Integrated Continuous Berth Allocation and Time-Invariant Specific Quay Crane Assignment: A Mixed-Integer Model and a Greedy Genetic Algorithm

Efficient coordination of berth and quay crane resources is essential for improving the operational performance of container terminals under increasing vessel traffic and limited shoreline capacity. This paper studies an integrated optimization problem that combines continuous berth allocation with specific quay crane assignment. Unlike studies that determine only the number of quay cranes assigned to each vessel, the present work explicitly determines the identities of assigned quay cranes while considering practical operational constraints, including continuous berth positions, ship-specific crane quantity limits, contiguous crane assignment, vessel non-overlap, and crane non-crossing requirements. A mixed-integer programming model is formulated with the objective of minimizing the total time that vessels spend in port. Since exact optimization becomes computationally expensive as the problem size increases, a greedy genetic algorithm (GGA) is developed to obtain high-quality feasible solutions within limited computational time. The proposed algorithm combines greedy initialization with a feasibility-repair procedure for offspring generated during crossover and mutation, thereby improving feasibility maintenance during the evolutionary search process. Computational experiments are conducted using real operational data collected from a container port in Liaoning, China, together with synthetic instances of different scales. The results indicate that the proposed method provides better average solution quality and higher stability than a standard genetic algorithm while maintaining competitive computational efficiency. For medium- and large-scale instances, the proposed GGA can generate high-quality feasible schedules within practical time limits, which supports its potential applicability to real-world port operations.