Skip to main content
SpringerLink
Log in

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

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

In this study, a freight routing problem considering both soft delivery time windows and demand and capacity uncertainty in a road–rail intermodal transportation system is investigated. According to fuzzy set theory, uncertain demands and capacities are formulated as trapezoidal fuzzy numbers. Soft delivery time windows under a fuzzy environment is established, in which fuzzy periods caused by early and late deliveries that lead to penalty are modeled based on maximum functions. To solve the routing problem yielding the above characteristics, this study designs a fuzzy mixed-integer nonlinear programming model whose objective is to minimize the total costs created in the road–rail intermodal transportation activities. After using the fuzzy expected value method to address the fuzzy objective, two fuzzy approaches, i.e., fuzzy chance-constrained programming method and fuzzy ranking method, are separately adopted to undertake the defuzzification of the fuzzy constraints. Improved linear formulations of the model are then produced to make it easier to solve. A simulation-based reliability modeling is developed to quantify the reliability of the optimization results given by different fuzzy approaches under different parameter settings in a simulation environment. Finally, an empirical case is presented to verify the feasibility of the proposed methods. The effects of demand and capacity fuzziness on the routing optimization are revealed, and an optimization procedure that helps decision-makers to select a more suitable fuzzy approach and determine the best parameter setting for a given case is demonstrated. Some insights that are helpful for organizing a reliable transportation are also drawn.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Yang, K., Wang, R., & Yang, L. Fuzzy reliability-oriented optimization for the road–rail intermodal transport system using tabu search algorithm. J. Intell. Fuzzy Syst., 1–17

  2. Bierwirth, C., Kirschstein, T., Meisel, F.: On transport service selection in intermodal rail/road distribution networks. Business Res. 5(2), 198–219 (2012)

    Google Scholar 

  3. Kuzmicz, K.A., Pesch, E.: Approaches to empty container repositioning problems in the context of Eurasian intermodal transportation. Omega 85, 194–213 (2019)

    Google Scholar 

  4. Resat, H.G., Turkay, M.: Design and operation of intermodal transportation network in the Marmara region of Turkey. Transport. Res. E 83, 16–33 (2015)

    Google Scholar 

  5. Tokcaer, S., Özpeynirci, Ö.: A bi-objective multimodal transportation planning problem with an application to a petrochemical ethylene manufacturer. Maritime Econ. Logist. 20(1), 72–88 (2018)

    Google Scholar 

  6. 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. Transport. 2020, 1–21 (2020)

    Google Scholar 

  7. Guo, W., Atasoy, B., Beelaerts van Blokland, W., & Negenborn, R. R. (2020). Dynamic and Stochastic Shipment Matching Problem in Multimodal Transportation. Transport. Res. Rec., 0361198120905592

  8. Fazayeli, S., Eydi, A., Kamalabadi, I.N.: Location–routing problem in multimodal transportation network with time windows and fuzzy demands: presenting a two-part genetic algorithm. Comput. Industr. Eng. 119, 233–246 (2018)

    Google Scholar 

  9. Bast, H., et al.: Route planning in transportation networks. Lect. Notes Comput. Sci. 9220, 19–80 (2016)

    MathSciNet  Google Scholar 

  10. Winebrake, J.J., Corbett, J.J., Falzarano, A., Hawker, J.S., Korfmacher, K., Ketha, S., Zilora, S.: Assessing energy, environmental, and economic tradeoffs in intermodal freight transportation. J. Air Waste Manag. Assoc. 58(8), 1004–1013 (2008)

    Google Scholar 

  11. Caris, A., Macharis, C., Janssens, G.K.: Decision support in intermodal transport: a new research agenda. Comput. Ind. 64(2), 105–112 (2013)

    Google Scholar 

  12. Göçmen, E., Erol, R.: Transportation problems for intermodal networks: mathematical models, exact and heuristic algorithms, and machine learning. Expert Syst. Appl. 135, 374–387 (2019)

    Google Scholar 

  13. Baykasoğlu, A., Subulan, K., Taşan, A.S., Dudaklı, N.: A review of fleet planning problems in single and multimodal transportation systems. Transportmetrica A 15(2), 631–697 (2019)

    Google Scholar 

  14. Wang, Q.Z., Chen, J.M., Tseng, M.L., Luan, H.M., Ali, M.H.: Modelling green multimodal transport route performance with witness simulation software. J Clean. Prod. 248, 119245 (2020)

    Google Scholar 

  15. Bontekoning, Y.M., Macharis, C., Trip, J.J.: Is a new applied transportation research field emerging?-A review of intermodal rail-truck freight transport literature. Transport. Res. A 38(1), 1–34 (2004)

    Google Scholar 

  16. Min, H.: International intermodal choices via chance-constrained goal programming. Transport. Res. A 25(6), 351–362 (1991)

