Irreducible Bin Packing: Complexity, Solvability and Application to the Routing Open Shop

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

1 Citation (Scopus)

Abstract

We introduce the following version of an “inefficient” bin packing problem: maximize the number of bins under the restriction that the total content of any two bins is larger than the bin capacity. There is a trivial upper bound on the optimum in terms of the total size of the items. We refer to the decision version of this problem with the number of bins equal to the trivial upper bound as Irreducible Bin Packing. We prove that this problem is NP-complete in an ordinary sense and derive a sufficient condition for its polynomial solvability. The problem has a certain connection to a routing open shop problem which is a generalization of the metric TSP and open shop, known to be NP-hard even for two machines on a 2-node network. So-called job aggregation at some node of a transportation network can be seen as an instance of a bin packing problem. We show that for a two-machine case a positive answer to the Irreducible Bin Packing problem question at some node leads to a linear algorithm of constructing an optimal schedule subject to some restrictions on the location of that node.

Original languageEnglish
Title of host publicationLearning and Intelligent Optimization - 13th International Conference, LION 13, Revised Selected Papers
EditorsNikolaos F. Matsatsinis, Yannis Marinakis, Panos Pardalos
PublisherSpringer Gabler
Pages106-120
Number of pages15
ISBN (Print)9783030386283
DOIs
Publication statusPublished - 22 Jan 2020
Event13th International Conference on Learning and Intelligent Optimization, LION 13 - Chania, Greece
Duration: 27 May 201931 May 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11968 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Conference on Learning and Intelligent Optimization, LION 13
CountryGreece
CityChania
Period27.05.201931.05.2019

Keywords

  • Bin packing to the maximum
  • Efficient normality
  • Irreducible Bin Packing
  • Job aggregation
  • Polynomially solvable subcase
  • Routing open shop
  • Superoverloaded node

Fingerprint

Dive into the research topics of 'Irreducible Bin Packing: Complexity, Solvability and Application to the Routing Open Shop'. Together they form a unique fingerprint.

Cite this