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

Abstract

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 f 0 , while maintaining the regular objective function of each agent, f k , at a level no greater than a fixed value, e k ( f k ∈ { f k max , ∑ f k }, 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.