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International Conference on Learning and Intelligent Optimization

LION 2019: Learning and Intelligent Optimization pp 106–120Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11968))

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.

This research was supported by the program of fundamental scientific researches of the SB RAS No. I.5.1., project No. 0314-2019-0014, by the Russian Foundation for Basic Research, projects 17-01-00170 and 18-01-00747, and by the Russian Ministry of Science and Education under the 5–100 Excellence Programme.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Koptyug Avenue 4, Novosibirsk, 630090, Russia

    Ilya Chernykh & Artem Pyatkin

  2. Novosibirsk State University, Pirogova Street 2, Novosibirsk, 630090, Russia

    Ilya Chernykh & Artem Pyatkin

  3. Novosibirsk State Technical University, Marksa Avenue 20, Novosibirsk, 630073, Russia

    Ilya Chernykh

Authors
  1. Ilya Chernykh
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  2. Artem Pyatkin
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Correspondence to Ilya Chernykh .

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Editors and Affiliations

  1. Technical University of Crete, Chania, Greece

    Nikolaos F. Matsatsinis

  2. Technical University of Crete, Chania, Greece

    Yannis Marinakis

  3. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Chernykh, I., Pyatkin, A. (2020). Irreducible Bin Packing: Complexity, Solvability and Application to the Routing Open Shop. In: Matsatsinis, N., Marinakis, Y., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 2019. Lecture Notes in Computer Science(), vol 11968. Springer, Cham. https://doi.org/10.1007/978-3-030-38629-0_9

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