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Packing While Traveling: Mixed Integer Programming for a Class of Nonlinear Knapsack Problems

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Integration of AI and OR Techniques in Constraint Programming (CPAIOR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9075))

Abstract

Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel time. We investigate constrained and unconstrained versions of the problem and show that both are \(\mathcal {NP}\)-hard. In order to solve the problems, we provide a pre-processing scheme as well as exact and approximate mixed integer programming (MIP) solutions. Our experimental results show the effectiveness of the MIP solutions and in particular point out that the approximate MIP approach often leads to near optimal results within far less computation time than the exact approach.

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Author information

Authors and Affiliations

  1. Optimisation and Logistics School of Computer Science, The University of Adelaide, Adelaide, Australia

    Sergey Polyakovskiy & Frank Neumann

Authors
  1. Sergey Polyakovskiy
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  2. Frank Neumann
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Corresponding author

Correspondence to Sergey Polyakovskiy .

Editor information

Editors and Affiliations

  1. University of Connecticut, Storrs, Connecticut, USA

    Laurent Michel

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Polyakovskiy, S., Neumann, F. (2015). Packing While Traveling: Mixed Integer Programming for a Class of Nonlinear Knapsack Problems. In: Michel, L. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2015. Lecture Notes in Computer Science(), vol 9075. Springer, Cham. https://doi.org/10.1007/978-3-319-18008-3_23

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  • DOI: https://doi.org/10.1007/978-3-319-18008-3_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18007-6

  • Online ISBN: 978-3-319-18008-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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