Delays in international multimodal marine transport can result in subsequent connection delays, leading to prolonged transportation time and increased uncertainty. To identify more reliable and cost-effective robust transportation routes, this study establishes a constrained planning model for multimodal transportation routes. Employing uncertainty theory, the model is transformed into a deterministic equivalent class model and ultimately incorporates an adaptive differential evolution (ADE) algorithm. Results of a case study indicate that: (i) the proposed model, compared with deterministic models, exhibits greater robustness and better aligns with practical transportation scenarios, resulting in substantial reductions in actual transportation time and cost; (ii) the solution efficiency of the ADE algorithm surpasses that of the genetic algorithm and Dijkstra algorithm; (iii) the start time of transportation and the confidence level of uncertainty also play crucial roles in influencing route selection. Therefore, decision-makers should consider a multifaceted approach when formulating transportation routes.
UdomwannakhetJ.VajarodayaP.ManichoS.KaewfakK.RuizJ. B.AmmarapalaV.A Review of Multimodal Transportation Optimization Model. Proc., 2018 5th International Conference on Business and Industrial Research (ICBIR), Bangkok, Thailand, IEEE, New York, 2018, pp. 333–338.
2.
LvB.YangB.ZhuX.LiJ.Operational Optimization of Transit Consolidation in Multimodal Transport. Computers & Industrial Engineering, Vol. 129, 2019, pp. 454–464.
3.
TsangY. P.WuC.-H.LamH. Y.ChoyK. L.HoG. T. S.Integrating Internet of Things and Multi-Temperature Delivery Planning for Perishable Food E-Commerce Logistics: A Model and Application. International Journal of Production Research, Vol. 59, No. 5, 2021, pp. 1534–1556.
4.
CavoneG.DotoliM.SeatzuC.A Survey on Petri Net Models for Freight Logistics and Transportation Systems. IEEE Transactions on Intelligent Transportation Systems, Vol. 19, No. 6, 2017, pp. 1795–1813.
5.
ZhaoJ.ZhuX.WangL.Study on Scheme of Outbound Railway Container Organization in Rail-Water Intermodal Transportation. Sustainability, Vol. 12, No. 4, 2020, p. 1519.
6.
RossiT.PozziR.PirovanoG.CigoliniR.PeroM.A New Logistics Model for Increasing Economic Sustainability of Perishable Food Supply Chains Through Intermodal Transportation. International Journal of Logistics Research and Applications, Vol. 24, No. 4, 2021, pp. 346–363.
7.
LiuS.Multimodal Transportation Route Optimization of Cold Chain Container in Time-Varying Network Considering Carbon Emissions. Sustainability, Vol. 15, No. 5, 2023, p. 4435.
8.
ZiaeiZ.JabbarzadehA.A Multi-Objective Robust Optimization Approach for Green Location-Routing Planning of Multi-Modal Transportation Systems Under Uncertainty. Journal of Cleaner Production, Vol. 291, 2021, p. 125293.
9.
DibO.ManierM.-A.CaminadaA.Memetic Algorithm for Computing Shortest Paths in Multimodal Transportation Networks. Transportation Research Procedia, Vol. 10, 2015, pp. 745–755.
10.
IdriA.OukarfiM.BoulmakoulA.ZeitouniK.MasriA.A New Time-Dependent Shortest Path Algorithm for Multimodal Transportation Network. Procedia Computer Science, Vol. 109, 2017, pp. 692–697.
11.
BożejkoW.GryminR.PemperaJ.Scheduling and Routing Algorithms for Rail Freight Transportation. Procedia Engineering, Vol. 178, 2017, pp. 206–212.
12.
GräbenerT.BerroA.DuthenY.Time Dependent Multiobjective Best Path for Multimodal Urban Routing. Electronic Notes in Discrete Mathematics, Vol. 36, 2010, pp. 487–494.
13.
XiaoH.GongH.WangX.HangB.Routes Choice in the International Intermodal Networks Under the Soft Time Window. Wireless Communications and Mobile Computing, Vol. 2022, 2022. https://doi.org/10.1155/2022/3355883.
14.
MnifM.BouamamaS.Firework Algorithm for Multi-Objective Optimization of a Multimodal Transportation Network Problem. Procedia Computer Science, Vol. 112, 2017, pp. 1670–1682.
15.
ZhangX.JinF.-Y.YuanX.-M.ZhangH.-Y.Low-Carbon Multimodal Transportation Path Optimization Under Dual Uncertainty of Demand and Time. Sustainability, Vol. 13, No. 15, 2021, p. 8180.
