We consider the Ordered Open End Bin Packing problem. Items of sizes in (0, 1] are presented one by one, to be assigned to bins in this order. An item can be assigned to any bin for which the current total size is strictly below 1. This means also that the bin can be overloaded by its last packed item. We improve lower and upper bounds on the asymptotic competitive ratio in the online case. Specifically, we design the first algorithm whose asymptotic competitive ratio is strictly below 2, and its value is close to the lower bound. This is in contrast to the best possible absolute competitive ratio, which is equal to 2. We also study the offline problem where the sequence of items is known in advance, while items are still assigned to bins based on their order in the sequence. For this scenario, we design an asymptotic polynomial time approximation scheme.

我们考虑有序开放式装箱问题。大小在 (0, 1] 中的项目被一个一个地呈现，按照这个顺序分配到 bin。一个项目可以被分配到当前总大小严格小于 1 的任何 bin。这也意味着 bin 可以被它的最后一个打包项目重载。我们改进了在线情况下渐近竞争比的下限和上限。具体来说，我们设计了第一个渐近竞争比严格小于2的算法，其值接近下限。这与最好的绝对竞争比率形成对比，后者等于 2。我们还研究了离线问题，其中项目的顺序是预先知道的，而项目仍然根据它们在序列中的顺序分配到箱中。对于这个场景，