We analyze a recently introduced concept, called the price of clustering, for variants of bin packing called open-end bin packing problems (OEBP). Input items have sizes, and they also belong to a certain number of types. The new concept deals with the comparison of optimal solutions for the cases where items of distinct types can and cannot be packed together, respectively. The problem is related to greedy bin packing algorithms and to batched bin packing, and we discuss some of those concepts as well. We analyze max-OEBP, where a packed bin is valid if by excluding its largest item, the total size of items is below 1. For this variant, we study the case of general item sizes, and the parametric case with bounded item sizes, which shows the effect of small items. Finally, we briefly discuss min-OEBP, where a bin is valid if the total size of its items excluding the smallest item is below 1, which is known to be an entirely different problem.

翻译：我们分析了最近采用的概念,即所谓开放端包装问题(OEBP)的组合价格。输入项有大小,它们也属于一定种类。新概念涉及对不同类型物品能够和不能一起包装的个案的最佳解决办法进行比较。问题与贪婪的包装包装算法和分批包装包装有关,我们也讨论其中的一些概念。我们分析了最大-OEBP,如果通过排除其最大项目,包装箱是有效的,那么包装箱的总尺寸低于1。对于这个变量,我们研究了一般项目大小的事例,以及约束项目大小的参数案例,这显示了小项目的效果。最后,我们简要讨论了小项目的效果。如果其不包括最小项目的总尺寸低于1,那么一个硬盘是有效的,众所周知,这是一个完全不同的问题。