Integrated berth allocation and yard assignment with conflict-induced preemptive operations in bulk cargo ports

Frequent conflicts among stacking and reclaiming operations within the stockyard are a common challenge in the operation of bulk cargo ports. This paper incorporates the practically relevant setting of preemptive operations induced by stacking-reclaiming conflict into the integrated berth allocation and yard assignment problem (IBYP) in bulk cargo ports. Compact mathematical formulations and branch-and-price (B&P) solution methods tailored for preemptive stacking are developed to jointly optimize the interdependent decisions of vessel unloading sequences and storage locations, thereby improving operational efficiency in bulk materials. To speed up the column generation procedure at each branching node, we first disaggregate each pricing problem and introduce a set of easier surrogate subproblems. Then, a unified label-setting algorithm framework is developed to efficiently solve all surrogate subproblems sequentially, potentially leading to a negative reduced-cost column and thus skipping the time-consuming exact pricing procedure. Furthermore, by leveraging this label-setting procedure, we propose a greedy-and-repair heuristic that delivers fast, near-optimal solutions for practice and provides high-quality warm starts for B&P. In particular, we also investigate the non-preemptive special case and design a time-indexed dynamic programming algorithm for exact pricing, which is orders of magnitude faster than solver-based methods while preserving optimality. Experiments on instances derived from real port data demonstrate strong scalability and competitive runtimes on large-scale cases. We publicly release code, instance data, and detailed results to support future research.