# Optimum Route and Transport Mode Selection of Multimodal Transport with Time Window under Uncertain Conditions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- To solve the problem of multimodal transport path planning under uncertain environments, a multi-objective fuzzy nonlinear programming model considering mixed-time window constraints is established.
- To make the model solvable, the fuzzy expected value method and the fuzzy chance-constrained programming method are used to de-fuzzify the established multi-objective fuzzy programming model and obtain the deterministic parameters of the model.
- Combining the game theory method with the weighted sum method, a multi-objective optimization method of multimodal transport based on cooperative game theory is proposed. The weights of each objective are dynamically adjusted in the algorithm optimization process through cooperative game theory to obtain the optimal path of multimodal transportation.

## 2. Problem Description and Model Formulation

#### 2.1. Description of Multimodal Transport Path Planning Problem

#### 2.2. Fuzzy Demand Modeling

#### 2.3. Multi-Objective Optimization Modeling of MULTIMODAL Transport

#### 2.3.1. Parameter and Variable Definitions

#### 2.3.2. Multi-Objective Optimization Model Construction Considering Mixed-Time Windows

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

**Assumption**

**4.**

**Assumption**

**5.**

**Assumption**

**6.**

- Model objective function

- 2.
- Model Constraints

## 3. Solution Method

#### 3.1. Model Defuzzification

#### 3.1.1. Defuzzification of the Objective Function

#### 3.1.2. Defuzzification of the Fuzzy Constraint

#### 3.2. Design of Multimodal Transport Route Optimization Algorithm

#### 3.2.1. Dynamic Optimization of Multi-Objective Weights Based on Game Theory Approach

#### 3.2.2. Solving Multimodal Transport Models Based on PSO Optimization

**Step 1:**Minimize each objective separately and obtain the optimal value ${f}_{i,\mathrm{min}}$ and the worst value ${f}_{i,wst}$ for the $i$-th objective.

**Step 2:**Initialize the weights and convert the multi-objective problem to a single-objective problem using the weighted sum method.

**Step 3:**$Z$ in Equation (25) is used as the cost function of the PSO, the current optimal solution is obtained by optimization, and the value of each objective ${f}_{i}$ is recorded.

**Step 4:**The values of each objective obtained from the solution of the optimization algorithm are normalized, and the weights of each objective are dynamically adjusted by the cooperative game theory method using Equation (27).

**Step 5:**Determine whether the termination condition is satisfied (the maximum number of iterations G is reached). If not, return to Step 3 to continue optimization; if yes, obtain the optimal path by comparing all the recorded paths.

## 4. Empirical Case Study

#### 4.1. Case Description

#### 4.2. Result Analysis

#### 4.2.1. Algorithm Validity

**H0**

**(null**

**hypothesis):**

**H1**

**(Alternative**

**hypothesis):**

^{−5}, which is much less than the significance level. Therefore, it means that at a 5% level of significance, we can reject the null hypothesis and conclude that there is a significant difference between the three multi-objective algorithms.

#### 4.2.2. Analysis of the Impact of Uncertainty

- (1)
- When the conditions of time factor are the same, the uncertainty of demand will lead to an increase in transportation cost and carbon emission and have some influence on the transportation time. When the time factors are determined, the cost of Scenario II increases by 39.0%, the carbon emission increases by 34%, and the time decreases by 9.44% compared to Scenario I. When the time factors are uncertain, Scenario IV increases the cost by 8.27%, carbon emission by 5.57%, and time by 1.74% compared to Scenario III.
- (2)
- When the demand factor conditions are the same, the uncertainty of time leads to a slight increase in transportation time and has some impact on transportation costs and carbon emissions. When the demand factors are deterministic, Scenario III increases costs by 7.30%, carbon emissions by 5.82%, and time by 2.85% compared to Scenario I. When the demand factors are uncertain, Scenario IV has 16.42% less cost, 16.66% less carbon emissions, and 14.52% more time than Scenario II.
- (3)
- According to the analysis of the results in (1) and (2), demand uncertainty has a more significant impact on the optimization results of the multimodal transport model. When the time factors are determined, demand uncertainty increases transportation costs and carbon emissions significantly, whereas when the demand factors are determined, time uncertainty increases the transportation time but has insignificant effects on transportation costs and carbon emissions.

