Mixed-Integer Linear Programming Model for Integrated Liner Shipping Route and Schedule Optimization with Weekly Port Time Windows
DOI:
https://doi.org/10.23055/ijietap.2026.33.5.11731Keywords:
liner shipping route design, weekly multiple port time windows, container lines, port call sequence, ship schedule, sailing speedAbstract
Designing an efficient and cost-effective port network requires accounting for practical constraints, such as port time operation windows. Ignoring these constraints can lead to impractical schedules. This paper presents a method for optimizing liner shipping routes and schedules while accommodating multiple weekly port time windows. A mathematical model is developed to minimize overall costs by optimizing the sequence of port calls, schedules, and sailing speeds. The model is linearized as a mixed-integer program and validated through numerical experiments using commercial optimization solvers. A case study based on SITC Container Lines validates the proposed model and confirms its cost-saving effectiveness, showing total cost reductions of 13.28%, 32.74%, and 16.26% across three port time window scenarios compared with the original port call sequence. Sensitivity analyses further examine the effects of bunker prices, port time windows, and shipping demand volume.
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