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DOI: 10.4230/OASIcs.ATMOS.2012.58
URN: urn:nbn:de:0030-drops-37034
URL: http://drops.dagstuhl.de/opus/volltexte/2012/3703/
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König, Felix G. ; Matuschke, Jannik ; Richter, Alexander

Multi-Dimensional Commodity Covering for Tariff Selection in Transportation

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Abstract

In this paper, we study a multi-dimensional commodity covering problem, which we encountered as a subproblem in optimizing large scale transportation networks in logistics. The problem asks for a selection of containers for transporting a given set of commodities, each commodity having different extensions of properties such as weight or volume. Each container can be selected multiple times and is specified by a fixed charge and capacities in the relevant properties. The task is to find a cost minimal collection of containers and a feasible assignment of the demand to all selected containers. From theoretical point of view, by exploring similarities to the well known SetCover problem, we derive NP-hardness and see that the non-approximability result known for set cover also carries over to our problem. For practical applications we need very fast heuristics to be integrated into a meta-heuristic framework that - depending on the context - either provide feasible near optimal solutions or only estimate the cost value of an optimal solution. We develop and analyze a flexible family of greedy algorithms that meet these challenges. In order to find best-performing configurations for different requirements of the meta-heuristic framework, we provide an extensive computational study on random and real world instance sets obtained from our project partner 4flow AG. We outline a trade-off between running times and solution quality and conclude that the proposed methods achieve the accuracy and efficiency necessary for serving as a key ingredient in more complex meta-heuristics enabling the optimization of large-scale networks.

BibTeX - Entry

@InProceedings{knig_et_al:OASIcs:2012:3703,
  author =	{Felix G. K{\"o}nig and Jannik Matuschke and Alexander Richter},
  title =	{{Multi-Dimensional Commodity Covering for Tariff Selection in Transportation}},
  booktitle =	{12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{58--70},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-45-3},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{25},
  editor =	{Daniel Delling and Leo Liberti},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3703},
  URN =		{urn:nbn:de:0030-drops-37034},
  doi =		{http://dx.doi.org/10.4230/OASIcs.ATMOS.2012.58},
  annote =	{Keywords: Covering, Heuristics, Transportation, Tariff Selection}
}

Keywords: Covering, Heuristics, Transportation, Tariff Selection
Seminar: 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems
Issue Date: 2012
Date of publication: 11.09.2012


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