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Chen, M.F.; Liu, Y.Q.; Song, Y.; Sun, Q.; Cong, C.C. Multimodal Transport Network Optimization Considering Safety Stock under Real-Time Information. Discret. Dyn. Nat. Soc.
**2019**, 2019, 5480135. [Google Scholar] [CrossRef] [Green Version] - Ji, S.F.; Luo, R.J. A Hybrid Estimation of Distribution Algorithm for Multi-Objective Multi-Sourcing Intermodal Transportation Network Design Problem Considering Carbon Emissions. Sustainability
**2017**, 9, 1133. [Google Scholar] [CrossRef] [Green Version] - Rudi, A.; Fröhling, M.; Zimmer, K.; Schultmann, F. Freight transportation planning considering carbon emissions and in-transit holding costs: A capacitated multi-commodity network flow model. EURO J. Transp. Logist.
**2016**, 5, 123–160. [Google Scholar] [CrossRef] - Tian, W.L.; Cao, C.X. A generalized interval fuzzy mixed integer programming model for a multimodal transportation problem under uncertainty. Eng. Optim.
**2017**, 49, 481–498. [Google Scholar] [CrossRef] - Sun, Y.; Hrusovsky, M.; Zhang, C.; Lang, M.X. A Time-Dependent Fuzzy Programming Approach for the Green Multimodal Routing Problem with Rail Service Capacity Uncertainty and Road Traffic Congestion. Complexity
**2018**, 2018, 8645793. [Google Scholar] [CrossRef] [Green Version] - Ramezani, M.; Bashiri, M.; Tavakkoli-Moghaddam, R. A new multi-objective stochastic model for a forward/reverse logistic network design with responsiveness and quality level. Appl. Math. Model.
**2013**, 37, 328–344. [Google Scholar] [CrossRef] [Green Version] - Sun, Y. Fuzzy Approaches and Simulation-Based Reliability Modeling to Solve a Road-Rail Intermodal Routing Problem with Soft Delivery Time Windows When Demand and Capacity are Uncertain. Int. J. Fuzzy Syst.
**2020**, 22, 2119–2148. [Google Scholar] [CrossRef] - Zarandi, M.H.F.; Hemmati, A.; Davari, S. The multi-depot capacitated location-routing problem with fuzzy travel times. Expert Syst. Appl.
**2011**, 38, 10075–10084. [Google Scholar] [CrossRef] - Baykasoglu, A.; Subulan, K. A fuzzy-stochastic optimization model for the intermodal fleet management problem of an international transportation company. Transp. Plan. Technol.
**2019**, 42, 777–824. [Google Scholar] [CrossRef] - Demir, E.; Burgholzer, W.; Hrušovský, M.; Arıkan, E.; Jammernegg, W.; Van Woensel, T. A green intermodal service network design problem with travel time uncertainty. Transp. Res. Part B Methodol.
**2016**, 93, 789–807. [Google Scholar] [CrossRef] - Zhao, Y.; Liu, R.H.; Zhang, X.; Whiteing, A. A chance-constrained stochastic approach to intermodal container routing problems. PLoS ONE
**2018**, 13, e0192275. [Google Scholar] [CrossRef] - Lu, Y.; Lang, M.; Yu, X.; Li, S. A sustainable multimodal transport system: The two-echelon location-routing problem with consolidation in the Euro–China expressway. Sustainability
**2019**, 11, 5486. [Google Scholar] [CrossRef] [Green Version] - Chen, C.; Demir, E.; Huang, Y. An adaptive large neighborhood search heuristic for the vehicle routing problem with time windows and delivery robots. Eur. J. Oper. Res.
**2021**, 294, 1164–1180. [Google Scholar] [CrossRef] - Zheng, C.J.; Sun, K.; Gu, Y.H.; Shen, J.X.; Du, M.Q. Multimodal Transport Path Selection of Cold Chain Logistics Based on Improved Particle Swarm Optimization Algorithm. J. Adv. Transp.
**2022**, 2022, 5458760. [Google Scholar] [CrossRef] - Zhang, Y.; Hua, G.W.; Cheng, T.C.E.; Zhang, J.L. Cold chain distribution: How to deal with node and arc time windows? Ann. Oper. Res.
