A Decomposition Method for the Group-Based Quay Crane Scheduling Problem

This study addresses the quay crane scheduling problem (QCSP), which involves scheduling a fixed number of quay cranes to load and unload containers from ships in a maritime container terminal. The objective is to minimize the completion time while adhering to precedence, safety margin, and noncrossing constraints. Efficient scheduling of quay cranes plays a crucial role in reducing the time vessels spend at terminals. To solve the QCSP, we explore different schedule directions for the quay cranes. Specifically, we consider three directions: unidirectional, where the quay cranes maintain a consistent movement direction from upper to lower bays or vice versa after initial repositioning; bidirectional, allowing the cranes to change direction once during operations; and multidirectional, permitting freely changing movement direction during operations. For the bidirectional QCSP, we propose a new compact mathematical formulation. To obtain valid lower bounds on the optimal completion time, we derive various relaxations of this new formulation based on the different schedule directions. Our solution framework employs logic-based Benders decomposition, decomposing the problem into an assignment master problem and operation-sequence slave subproblems. Extensive computational experiments using benchmark instances from existing literature and newly generated instances validate the efficiency and effectiveness of the lower bounds and the exact solution approach.