Double-cycling problem is motivated in quay crane scheduling practice at container ports, where a quay crane is enabled to simultaneously unload and load one container in a cycle. As container vessels are generally equipped with hatch covers, which induce precedence constraints. Regarding the impact of hatch covers, this paper proposes models and algorithm for the general double-cycling problem with internal-reshuffles, where reshuffle containers are allowed to move directly from one stack to another. As there is no exact solution to double-cycling problem with internal reshuffles, we present a branch-and-price framework to optimally solve it.
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