    Google Scholar 

  17. Barnhart, C., Ratliff, H.D.: Modeling intermodal routing. J. Busin. Log. 14(1), 205 (1993)

    Google Scholar 

  18. Boardman, B.S., Malstrom, E.M., Butler, D.P., Cole, M.H.: Computer assisted routing of intermodal shipments. Comput. Ind. Eng. 33(1–2), 311–314 (1997)

    Google Scholar 

  19. Bookbinder, J.H., Fox, N.S.: Intermodal routing of Canada-Mexico shipments under NAFTA. Transport Res. Part E 34(4), 289–303 (1998)

    Google Scholar 

  20. Chang, T.S.: Best routes selection in international intermodal networks. Comput. Oper. Res. 35(9), 2877–2891 (2008)

    MATH  Google Scholar 

  21. Moccia, L., Cordeau, J.F., Laporte, G., Ropke, S., Valentini, M.P.: Modeling and solving a multimodal transportation problem with flexible-time and scheduled services. Networks 57(1), 53–68 (2011)

    MathSciNet  MATH  Google Scholar 

  22. Ayar, B., Yaman, H.: An intermodal multicommodity routing problem with scheduled services. Comput. Optimiz. Appl. 53(1), 131–153 (2012)

    MathSciNet  MATH  Google Scholar 

  23. Verma, M., Verter, V., Zufferey, N.: A bi-objective model for planning and managing rail-truck intermodal transportation of hazardous materials. Transport. Res. E 48(1), 132–149 (2012)

    Google Scholar 

  24. Sawadogo, M., Anciaux, D., Daniel, R.O.Y.: Reducing intermodal transportation impacts on society and environment by path selection: a multiobjective shortest path approach. IFAC Proc. Vol. 45(6), 505–513 (2012)

    Google Scholar 

  25. Demir, E., Hrušovský, M., Jammernegg, W., Van Woensel, T.: Green intermodal freight transportation: bi-objective modelling and analysis. Int. J. Prod. Res. 57(19), 6162–6180 (2019)

    Google Scholar 

  26. Dua, A., Sinha, D.: Quality of multimodal freight transportation: a systematic literature review. World Rev. Int. Transport. Res. 8(2), 167–194 (2019)

    Google Scholar 

  27. Hoogeboom, M., Dullaert, W., Lai, D., Vigo, D.: Efficient neighborhood evaluations for the vehicle routing problem with multiple time windows. Transport. Sci. 54(2), 299–564 (2020)

    Google Scholar 

  28. Liu, R., Tao, Y., Xie, X.: An adaptive large neighborhood search heuristic for the vehicle routing problem with time windows and synchronized visits. Comput. Oper. Res. 101, 250–262 (2019)

    MathSciNet  MATH  Google Scholar 

  29. Karoonsoontawong, A., Punyim, P., Nueangnitnaraporn, W., & Ratanavaraha, V. (2020). Multi-Trip Time-Dependent Vehicle Routing Problem with Soft Time Windows and Overtime Constraints. Networks and Spatial Economics, 1–50

  30. Xu, Z., Elomri, A., Pokharel, S., Mutlu, F.: A model for capacitated green vehicle routing problem with the time-varying vehicle speed and soft time windows. Comput. Ind. Eng. 137, 106011 (2019)

    Google Scholar 

  31. Tang, J., Pan, Z., Fung, R.Y., Lau, H.: Vehicle routing problem with fuzzy time windows. Fuzzy Sets Syst. 160(5), 683–695 (2009)

    MathSciNet  MATH  Google Scholar 

  32. Sun, Y., Liang, X., Li, X., Zhang, C.: A fuzzy programming method for modeling demand uncertainty in the capacitated road-rail multimodal routing problem with time windows. Symmetry 11(1), 91 (2019)

    MATH  Google Scholar 

  33. Mi, X., Mei, M., & Zheng, X. (2019, May). Study on Optimal Routes of Multimodal Transport under Time Window Constraints. In: 2019 IEEE 23rd International Conference on Computer Supported Cooperative Work in Design (CSCWD) (pp. 512–516). IEEE

  34. Zhao, Y., Liu, R., Zhang, X., Whiteing, A.: A chance-constrained stochastic approach to intermodal container routing problems. PLoS ONE 13(2), e0192275 (2018)

    Google Scholar 

  35. Zhang, D., He, R., Li, S., Wang, Z.: A multimodal logistics service network design with time windows and environmental concerns. PLoS ONE 12(9), e0185001 (2017)

    Google Scholar 

  36. Grossmann, I.E., Apap, R.M., Calfa, B.A., García-Herreros, P., Zhang, Q.: Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty. Comput. Chem. Eng. 91, 3–14 (2016)

