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

TL;DR

This paper investigates scheduling arc maintenance in a network to maximize total flow over multiple periods, introducing a constraint on the maximum number of maintenance jobs per period and analyzing its effect on problem complexity.

Contribution

It proposes a new constraint limiting maintenance jobs per period and studies its impact on the NP-hardness of the network flow scheduling problem.

Findings

Adding a limit on maintenance jobs per period affects problem complexity.

The problem remains NP-hard under the new constraint.

Insights into special cases where the problem might be tractable.

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.