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In this research, we focus on a container dispatching and conflict-free yard crane routing problem that arises at a storage yard in an automated, maritime container terminal. A storage yard serves as an intermediate buffer for import/export containers and exchanges containers between the waterside and landside of a maritime terminal. The considered storage yard is perpendicular to the waterside and employs two rail-mounted gantry cranes that have different sizes and thus have the possibility to cross each other. The problem at hand evaluates in which order and by which crane the import/export containers should be transported to minimize the makespan and prevent crane interferences. We solve this problem to optimality by a branch-and-cut approach that decomposes the problem into two problem classes and connects them via logic-based Benders constraints. We assess the quality of our solution method in a …