**2020**, 291, 1127–1151. [Google Scholar] [CrossRef] - Chang, Y.-T.; Lee, P.T.-W.; Kim, H.-J.; Shin, S.-H. Optimization model for transportation of container cargoes considering short sea shipping and external cost: South Korean case. Transp. Res. Rec.
**2010**, 2166, 99–108. [Google Scholar] [CrossRef] - Vale, C.; Ribeiro, I.M. Intermodal routing model for sustainable transport through multi-objective optimization. In Proceedings of the 2nd EAI International Conference on Intelligent Transport Systems (INTSYS), Guimaraes, Portugal, 21–23 November 2018; pp. 144–154. [Google Scholar] [CrossRef]
- Sun, Y. Green and Reliable Freight Routing Problem in the Road-Rail Intermodal Transportation Network with Uncertain Parameters: A Fuzzy Goal Programming Approach. J. Adv. Transp.
**2020**, 2020, 7570686. [Google Scholar] [CrossRef] [Green Version] - Heinold, A.; Meisel, F. Emission limits and emission allocation schemes in intermodal freight transportation. Transp. Res. Part E-Logist. Transp. Rev.
**2020**, 141, 101963. [Google Scholar] [CrossRef] - Zheng, H.-y.; Wang, L. Reduction of carbon emissions and project makespan by a Pareto-based estimation of distribution algorithm. Int. J. Prod. Econ.
**2015**, 164, 421–432. [Google Scholar] [CrossRef] - Marler, R.T.; Arora, J.S. The weighted sum method for multi-objective optimization: New insights. Struct. Multidiscip. Optim.
**2010**, 41, 853–862. [Google Scholar] [CrossRef] - Majumder, S.; Kar, S.; Pal, T. Mean-entropy model of uncertain portfolio selection problem. In Multi-Objective Optimization: Evolutionary to Hybrid Framework; Springer: Berlin/Heidelberg, Germany, 2018; pp. 25–54. [Google Scholar] [CrossRef]
- Wang, R.; Yang, K.; Yang, L.X.; Gao, Z.Y. Modeling and optimization of a road-rail intermodal transport system under uncertain information. Eng. Appl. Artif. Intell.
**2018**, 72, 423–436. [Google Scholar] [CrossRef] - Li, H.X.; Wang, S.W. Model-based multi-objective predictive scheduling and real-time optimal control of energy systems in zero/low energy buildings using a game theory approach. Autom. Constr.
**2020**, 113, 103139. [Google Scholar] [CrossRef] - Li, X.Y.; Gao, L.; Li, W.D. Application of game theory based hybrid algorithm for multi-objective integrated process planning and scheduling. Expert Syst. Appl.
**2012**, 39, 288–297. [Google Scholar] [CrossRef] - Chen, X.H.; Zuo, T.S.; Lang, M.X.; Li, S.Q.; Li, S.Y. Integrated optimization of transfer station selection and train timetables for road-rail intermodal transport network. Comput. Ind. Eng.
**2022**, 165, 107929. [Google Scholar] [CrossRef] - Peng, Y.; Yong, P.C.; Luo, Y.J. The route problem of multimodal transportation with timetable under uncertainty: Multi-objective robust optimization model and heuristic approach. Rairo-Oper. Res.
**2021**, 55, S3035–S3050. [Google Scholar] [CrossRef] - Marinakis, Y.; Migdalas, A.; Sifaleras, A. A hybrid Particle Swarm Optimization—Variable Neighborhood Search algorithm for Constrained Shortest Path problems. Eur. J. Oper. Res.
**2017**, 261, 819–834. [Google Scholar] [CrossRef] - Deng, L.X.; Chen, H.Y.; Zhang, X.Y.Q.; Liu, H.Y. Three-Dimensional Path Planning of UAV Based on Improved Particle Swarm Optimization. Mathematics
**2023**, 11, 1987. [Google Scholar] [CrossRef] - Singh, N.; Singh, S.B.; Houssein, E.H. Hybridizing salp swarm algorithm with particle swarm optimization algorithm for recent optimization functions. Evol. Intell.
