Journal of Combinatorial Optimization

, Volume 32, Issue 3, pp 885–905 | Cite as

Scheduling arc shut downs in a network to maximize flow over time with a bounded number of jobs per time period

  • Natashia Boland
  • Thomas Kalinowski
  • Simranjit Kaur
Article

Abstract

We study the problem of scheduling maintenance on arcs of a capacitated network so as to maximize the total flow from a source node to a sink node over a set of time periods. Maintenance on an arc shuts down the arc for the duration of the period in which its maintenance is scheduled, making its capacity zero for that period. A set of arcs is designated to have maintenance during the planning period, which will require each to be shut down for exactly one time period. In general this problem is known to be NP-hard, and several special instance classes have been studied. Here we propose an additional constraint which limits the number of maintenance jobs per time period, and we study the impact of this on the complexity.

Keywords

Network models Complexity theory Maintenance scheduling Mixed integer programming 

Mathematics Subject Classification

90C10 90B10 68Q25 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Natashia Boland
    • 1
    • 2
  • Thomas Kalinowski
    • 1
  • Simranjit Kaur
    • 1
  1. 1.University of NewcastleNewcastleAustralia
  2. 2.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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