Transportation problems for intermodal networks: Mathematical models, exact and heuristic algorithms, and machine learning

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EXPERT SYSTEMS WITH APPLICATIONS, vol.135, pp.374-387, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 135
  • Publication Date: 2019
  • Doi Number: 10.1016/j.eswa.2019.06.023
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.374-387


This paper presents a combinatorial problem called a pick-up routing problem with a three-dimensional (3D-PRP) loading constraint, clustered backhauls at the operational level, and train loading at the tactical level for an intermodal transportation network. A two-phase approach, called clustering first, packing-routing second, is proposed for use during the first stage. The clustering of backhauls is carried out using the k-means algorithm. A hybrid approach is provided, which combines the packing of orders by first solving a 3D loading problem for each cluster using machine learning with a best-fit-first strategy, with routing using a genetic algorithm. During the second stage, the train-loading problem is solved using a mixed integer programming approach to minimise the total costs by incorporating various cost types, in which detention and demurrage costs are taken into account. All solution approaches are computationally evaluated on real-world data provided by an international logistics firm and new randomly generated instances. Comparisons are carried out using both exact solution methods and heuristic approaches, and the proposed approach was shown to be more effective for real-world problems. (C) 2019 Elsevier Ltd. All rights reserved.