More on ordered open end bin packing

János Balogh, Leah Epstein, Asaf Levin

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)589-614
Number of pages26
JournalJournal of Scheduling
Issue number6
StatePublished - Dec 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Approximation scheme
  • Bin packing
  • Online algorithms

ASJC Scopus subject areas

  • Software
  • General Engineering
  • Management Science and Operations Research
  • Artificial Intelligence


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