After a natural disaster such as a hurricane or flooding, the navy can help by bringing supplies, clearing roads, and evacuating victims. If destinations cannot be reached over land, resources can be transported using smaller ships and helicopters, called connectors. To start aid on land as soon as possible this must be done efficiently. In the ship-to-shore problem, trips with their accompanying resources are determined while minimising the makespan. Limited (un)loading capacities, heterogeneous connector characteristics and constraints posed by priority of the resources and grouping of the resources (resource sets) all require that the connector trips are carefully coordinated. Despite the criticality of this coordination, existing literature does not consider resource sets and has only developed heuristics. We provide a formulation that incorporates resource sets and develop (i) an exact branch-and-price algorithm and (ii) a tailored greedy heuristic that can provide upper bounds. We find that 84% of our 98 practical instances terminate within an hour in on average 80 s. Our greedy heuristic can find optimal solutions in two-thirds of these instances, mostly for instances that are very constrained in terms of the delivery order of resources. When improvements are found by the branch-and-price algorithm, the average gap with the makespan of the greedy solution is 40% and, in most cases, these improvements are obtained within three minutes. For the 20 artificial instances, the greedy heuristic has consistent performance on the different types of instances. For these artificial instances improvements of on average 35% are found in reasonable time.

中文翻译：

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船到岸问题的精确启发式方法


飓风或洪水等自然灾害发生后，海军可以提供物资、清理道路和疏散受害者等方式提供帮助。如果无法通过陆地到达目的地，可以使用较小的船只和直升机（称为连接器）运输资源。为了尽快启动陆地援助，必须有效地完成。在船到岸问题中，确定行程及其伴随资源，同时最小化完工时间。有限的（卸载）加载能力、异构连接器特性以及资源优先级和资源（资源集）分组所造成的约束都要求仔细协调连接器行程。尽管这种协调至关重要，但现有文献并未考虑资源集，而仅开发了启发式方法。我们提供了一个包含资源集的公式，并开发了（i）精确的分支和价格算法和（ii）可以提供上限的定制贪婪启发式算法。我们发现 98 个实际实例中有 84% 在平均 80 秒内在一小时内终止。我们的贪婪启发式可以在三分之二的实例中找到最佳解决方案，主要是对于资源交付顺序非常有限的实例。当分支与价格算法发现改进时，与贪婪解决方案的完工时间的平均差距为 40%，并且在大多数情况下，这些改进在三分钟内获得。对于 20 个人工实例，贪婪启发式在不同类型的实例上具有一致的性能。对于这些人工实例，在合理的时间内平均可以实现 35% 的改进。