**2022**, 15, 23–56. [Google Scholar] [CrossRef] - Sun, Y.; Zhang, G.; Hong, Z.; Dong, K. How uncertain information on service capacity influences the intermodal routing decision: A fuzzy programming perspective. Information
**2018**, 9, 24. [Google Scholar] [CrossRef] [Green Version] - Yan, S.; Maoxiang, L.; Jiaxi, W. On solving the fuzzy customer information problem in multicommodity multimodal routing with schedule-based services. Information
**2016**, 7, 13. [Google Scholar] [CrossRef] [Green Version] - Kundu, P.; Kar, S.; Maiti, M. Multi-objective multi-item solid transportation problem in fuzzy environment. Appl. Math. Model.
**2013**, 37, 2028–2038. [Google Scholar] [CrossRef] - Sun, Y.; Liang, X.; Li, X.Y.; Zhang, C. A Fuzzy Programming Method for Modeling Demand Uncertainty in the Capacitated Road-Rail Multimodal Routing Problem with Time Windows. Symmetry-Basel
**2019**, 11, 91. [Google Scholar] [CrossRef] [Green Version] - Vahdani, B.; Tavakkoli-Moghaddam, R.; Jolai, F.; Baboli, A. Reliable design of a closed loop supply chain network under uncertainty: An interval fuzzy possibilistic chance-constrained model. Eng. Optim.
**2013**, 45, 745–765. [Google Scholar] [CrossRef] - Habib, M.S.; Asghar, O.; Hussain, A.; Imran, M.; Mughal, M.P.; Sarkar, B. A robust possibilistic programming approach toward animal fat-based biodiesel supply chain network design under uncertain environment. J. Clean. Prod.
**2021**, 278, 122403. [Google Scholar] [CrossRef] - Zhu, H.; Zhang, J. A credibility-based fuzzy programming model for APP problem. In Proceedings of the 2009 International Conference on Artificial Intelligence and Computational Intelligence, Shanghai, China, 7–8 November 2009; pp. 455–459. [Google Scholar] [CrossRef]
- Han, B.; Shi, S.S.; Gao, H.T.; Hu, Y. A Sustainable Intermodal Location-Routing Optimization Approach: A Case Study of the Bohai Rim Region. Sustainability
**2022**, 14, 3987. [Google Scholar] [CrossRef] - Mahjoubi, S.; Bao, Y. Game theory-based metaheuristics for structural design optimization. Comput. -Aided Civ. Infrastruct. Eng.
**2021**, 36, 1337–1353. [Google Scholar] [CrossRef] - Cheng, X.Z.; Li, J.M.; Zheng, C.Y.; Zhang, J.H.; Zhao, M. An Improved PSO-GWO Algorithm With Chaos and Adaptive Inertial Weight for Robot Path Planning. Front. Neurorobot.
**2021**, 15, 770361. [Google Scholar] [CrossRef] - Arasomwan, M.A.; Adewumi, A.O. On the Performance of Linear Decreasing Inertia Weight Particle Swarm Optimization for Global Optimization. Sci. World J.
**2013**, 2013, 860289. [Google Scholar] [CrossRef] [Green Version] - Chrouta, J.; Farhani, F.; Zaafouri, A. A modified multi swarm particle swarm optimization algorithm using an adaptive factor selection strategy. Trans. Inst. Meas. Control.
**2021**, 3, 01423312211029509. [Google Scholar] [CrossRef] - Resat, H.G.; Turkay, M. Design and operation of intermodal transportation network in the Marmara region of Turkey. Transp. Res. Part E-Logist. Transp. Rev.
**2015**, 83, 16–33. [Google Scholar] [CrossRef] - Zhang, H.; Li, Y.; Zhang, Q.P.; Chen, D.J. Route Selection of Multimodal Transport Based on China Railway Transportation. J. Adv. Transp.
**2021**, 2021, 9984659. [Google Scholar] [CrossRef] - Wan, X.L.; Yamada, Y. An Acceleration-Based Nonlinear Time-Series Analysis of Effects of Robotic Walkers on Gait Dynamics During Assisted Walking. IEEE Sens. J.
**2022**, 22, 21188–21196. [Google Scholar] [CrossRef]

