Jean-Charles Billaut

Solving multi-agent scheduling problems on parallel machines with a global objective function

In this study, we consider a scheduling environment with m ( m xa0≥xa01) parallel machines.n The set of jobs to schedule is divided into K disjoint subsets. Each subset of jobs isn associated with one agent. The K agents compete to perform their jobs on commonn resources. The objective is to find a schedule that minimizes a global objective functionn f 0 , while maintaining the regularn objective function of each agent, f k , at a level non greater than a fixed value, e k ( f k ∈ { f k max , ∑ f k }, k = 0, ..., K ). This problem is a multi-agent schedulingn problem with a global objective function . In this study, we consider the casen with preemption and the case without preemption. If preemption is allowed, we propose an polynomial time algorithm based on a network flow approach for the unrelated paralleln machine case. If preemption is not allowed, we propose some general complexity results andn develop dynamic programming algorithms.