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We study the problem of scheduling maintenance on arcs of a capacitatednetwork so as to maximize the total flow from a source node to a sink node overa set of time periods. Maintenance on an arc shuts down the arc for theduration of the period in which its maintenance is scheduled, making itscapacity zero for that period. A set of arcs is designated to have maintenanceduring the planning period, which will require each to be shut down for exactlyone time period. In general this problem is known to be NP-hard, and severalspecial instance classes have been studied. Here we propose an additionalconstraint which limits the number of maintenance jobs per time period, and westudy the impact of this on the complexity.

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