**Figure 4.**Multi-objective dynamic optimization method for multimodal transport based on cooperative game theory.

Sets | |
---|---|

$N$ | Transport node set |

$K$ | Transport mode set |

$H$ | Transshipment node set |

Parameters | |

$\tilde{d}$ | Fuzzy demand of customer orders, $\tilde{d}=\left({d}^{\mathrm{min}},{d}^{L},{d}^{U},{d}^{\mathrm{max}}\right)$ |

${Q}_{ij}^{k}$ | The maximum transport capacity between transport node $i$ and $j$ using transport mode $k$ |

${Q}_{h}^{kl}$ | The maximum transshipment capacity at transshipment node $h$ where the mode of transport is converted from $k$ to $l$ |

${c}^{k}$ | Unit transportation cost of transport mode $k$ |

${c}_{h}^{kl}$ | Unit transshipment cost of converting transport mode $k$ to $l$ at transshipment node $h$ |

${c}_{s}$ | Unit storage cost of early arrival of goods |

${c}_{p}$ | Unit penalty cost for late arrival of goods |

${e}^{k}$ | Unit transportation carbon emissions for transportation mode $k$ |

${e}_{h}^{kl}$ | Unit transshipment carbon emissions of converting transport mode $k$ to $l$ at transshipment node $h$ |

${D}_{ij}^{k}$ | Transportation distance by transport mode $k$ between transport node $i$ and $j$ |

${\nu}_{k}$ | The average travel speed of transport mode $k$ |

${t}_{ij}^{k}$ | Transportation time by transport mode $k$ between transport node $i$ and $j$ |

${t}_{h}^{kl}$ | The transshipment time at transshipment node $h$ where the mode of transport is converted from $k$ to $l$ |

${t}_{i}$ | Time of arrival of goods at place $i$ |

$\left[{T}_{Li},{T}_{Ui}\right]$ | The soft time window of cargo expiration that can be accepted at place $i$, ${T}_{Li}$ and ${T}_{Ui}$ are the lower and upper bounds of the time window, respectively |

$\left[{T}_{\mathrm{min}},{T}_{\mathrm{max}}\right]$ | The hard time window for the expiration of the customer’s shipping order, ${T}_{\mathrm{min}}$ and ${T}_{\mathrm{max}}$ are the lower and upper bounds of the time window, respectively |

Decision Variables | |

${X}_{ij}^{k}$ | Binary variable with a value of 1 if the transport mode $k$ is selected from node $i$ to $j$, and 0 otherwise |

${Y}_{h}^{kl}$ | Binary variable with a value of 1 if the transport mode is converted from $i$ to $j$ at transshipment node $h$, and 0 otherwise |

