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<p>Efficient terminal management relies heavily on the synchronized scheduling of berth space and the assignment of operational equipment. This study addresses the integrated Berth Allocation Problem (BAP) and machine assignment problem through the introduction of a novel <i>machine-pattern</i> modeling approach. In contrast to traditional formulations that rely on individual machine-allocation variables, the proposed framework utilizes machine patterns to represent resource availability. This approach significantly reduces model complexity and enables the simultaneous allocation of multiple machine types within a continuous-time framework. Two Mixed-Integer Linear Programming (MILP) formulations are presented, one at the quay level and another at the berth level, with the primary objective of minimizing the total weighted sum of vessel waiting and handling times. To address the computational challenges of real-world port operations, a dedicated heuristic algorithm is developed for large-scale instances. Computational experiments demonstrate the effectiveness of these methods; the heuristic is capable of solving instances involving up to 100 berths and 500 vessels in under three seconds. Furthermore, the heuristic solutions maintain high quality, averaging within 9% of the optimal MILP results. The findings suggest that the machine-pattern approach provides a scalable and efficient solution for integrated port resource management in high-traffic terminals.</p>

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A new mathematical model and solution method for the berth allocation problem with machine patterns

  • 期刊论文

  • 发表日期：

    2026年7月25日

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  • Bruno Luís Hönigmann Cereser,
  • Aurelio Ribeiro Leite de Oliveira,
  • Antonio Carlos Moretti

摘要

Efficient terminal management relies heavily on the synchronized scheduling of berth space and the assignment of operational equipment. This study addresses the integrated Berth Allocation Problem (BAP) and machine assignment problem through the introduction of a novel machine-pattern modeling approach. In contrast to traditional formulations that rely on individual machine-allocation variables, the proposed framework utilizes machine patterns to represent resource availability. This approach significantly reduces model complexity and enables the simultaneous allocation of multiple machine types within a continuous-time framework. Two Mixed-Integer Linear Programming (MILP) formulations are presented, one at the quay level and another at the berth level, with the primary objective of minimizing the total weighted sum of vessel waiting and handling times. To address the computational challenges of real-world port operations, a dedicated heuristic algorithm is developed for large-scale instances. Computational experiments demonstrate the effectiveness of these methods; the heuristic is capable of solving instances involving up to 100 berths and 500 vessels in under three seconds. Furthermore, the heuristic solutions maintain high quality, averaging within 9% of the optimal MILP results. The findings suggest that the machine-pattern approach provides a scalable and efficient solution for integrated port resource management in high-traffic terminals.