JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (6): 128-140.doi: 10.6040/j.issn.1671-9352.0.2024.067

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Optimization and simulation for an intermodal routing problem with fuzzy soft time window under multiple uncertainty

SUN Yan1, ZHANG Zheng1, ZHANG Xiaran2*, LIU Yunlin1, SUN Guohua1   

  1. 1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, Shandong, China;
    2. School of Management, Shandong University of Traditional Chinese Medicine, Jinan 250355, Shandong, China
  • Published:2025-06-20

Abstract: To solve the high cost and low efficiency of the intermodal transportation applied in long-distance and bulk transportation, this study explores an intermodal routing problem with fuzzy soft time window whose aim is to minimize the transportation costs. Meanwhile to improve the reliability of the intermodal routing in the actual transportation, this study formulates the uncertainty of the goods demand of the customer, and further explore the multiple uncertainty introduced by the uncertain demand that includes the uncertainty of transportation costs and time and of the service level constraints and capacity constraints. Based on the utilization of the trapezoidal fuzzy number to describe the uncertainty, this study establishes a fuzzy programming model to deal with the intermodal routing problem under multiple uncertainty, and utilizes the fuzzy chance-constrained programming method based on credibility measure to realize the crisp reformulation of the model to make the problem solvable. This study further develops an Ant Colony Optimization algorithm based on network transformation to solve the crisp model efficiently. The results of the numerical case demonstrate the feasibility of the chance-constrained programming model and Ant Colony Optimization algorithm. The influence of improving the service level and the confidence level on the costs of the intermodal transportation is clarified by using the sensitivity analysis. The experimental simulation of the numerical case further indicates the relationship between the confidence level and the reliability of the route that the reliability of the route trends to enhance with the improvement of the confidence level, however, they are not equivalent, and improving the confidence level will not lead to an absolute reliability enhancement. The numerical case simulation also verifies that considering demand uncertainty significantly improves the reliability of the routing in the actual transportation, and further reveals that the economy and reliability objectives of the routing are in conflict with each other. The customer and intermodal transportation operator can accordingly make tradeoffs among the economy, timeliness and reliability of the transportation to effectively improve the comprehensive level of the intermodal transportation.

Key words: intermodal transportation, routing, fuzzy soft time window, multiple uncertainty, fuzzy chance-constrained programming, Ant Colony Optimization algorithm

CLC Number: 

  • F542
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