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

  • Sergey PolyakovskiyEmail author
  • Frank Neumann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Non-linear knapsack problem NP-hardness Mixed integer programming Linearization technique Approximation technique 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Optimisation and Logistics School of Computer ScienceThe University of AdelaideAdelaideAustralia

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