Reoptimization of the minimum total flow-time scheduling problem

•We consider dynamic systems that are modified along time.•We combine the objective of minimum total flow-time with the objective of minimizing the transition cost to a new configuration.•The goal can be either achieving an optimal solution using the minimal possible transition cost, or achieving the best possible solution using a given limited budget for the transition.•We provide optimal algorithms to various classes of these reoptimization problems.

We consider reoptimization problems arising in dynamic scheduling environments, such as manufacturing systems and virtual machine managers. Due to changes in the environment (out-of-order or new resources, modified jobs’ processing requirements, etc.), the schedule needs to be modified. That is, jobs might be migrated from their current machine to a different one. Migrations are associated with a cost – due to relocation overhead and machine set-up times. In some systems, a migration is also associated with job extension. The goal is to find a good modified schedule, with a low transition cost from the initial one. We consider the objective of minimizing the total flow-time.We present optimal algorithms for the problem of achieving an optimal solution using the minimal possible transition cost. The algorithms and their running times depend on our assumptions on the instance and the allowed modifications. For the modification of machines’ addition, we also present an optimal algorithm for achieving the best possible schedule using a given limited budget for the transition.