Scheduling arc shut downs in a network to maximize flow over time with a bounded number of jobs per time period
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.
KeywordsNetwork models Complexity theory Maintenance scheduling Mixed integer programming
Mathematics Subject Classification90C10 90B10 68Q25
We would like to thank two anonymous referees for valuable comments that significantly improved the presentation of our results, in particular the proof of Proposition 2. This research was supported by the ARC Linkage Grants Nos. LP0990739 and LP1102000524 and HVCCC P/L.
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