Scheduling two interfering job sets on identical parallel machines with makespan and total completion time minimization

Abstract

We consider a two-agent scheduling problem with interfering job sets. Agent A—which can be considered as the resource manager—is associated with the whole set of jobs, and agent B—which can be considered as an application master—is associated with a subset of jobs. Each agent aims at minimizing either the maximum or the total completion time of its jobs. Considering an identical parallel machines environment, the goal is to find an assignment and a schedule of jobs which represents the best compromise between the requirements of the agents. The class of multi-agent scheduling problems has drawn a significant interest to researchers in the area of scheduling and operational research. When both agents minimize the makespan, we prove that the number of Pareto solutions is bounded and we show that this bound is reached. Using the \(\varepsilon \)-constraint approach, we propose two integer programming formulations that allow to obtain the exact Pareto front for each problem. Given that the studied problems are NP-hard, we propose genetic algorithms (NSGA-II) to generate approximated Pareto fronts. Computational experiments are conducted to analyze the performances of the proposed methods. The results indicate that the genetic algorithms provide high-quality Pareto fronts and are computationally efficient.