Adjacent Node | Distance (km) | ||
---|---|---|---|

Highway | Railway | Airway | |

(1,2) | 632 | 757 | 515 |

(1,4) | 670 | 707 | 562 |

(1,5) | 780 | 1049 | 667 |

(2,3) | 259 | 316 | — |

(2,5) | 636 | 688 | — |

(3,7) | 868 | 937 | 665 |

(3,8) | 770 | 883 | 609 |

(4,5) | 336 | 342 | — |

(4,6) | 340 | 362 | — |

(5,6) | 342 | — | — |

(5,7) | 587 | 838 | — |

(6,9) | 513 | 536 | — |

(6,10) | 855 | 1226 | 729 |

(7,8) | 297 | — | — |

(7,10) | 622 | 667 | 579 |

(8,10) | 813 | 912 | 739 |

(9,10) | 446 | — | — |

(9,11) | 419 | 408 | — |

(10,11) | 316 | — | — |

(10,12) | 320 | 301 | — |

(11,12) | 311 | 292 | — |

(11,13) | 292 | 281 | — |

(12,13) | 134 | — | — |

Transportation Mode | Average Speed (km/h) | Transportation Cost (¥/(t∙km)) | Transportation Carbon Emission (kg/(t∙km)) |
---|---|---|---|

Highway | 90 | 0.35 | 0.12 |

Railway | 60 | 0.165 | 0.025 |

Airway | 600 | 0.6 | 1.05 |

Transshipment | Highway | Railway | Airway | |||
---|---|---|---|---|---|---|

Cost (¥/t) | Carbon Emission (kg/t) | Cost (¥/t) | Carbon Emission (kg/t) | Cost (¥/t) | Carbon Emission (kg/t) | |

Highway | — | — | 10 | 1.56 | 12 | 3.12 |

Railway | 10 | 1.56 | — | — | 15 | 6 |

Airway | 12 | 3.12 | 15 | 6 | — | — |

Origin | Destination | Highway | Railway | Airway |
---|---|---|---|---|

1 | 2 | 20 | 25 | 15 |

1 | 4 | 28 | 22 | 25 |

1 | 5 | 19 | 21 | 20 |

2 | 3 | 20 | 25 | — |

2 | 5 | 32 | 26 | — |

3 | 7 | 18 | 24 | 20 |

3 | 8 | 22 | 20 | 26 |

4 | 5 | 20 | 15 | — |

4 | 6 | 24 | 28 | — |

5 | 6 | 30 | — | — |

5 | 7 | 21 | 24 | — |

6 | 9 | 24 | 26 | — |

6 | 10 | 28 | 24 | 22 |

7 | 8 | 25 | — | — |

7 | 10 | 24 | 24 | 20 |

8 | 10 | 20 | 25 | 26 |

9 | 10 | 20 | — | — |

9 | 11 | 30 | 24 | — |

10 | 11 | 26 | — | — |

10 | 12 | 28 | 25 | — |

11 | 12 | 24 | 26 | — |

11 | 13 | 19 | 24 | — |

12 | 13 | 22 | — | — |

Node | Highway—Railway | Railway—Airway | Highway—Airway |
---|---|---|---|

1 | — | — | — |

2 | 20 | 25 | 21 |

3 | 25 | 20 | 18 |

4 | 24 | 30 | 22 |

5 | 30 | 25 | 15 |

6 | 24 | 22 | 25 |

7 | 18 | 21 | 20 |

8 | 20 | 25 | 22 |

9 | 28 | — | — |

10 | 30 | 25 | 26 |

11 | 24 | — | — |

12 | 22 | — | — |

13 | — | — | — |

Node | Lower Limit of Soft Time Window | Upper Limit of Soft Time Window | Upper Limit of Hard Time Window |
---|---|---|---|