16.
XuW.RongM.Research on Optimization of Expressway Logistics Path Based on the Advantages of Multimodal Transport in the Environment of Internet of Things. Wireless Personal Communications, Vol. 126, No. 3, 2022, pp. 1981–1997.
17.
BastH.DellingD.GoldbergA.Müller-HannemannM.PajorT.SandersP.WagnerD.WerneckR. F.Route Planning in Transportation Networks. In Algorithm Engineering: Selected Results and Surveys (L.KliemannSandersP., eds.), Springer, Cham, 2016, pp. 19–80.
18.
CrainicT. G.KimK. H.Intermodal Transportation. Handbooks in Operations Research and Management Science, Vol. 14, 2007, pp. 467–537.
19.
DemeyerS.AudenaertP.PickavetM.DemeesterP.Dynamic and Stochastic Routing for Multimodal Transportation Systems. IET Intelligent Transport Systems, Vol. 8, No. 2, 2014, pp. 112–123.
20.
FagerholtK.Ship Scheduling with Soft Time Windows: An Optimisation Based Approach. European Journal of Operational Research, Vol. 131, No. 3, 2001, pp. 559–571.
21.
BalakrishnanN.Simple Heuristics for the Vehicle Routeing Problem with Soft Time Windows. Journal of the Operational Research Society, Vol. 44, No. 3, 1993, pp. 279–287.
22.
HulmeP. E.Trade, Transport and Trouble: Managing Invasive Species Pathways in an Era of Globalization. Journal of Applied Ecology, Vol. 46, No. 1, 2009, pp. 10–18.
23.
SaranenJ.Intermodal Transportation in Emergency Situations in the Gulf of Finland. Technical Report, Research Report 223. Department of Industrial Management, Lappeenranta University of Technology, Finland, 2010.
24.
PlomaritouE.JeropoulosS.The Digitalisation in Chartering Business: Special Reference to the Role of E-Bill of Lading in the Bulk and Liner Markets. Journal of Shipping and Trade, Vol. 7, No. 1, 2022, pp. 1–22.
25.
ShinS.-H.LeeP. T.-W.LeeS.-W.Lessons from Bankruptcy of Hanjin Shipping Company in Chartering. Maritime Policy & Management, Vol. 46, No. 2, 2019, pp. 136–155.
26.
Okurİ. G.TunaO.Schedule Reliability in Liner Shipping: A Study on Global Shipping Lines. Pomorstvo, Vol. 36, No. 2, 2022, pp. 389–400.
27.
LiuJ.QiY.LyuW.Port Resilience in the Post-COVID-19 Era. Ocean & Coastal Management, Vol. 238, 2023, p. 106565.
28.
GhilasV.DemirE.Van WoenselT.A Scenario-Based Planning for the Pickup and Delivery Problem with Time Windows, Scheduled Lines and Stochastic Demands. Transportation Research Part B: Methodological, Vol. 91, 2016, pp. 34–51.
29.
XieS.HuZ.WangJ.Two-Stage Robust Optimization for Expansion Planning of Active Distribution Systems Coupled with Urban Transportation Networks. Applied Energy, Vol. 261, 2020, p. 114412.
30.
CadarsoL., and Á. Marín. Combining Robustness and Recovery in Rapid Transit Network Design. Transportmetrica A: Transport Science, Vol. 12, No. 3, 2016, pp. 203–229.
31.
BagloeeS. A.SarviM.WolshonB.DixitV.Identifying Critical Disruption Scenarios and a Global Robustness Index Tailored to Real Life Road Networks. Transportation Research Part E: Logistics and Transportation Review, Vol. 98, 2017, pp. 60–81.
32.
XieS.HuZ.WangJ.Scenario-Based Comprehensive Expansion Planning Model for a Coupled Transportation and Active Distribution System. Applied Energy, Vol. 255, 2019, p. 113782.
33.
XieS.HuZ.ZhouD.LiY.KongS.LinW.ZhengY.Multi-Objective Active Distribution Networks Expansion Planning by Scenario-Based Stochastic Programming Considering Uncertain and Random Weight of Network. Applied Energy, Vol. 219, 2018, pp. 207–225.
34.
BalcikB.Yanıkoğluİ.A Robust Optimization Approach for Humanitarian Needs Assessment Planning Under Travel Time Uncertainty. European Journal of Operational Research, Vol. 282, No. 1, 2020, pp. 40–57.
35.