    Google Scholar 

  37. Grossmann, I. E., Apap, R. M., Calfa, B. A., Garcia-Herreros, P., & Zhang, Q. (2015). Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty. In Computer Aided Chemical Engineering (Vol. 37, pp. 1–14). Elsevier

  38. Uddin, M., Huynh, N.: Reliable routing of road-rail intermodal freight under uncertainty. Netw. Spatial Econ. 19(3), 929–952 (2019)

    Google Scholar 

  39. Hrušovský, M., Demir, E., Jammernegg, W., Van Woensel, T.: Hybrid simulation and optimization approach for green intermodal transportation problem with travel time uncertainty. Flexible Serv. Manuf. J. 30(3), 486–516 (2018)

    Google Scholar 

  40. Sun, Y., Li, X.: Fuzzy programming approaches for modeling a customer-centred freight routing problem in the road-rail intermodal hub-and-spoke network with fuzzy soft time windows and multiple sources of time uncertainty. Mathematics 7(8), 739 (2019)

    Google Scholar 

  41. Lu, Y., Lang, M., Sun, Y., Li, S.: A fuzzy intercontinental road-rail multimodal routing model with time and train capacity uncertainty and fuzzy programming approaches. IEEE Access 8, 27532–27548 (2020)

    Google Scholar 

  42. Sun, Y., Hrušovský, M., Zhang, C., Lang, M.: A time-dependent fuzzy programming approach for the green multimodal routing problem with rail service capacity uncertainty and road traffic congestion. Complexity 2018, 1–22 (2018)

    MATH  Google Scholar 

  43. Kundu, P., Kar, S., Maiti, M.: Multi-objective multi-item solid transportation problem in fuzzy environment. Appl. Math. Model. 37(4), 2028–2038 (2013)

    MathSciNet  MATH  Google Scholar 

  44. Liu, P., Yang, L., Wang, L., Li, S.: A solid transportation problem with type-2 fuzzy variables. Appl. Soft Comput. 24, 543–558 (2014)

    Google Scholar 

  45. Mula, J., Peidro, D., Poler, R.: The effectiveness of a fuzzy mathematical programming approach for supply chain production planning with fuzzy demand. Int. J. Prod. Econ. 128(1), 136–143 (2010)

    MATH  Google Scholar 

  46. Özceylan, E., Paksoy, T.: Interactive fuzzy programming approaches to the strategic and tactical planning of a closed-loop supply chain under uncertainty. Int. J. Prod. Res. 52(8), 2363–2387 (2014)

    Google Scholar 

  47. J-Sharahi, S., Khalili-Damghani, K., Abtahi, A.R., Rashidi-Komijan, A.: Type-II fuzzy multi-product, multi-level, multi-period location-allocation, production-distribution problem in supply chains: modelling and optimisation approach. Fuzzy Inform. Eng. 10(2), 260–283 (2018)

    Google Scholar 

  48. Pishvaee, M.S., Torabi, S.A.: A possibilistic programming approach for closed-loop supply chain network design under uncertainty. Fuzzy Sets Syst. 161(20), 2668–2683 (2010)

    MathSciNet  MATH  Google Scholar 

  49. Tian, W., Cao, C.: A generalized interval fuzzy mixed integer programming model for a multimodal transportation problem under uncertainty. Eng. Optimiz. 49(3), 481–498 (2017)

    MathSciNet  Google Scholar 

  50. Zarandi, M.H.F., Hemmati, A., Davari, S.: The multi-depot capacitated location–routing problem with fuzzy travel times. Expert Syst. Appl. 38(8), 10075–10084 (2011)

    Google Scholar 

  51. Demir, E., Burgholzer, W., Hrušovský, M., Arıkan, E., Jammernegg, W., Van Woensel, T.: A green intermodal service network design problem with travel time uncertainty. Transport. Res. B. 93, 789–807 (2016)

    Google Scholar 

  52. Pishvaee, M.S., Rabbani, M., Torabi, S.A.: A robust optimization approach to closed-loop supply chain network design under uncertainty. Appl. Math. Model. 35(2), 637–649 (2011)

    MathSciNet  MATH  Google Scholar 

  53. Wang, R., Yang, K., Yang, L., Gao, Z.: Modeling and optimization of a road–rail intermodal transport system under uncertain information. Eng. Appl. Artif. Intell. 72, 423–436 (2018)

    Google Scholar 

  54. Ishfaq, R., Sox, C.R.: Design of intermodal logistics networks with hub delays. Eur. J. Oper. Res. 220(3), 629–641 (2012)

    MathSciNet  MATH  Google Scholar 

  55. Sun, Y., & Lang, M. (2015). Modeling the multicommodity multimodal routing problem with schedule-based services and carbon dioxide emission costs. Mathematical Problems in Engineering, 2015

