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The container relocation problem, where containers that are stored in bays are retrieved in a fixed sequence, is a crucial port operation. Existing approaches using branch and bound algorithms are only able to optimally solve small cases in a practical time frame. In this paper, we investigate iterative deepening A* algorithms (rather than branch and bound) using new lower bound measures and heuristics, and show that this approach is able to solve much larger instances of the problem in a time frame that is suitable for practical application. We also examine a more difficult variant of the problem that has been largely ignored in existing literature.