SchifferM.WaltherG.Strategic Planning of Electric Logistics Fleet Networks: A Robust Location-Routing Approach. Omega, Vol. 80, 2018, pp. 31–42.
36.
GuoW.AtasoyB.Beelaerts van BloklandW.NegenbornR. R.Dynamic and Stochastic Shipment Matching Problem in Multimodal Transportation. Transportation Research Record: Journal of the Transportation Research Board, 2020. 2674: 262–273.
37.
SunY.LiangX.LiX.ZhangC.A Fuzzy Programming Method for Modeling Demand Uncertainty in the Capacitated Road–Rail Multimodal Routing Problem with Time Windows. Symmetry, Vol. 11, No. 1, 2019, p. 91.
ZhangG.ShangJ.LiW.Collaborative Production Planning of Supply Chain Under Price and Demand Uncertainty. European Journal of Operational Research, Vol. 215, No. 3, 2011, pp. 590–603.
40.
KennéJ.-P.DejaxP.GharbiA.Production Planning of a Hybrid Manufacturing–Remanufacturing System Under Uncertainty Within a Closed-Loop Supply Chain. International Journal of Production Economics, Vol. 135, No. 1, 2012, pp. 81–93.
41.
HanB.RenS.Optimizing Stop Plan and Tickets Allocation for High-Speed Railway Based on Uncertainty Theory. Soft Computing, Vol. 24, 2020, pp. 6467–6482.
42.
ZhangB.PengJ.LiS.ChenL.Fixed Charge Solid Transportation Problem in Uncertain Environment and Its Algorithm. Computers & Industrial Engineering, Vol. 102, 2016, pp. 186–197.
43.
GaoY.Shortest Path Problem with Uncertain Arc Lengths. Computers & Mathematics with Applications, Vol. 62, No. 6, 2011, pp. 2591–2600.
44.
GaoY.Uncertain Models for Single Facility Location Problems on Networks. Applied Mathematical Modelling, Vol. 36, No. 6, 2012, pp. 2592–2599.
45.
NiuF.QiJ. G.QinJ.Optimization Model for Train Stopping Plan on High-Speed Railway Corridor with Uncertain Passenger Demands. Journal of the China Railway Society, Vol. 38, No. 7, 2016, pp. 1–7.
46.
LiuY. H.HaM.Expected Value of Function of Uncertain Variables. Journal of Uncertain Systems, Vol. 4, No. 3, 2010, pp. 181–186.
47.
QinZ.KarS.Single-Period Inventory Problem Under Uncertain Environment. Applied Mathematics and Computation, Vol. 219, No. 18, 2013, pp. 9630–9638.
48.
ChenX.LiuY.RalescuD. A.Uncertain Stock Model with Periodic Dividends. Fuzzy Optimization and Decision Making, Vol. 12, 2013, pp. 111–123.
49.
YangL.ZhangY.LiS.GaoY.A Two-Stage Stochastic Optimization Model for the Transfer Activity Choice in Metro Networks. Transportation Research Part B: Methodological, Vol. 83, 2016, pp. 271–297.
50.
YaoK.GaoJ.Uncertain Random Alternating Renewal Process with Application to Interval Availability. IEEE Transactions on Fuzzy Systems, Vol. 23, No. 5, 2014, pp. 1333–1342.
51.
DaiM. D. M.SchonfeldP.Metamodels for Estimating Waterway Delays Through Series of Queues. Transportation Research Part B: Methodological, Vol. 32, No. 1, 1998, pp. 1–19.
52.
LozanoA.StorchiG.Shortest Viable Path Algorithm in Multimodal Networks. Transportation Research Part A: Policy and Practice, Vol. 35, No. 3, 2001, pp. 225–241.
53.
AssadipourG.KeG. Y.VermaM.A Toll-Based Bi-Level Programming Approach to Managing Hazardous Materials Shipments over an Intermodal Transportation Network. Transportation Research Part D: Transport and Environment, Vol. 47, 2016, pp. 208–221.
54.
StornR.PriceK.Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization, Vol. 11, 1997, pp. 341–359.
OparaK. R.ArabasJ.Differential Evolution: A Survey of Theoretical Analyses. Swarm and Evolutionary Computation, Vol. 44, 2019, pp. 546–558.
57.
ElaalemM.ComberA.FisherP.A Comparison of Fuzzy AHP and Ideal Point Methods for Evaluating Land Suitability. Transactions in GIS, Vol. 15, No. 3, 2011, pp. 329–346.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
