Fair scheduling on parallel batch machines with non-identical capacities

The fairness of jobs from agents is considered in an advanced manufacturing factory and the fair scheduling of jobs on parallel batch machines is studied for two competing agents. Each agent and the system aim to minimize the makespan of their own jobs and the weighted sum makespans of the two agents, respectively. A modified full-batch longest processing time (MFBLPT) algorithm is proposed to minimize the makespan, and a Kalai–Smorodinsky fairness (KSF) algorithm is proposed to obtain fair schedules. These algorithms are analysed based on worst-case ratios, and the results show that these ratios are related to the workloads and importance of agents. Computational experiments are conducted to compare the performance of algorithm KSF with that of machine-centric and agent-centric algorithms. The results show that the pursuance of fairness leads to interest losses of a system, and that a proper preference of an agent leads to good performance of algorithm KSF.