Heuristics for job scheduling reoptimization

Many real-life applications involve systems that change dynamically over time. Thus, throughout the continuous operation of such a system, it is required to compute solutions for new problem instances, derived from previous instances. Since the transition from one solution to another incurs some cost, a natural goal is to have the solution for the new instance close to the original one (under a certain distance measure). We study reoptimization problems arising in scheduling systems. Formally, due to changes in the environment (out-of-order or new machines, 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 reoptimization with respect to the classical objectives of minimum makespan and minimum total flowtime. We first prove that the reoptimization variants of both problems are NP-hard, already for very restricted classes. We then develop and present several heuristics for each objective, implement these heuristics, compare their performance on various classes of instances and analyze the results.