Title: Loading and multi-trip routing problem using hierarchical ant colony optimisation algorithm

Authors: Tieu Trong Minh Luan; Truong Tran Mai Anh; Nguyen Van Hop

Addresses: School of Industrial Engineering and Management, International University – VNU-HCMC, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam ' School of Industrial Engineering and Management, International University – VNU-HCMC, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam ' School of Industrial Engineering and Management, International University – VNU-HCMC, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam

Abstract: In this paper, we formulate the loading and routing problem as a new mixed-integer programming model with multi-trip routing and loading constraints. The objective is to minimise the total costs of delivery and outbound cross-docking operations and delivery. We also modify an ant colony optimisation algorithm to a so-called four-level ant colony optimisation heuristics (FLACO) to search for the best loading and routing solution in hierarchical levels of trips, trucks, periods, and routes. At each level, the ACO parameters are updated iteratively to process the problem constraints. The case of a large dairy company in Vietnam is used to validate the proposed model and FLACO. The FLACO could give as close as about 2.46% to the optimal solution and outperform the genetic algorithm for small-sized and large-sized problems, respectively.

Keywords: loading; vehicle routing problem; ant colony optimisation; ACO.

DOI: 10.1504/IJLSM.2025.149653

International Journal of Logistics Systems and Management, 2025 Vol.52 No.2, pp.263 - 286

Received: 05 Jul 2022
Accepted: 25 Dec 2022
Published online: 10 Nov 2025 *

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