  56. Liu, Y.K., Liu, B.: Fuzzy random variables: a scalar expected value operator. Fuzzy Optim. Decis. Making 2(2), 143–160 (2003)

    MathSciNet  MATH  Google Scholar 

  57. Dalman, H., Güzel, N., Sivri, M.: A fuzzy set-based approach to multi-objective multi-item solid transportation problem under uncertainty. Int. J. Fuzzy Syst. 18(4), 716–729 (2016)

    MathSciNet  Google Scholar 

  58. Chen, S.M.: Evaluating weapon systems using fuzzy arithmetic operations. Fuzzy Sets Syst. 77(3), 265–276 (1996)

    MathSciNet  Google Scholar 

  59. Jiménez, M.: Ranking fuzzy numbers through the comparison of its expected intervals. Int. J. Uncertain. Fuzzin. Knowl. Based Syst. 4(04), 379–388 (1996)

    MathSciNet  MATH  Google Scholar 

  60. Zheng, Y., Liu, B.: Fuzzy vehicle routing model with credibility measure and its hybrid intelligent algorithm. Appl. Math. Comput. 176(2), 673–683 (2006)

    MathSciNet  MATH  Google Scholar 

  61. Govindan, K., Paam, P., Abtahi, A.R.: A fuzzy multi-objective optimization model for sustainable reverse logistics network design. Ecol. Ind. 67, 753–768 (2016)

    Google Scholar 

  62. 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. Optimiz. 45(6), 745–765 (2013)

    MathSciNet  Google Scholar 

  63. Dai, Z., Zheng, X.: Design of close-loop supply chain network under uncertainty using hybrid genetic algorithm: a fuzzy and chance-constrained programming model. Comput. Ind. Eng. 88, 444–457 (2015)

    Google Scholar 

  64. Zhu, H., & Zhang, J. (2009, November). A credibility-based fuzzy programming model for APP problem. In 2009 International Conference on Artificial Intelligence and Computational Intelligence (Vol. 1, pp. 455–459). IEEE

  65. Xie, Y., Lu, W., Wang, W., Quadrifoglio, L.: A multimodal location and routing model for hazardous materials transportation. J. Hazard. Mater. 227, 135–141 (2012)

    Google Scholar 

  66. China State Railway Group Company: http://hyfw.95306.cn/hyinfo/page/home-hyzx-index. Accessed 20 April 2020

  67. National Development and Reform Commission of China: http://jgjc.ndrc.gov.cn/Detail.aspx?TId=706&newsId=6894. Accessed 20 April 2020

  68. Ministry of Transport of China: http://cyfd.cnki.com.cn/Article/N2007030054000163.htm. Accessed 20 April 2020

  69. Khalilpourazari, S., Pasandideh, S.H.R., Ghodratnama, A.: Robust possibilistic programming for multi-item EOQ model with defective supply batches: whale Optimization and Water Cycle Algorithms. Neural Comput. Appl. 31(10), 6587–6614 (2019)

    Google Scholar 

  70. Rabbani, M., Hosseini-Mokhallesun, S.A.A., Ordibazar, A.H., Farrokhi-Asl, H.: A hybrid robust possibilistic approach for a sustainable supply chain location–allocation network design. Int. J. Syst. Sci. 7(1), 60–75 (2020)

    Google Scholar 

  71. Zahiri, B., Tavakkoli-Moghaddam, R., Pishvaee, M.S.: A robust possibilistic programming approach to multi-period location–allocation of organ transplant centers under uncertainty. Comput. Ind. Eng. 74, 139–148 (2014)

    Google Scholar 

  72. Castillo, O. et al: Special Issue “Trends and Developments on Type-2 Fuzzy Sets and Systems” of International Journal of Fuzzy Systems. https://www.springer.com/journal/40815/updates/17750482. Accessed 20 Apr 2020

Download references

Funding

This research was funded by the Shandong Provincial Natural Science Foundation of China under Grant No. ZR2019BG006, the Project for Humanities and Social Sciences Research of Ministry of Education of China under Grant No. 19YJC630149, and the Shandong Provincial Higher Educational Social Science Program of China under Grant No. J18RA053.

Author information

Authors and Affiliations

  1. School of Management Science and Engineering, Shandong University of Finance and Economics, No. 7366, Second Ring East Road, Jinan, 250014, Shandong, China

    Yan Sun

Authors
  1. Yan Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Sun.

Ethics declarations

Conflicts of interest

The author declares that there are no conflicts of interest regarding the publication of this paper.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 29 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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. 22, 2119–2148 (2020). https://doi.org/10.1007/s40815-020-00905-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-020-00905-x

Keywords

Search

Navigation