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Analysis of Integer Programming Model of Academic Load Distribution

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

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Abstract

The bicriteria problem of academic load distribution (ALD) and its integer linear programming (ILP) model are considered. Earlier it was shown that the search for a feasible solution to this problem is NP-hard and the cardinality of the complete set of alternatives is polynomial. For the ALD problem, the problem of finding a Pareto-optimal solution can be formulated as a weighted bin packing problem with color constraints and lower bounds on the load of the bins. In this problem, the number of bins is given and items have volume and color. For each bin, there is an upper bound on the number of different colors and this bound depends on the bin volume. For each item, coefficients of the efficiency of placing in any bin are set. In this paper, we study the ILP model for finding a Pareto-optimal solution. Parametric families of ALD instances are constructed and the L-coverings of these instances are studied. These instances have a small duality gap, in particular, it can be equal to one. We investigate the complexity of solving these families by the Land and Doig algorithm for some known branching rules. It is shown, that the iterations number grows exponentially with the number of bins.

Supported by the program of fundamental scientific researches of the SB RAS No. I.5.1., project No. 0314-2019-0019.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Lidia Zaozerskaya

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  1. Lidia Zaozerskaya
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Correspondence to Lidia Zaozerskaya .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

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Zaozerskaya, L. (2019). Analysis of Integer Programming Model of Academic Load Distribution. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_21

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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