org/10.1016/j.tra.2012.04.006.
Mishra, S., Welch, T. F., Torrens, P. M., et al. (2015). A tool for measuring and visualizing connectivity of transit stop, route and transfer center in a multimodal transportation network. Public Transport, 7(1), 77–99. https://doi.org/10.1007/s12469-014-0091-2.
Pan, Y., Li, X., Zhang, M., Zhou, M., & Duan, Y. (2017). Multimodal transportation network optimization with environmental and economic performance considered: An ongoing research. Paper presented at the 2017 international conference on service systems and service management.
Wang, Y., & Yeo, G.-T. (2016). A study on international multimodal transport networks from Korea to Central Asia: Focus on secondhand vehicles. The Asian Journal of Shipping and Logistics, 32(1), 41–47. https://doi.org/10.1016/j.ajsl.2016.03.005.
Yeh, W.-C. (2001). A simple algorithm to search for all d-MPs with unreliable nodes. Reliability Engineering & System Safety, 73(1), 49–54. https://doi.org/10.1016/S0951-8320(01)00032-1.
Yeh, W.-C. (2002). Search for minimal paths in modified networks. Reliability Engineering & System Safety, 75(3), 389–395. https://doi.org/10.1016/S0951-8320(01)00128-4.
Yeh, C.-T., Lin, Y.-K., & Yang, J.-Y. (2017). Network reliability maximization for stochastic-flow network subject to correlated failures using genetic algorithm and tabu search. Engineering Optimization. https://doi.org/10.1080/0305215X.2017.1353089.
Zuo, M. J., Tian, Z., & Huang, H.-Z. (2007). An efficient method for reliability evaluation of multistate networks given all minimal path vectors. IIE Transactions, 39(8), 811–817. https://doi.org/10.1080/07408170601013653.
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Lin, YK., Nguyen, TP. & Yeng, L.CL. Reliability evaluation of a stochastic multimodal transport network under time and budget considerations. Ann Oper Res 312, 369–387 (2022). https://doi.org/10.1007/s10479-019-03215-0
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DOI: https://doi.org/10.1007/s10479-019-03215-0