Title: An optimisation method for discrete berth allocation considering pier transitions

Authors: Zhaojing Yang; Min Xu; Yiwei Wu; Shuaian Wang

Addresses: Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, 11 Yuk Choi Rd., Hung Hom, Hong Kong ' Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, 11 Yuk Choi Rd., Hung Hom, Hong Kong ' Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, 11 Yuk Choi Rd., Hung Hom, Hong Kong ' Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, 11 Yuk Choi Rd., Hung Hom, Hong Kong

Abstract: Maritime transportation is vital for global trade but is experiencing increasing pressure at ports due to rising freight volumes and fleet sizes. This study addresses the problem of optimising berth allocation to enhance port efficiency. A mixed-integer linear programming model is proposed to minimise the product of ship cargo loading duration and ships' cargo loading completion times, reflecting the combined impact of these factors. The model uses cargo loading duration as a proxy for ship size to determine berth allocation and incorporates dynamic arrival times, draft compatibility between ships and piers, and necessary transitions between deep-and shallow-draft piers. A case study of Hong Kong Port demonstrates the model's practical applicability and effectiveness in providing feasible berth allocation solutions. A sensitivity analysis of transition times between piers reveals a phased pattern in the objective function value, which stabilises after reaching a certain threshold. An additional sensitivity analysis examining the number of quay cranes (QCs) shows diminishing marginal returns as QC deployment increases. The findings provide practical insights for port managers for optimising berth allocation plans and improving operation efficiency. The study also suggests adjusting ship speeds to manage transition times and identifying the optimal number of QCs.

Keywords: berth allocation problem; BAP; pier transition; mixed-integer linear programming; draft; port operations.

DOI: 10.1504/IJSTL.2026.155747

International Journal of Shipping and Transport Logistics, 2026 Vol.23 No.1, pp.99 - 123

Received: 26 Oct 2025
Accepted: 12 Apr 2026
Published online: 12 Aug 2026 *

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