This paper addresses the optimization of container unloading and loading operations at ports, integrating quaycrane dual-cycling (QCDC) with dockyard rehandle minimization. We present a unified model encompassing both operations: ship container unloading and loading by quay crane, and the other is reducing dockyard rehandles while loading the ship. We recognize that optimizing one aspect in isolation can lead to suboptimal outcomes due to interdependencies. Specifically, optimizing unloading sequences for minimal operation time may inadvertently increase dockyard rehandles during loading and vice versa. To address this NP-hard problem, we propose a hybrid genetic algorithm (GA) QCDC-DR-GA comprising 1dimensional and 2-dimensional GA components. Our model, QCDC-DR-GA, consistently outperforms four state-of-the-art methods in maximizing dual cycles and minimizing dockyard rehandles. Compared to those methods, it reduced 15-20% of total operation time for large vessels. Results underscore the inefficiency of separately optimizing QCDC and dockyard rehandles. Fragmented approaches, such as QCDC Scheduling Optimized by bi-level GA and GA-ILSRS (Scenario 2), show limited improvement compared to QCDC-DR-GA. As in GA-ILSRS (Scenario 1), neglecting dual-cycle optimization leads to inferior performance than our proposed QCDC-DR-GA.