An algorithm for multi-agent scheduling to minimize the makespan on m parallel machines

Abstract

This paper considers a multi-agent scheduling problem, in which each agent has a set of non-preemptive jobs, and jobs of all agents are to be processed on m identical parallel machines. The objective is to find a schedule to minimize the makespan of each agent. For an agent, the definition of $$\alpha $$ point is introduced, based on which an approximation algorithm is proposed for the problem. In the obtained schedule, the agent with the ith smallest $$\alpha $$ point value is the ith completed agent, and the agent’s completion time is at most $$i+ \left( \frac{1}{3}-\frac{1}{3m}\right) $$ times its minimum makespan. Finally, we show the performance analysis is tight.