1 | 0 | 72 | 72 |

2 | 7 | 15 | 72 |

3 | 11 | 20 | 72 |

4 | 7 | 14 | 72 |

5 | 8 | 20 | 72 |

6 | 12 | 23 | 72 |

7 | 20 | 30 | 72 |

8 | 25 | 36 | 72 |

9 | 26 | 35 | 72 |

10 | 30 | 40 | 72 |

11 | 32 | 40 | 72 |

12 | 35 | 42 | 72 |

13 | 30 | 50 | 72 |

Weighting Combination | Cost/CNY | Time/h | Carbon Emission/kg | Transportation Path | Transportation Mode |
---|---|---|---|---|---|

I | 12,974.0 | 33.6 | 2706.9 | 1-4-6-9-11-13 | Railway-Highway-Highway-Highway-Railway |

II | 8005.9 | 44.7 | 1515.2 | 1-5-6-9-11-13 | Railway-Highway-Railway-Railway-Railway |

III | 45,156.0 | 16.9 | 21,903.0 | 1-4-6-10-12-13 | Airway-Highway-Airway-Highway-Highway |

IV | 8234.7 | 46.2 | 1238.1 | 1-4-6-10-12-13 | Railway-Railway-Railway-Railway-Highway |

V | 5679.2 | 38.3 | 860.3 | 1-4-6-9-11-13 | Railway-Railway-Railway-Railway-Railway |

Algorithm | Cost/CNY | Time/h | Carbon Emission/kg | Transportation Path | Transportation Mode |
---|---|---|---|---|---|

MOPSO | 10,106.0 | 35.6 | 2268.2 | 1-4-6-9-11-13 | Highway-Railway-Railway-Railway-Highway |

NSGA-II | 7694.4 | 38.2 | 1629.5 | 1-4-6-9-11-13 | Railway-Railway-Highway-Railway-Railway |

CGT-WSM | 5679.2 | 38.3 | 860.3 | 1-4-6-9-11-13 | Railway-Railway-Railway-Railway-Railway |

Algorithm | HV | IGD | ||
---|---|---|---|---|

Mean | sd | Mean | sd | |

MOPSO | 2.61 × 10^{10} | 4.5 × 10^{9} | 1409.80 | 762.91 |

NSGA-II | 3.15 × 10^{10} | 1.28 × 10^{9} | 2252.94 | 404.31 |

CGT-WSM | 2.3 × 10^{10} | 5.74 × 10^{8} | 261.34 | 20.58 |

Transport Scenario | Cost/CNY | Time/h | Carbon Emission/kg | Transportation Path | Transportation Mode |
---|---|---|---|---|---|

I | 10,712.0 | 32.9 | 2627.5 | 1-4-6-9-11-13 | Railway-Railway-Highway-Highway-Highway |

II | 14,890.0 | 30.1 | 3522.1 | 1-4-6-9-11-13 | Highway-Railway-Highway-Highway-Highway |

III | 11,494.0 | 33.9 | 2780.5 | 1-4-6-10-11-13 | Railway-Railway-Highway-Highway-Highway |

IV | 12,445.0 | 34.4 | 2935.4 | 1-5-6-9-11-13 | Highway-Highway-Railway-Railway-Highway |

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## Share and Cite

**MDPI and ACS Style**

Li, L.; Zhang, Q.; Zhang, T.; Zou, Y.; Zhao, X.
Optimum Route and Transport Mode Selection of Multimodal Transport with Time Window under Uncertain Conditions. *Mathematics* **2023**, *11*, 3244.
https://doi.org/10.3390/math11143244

**AMA Style**

Li L, Zhang Q, Zhang T, Zou Y, Zhao X.
Optimum Route and Transport Mode Selection of Multimodal Transport with Time Window under Uncertain Conditions. *Mathematics*. 2023; 11(14):3244.
https://doi.org/10.3390/math11143244

**Chicago/Turabian Style**

Li, Lin, Qiangwei Zhang, Tie Zhang, Yanbiao Zou, and Xing Zhao.
2023. "Optimum Route and Transport Mode Selection of Multimodal Transport with Time Window under Uncertain Conditions" *Mathematics* 11, no. 14: 3244.
https://doi.org/10.3390/math11143244