In this study, we consider a scheduling environment with m(m ≥ 1) parallel machines.
The set of jobs to schedule is divided into K disjoint subsets. Each subset of jobs is
associated with one agent. The K agents compete to perform their jobs on common
resources. The objective is to find a schedule that minimizes a global objective function
f0, while maintaining the regular
objective function of each agent, fk, at a level no
greater than a fixed value, εk
(fk ∈ {fkmax,
∑fk}, k = 0, ..., K). This problem is a multi-agent scheduling
problem with a global objective function. In this study, we consider the case
with preemption and the case without preemption. If preemption is allowed, we propose a
polynomial time algorithm based on a network flow approach for the unrelated parallel
machine case. If preemption is not allowed, we propose some general complexity results and
develop dynamic programming algorithms.