An Optimization Framework for Berth Allocation and Quay-Crane Deployment Under Double-Line Ship Mooring with Direct Ship-to-Ship Transshipment

Double-line ship mooring (DLSM) can allow an outer feeder vessel to be handled alongside an inner mainline vessel and thereby enable direct ship-to-ship container transshipment. The aim of this study is to determine whether, and under what modeled conditions, a static one-to-one DLSM arrangement can improve berth and quay-crane planning while enabling direct transfer. A normative formulation represents berth sharing, vessel-length compatibility, temporal containment, terminal-wide crane capacity, and the lower productivity of a cross-over quay crane. The executable framework addresses a restricted decision space: particle swarm optimization (PSO) searches berth assignments, deterministic rules generate quay-crane counts and DLSM pairs, and a constructive scheduler produces and evaluates service times. Performance is assessed through a two-by-two FCFS/PSO and SLSM/DLSM ablation on 45 synthetic instances, supplemented by 20 independent runs of each PSO scheme on nine prospectively selected representative instances. PSO-DLSM reduced the composite objective by 49.27% relative to PSO-SLSM in the repeated-run analysis (two-sided paired t-test, Holm-adjusted p < 0.001; Cohen’s dz = 2.27), whereas PSO-SLSM did not significantly outperform FCFS-SLSM. Sensitivity analyses further show that DLSM performance is conditional on cross-over handling efficiency, the penalty assigned to indirect transshipment, and binding quay-crane capacity. The evidence therefore attributes the observed improvement to the complementarity between berth search and DLSM-enabled direct transfer rather than to PSO alone. An independent-feeder-arrival stress test showed that the benefit can disappear when compatible overlaps are scarce. The framework therefore supports conditional planning-level screening, not a general performance guarantee.