In maritime operations, ballast water operations and cargo handling operations are carried out simultaneously to determine the operational efficiency of vessels in port. However, the ballast water pumping rate lags behind the growing efficiency of bulk cargo handling, resulting in operational interruptions and extended stay times at ports. To address this challenge, this paper introduces a novel ballast water management strategy: vessels first handle a portion of their cargo and then shift to a lay-by berth for mid-pumping. This strategy results in multiple shifting movements of vessels within the berth allocation plan. Therefore, to better implement this strategy, we develop an integrated model of berth allocation and ballast water pumping management, with the special considerations of multi-berth shifting strategies and ballast water weight. To efficiently solve this model, we present a hybrid heuristic algorithm based on adaptive genetic algorithms and the critical path method. The computer experiments reveal that the mid-pumping strategy effectively circumvents untimely pumping, shortens the vessel port stay time, and yields a 9.42% reduction in the total stay time. This research further elucidates managerial insights to inform and enhance port operations.