Research On The Sorting Problem Of Two Agents And Multiple Machines Of The Same Type

The scheduling problem is widely used in the field of production management,and its purpose is to maximize the benefits of material resources,such as the resource scheduling of some large airports and production workshops.The multi-agent scheduling problem is a new kind of scheduling problem.In the multiagent scheduling problem,the artifacts or tasks belong to different agents,and different agents have different goals.For example,a cluster receives many different data requests at the same time,and these data requests belong to different agents.In fact,the application of multi-agent scheduling problem in actual production management is more extensive,and many problems can be transformed into multi-agent scheduling problems.This paper consider two-agent preemptive scheduling problem on two and three uniform machines.The speed of processing may vary and be constant for different machines.Each agent has a set of jobs.The job can be interrupted during processing.The goal of each agent is to minimize its completion time,the maximum completion time for all jobs of the agent.The objective function of the problem is a linear combination of two agent completion times.In the case of two machines.Block scheduling is first defined,then it is proved that any feasible scheduling can be converted to block scheduling.On this basis,an algorithm for optimal scheduling is designed,so we can find the optimal scheduling.Finally,the above results are extended to the case of three machines.An algorithm to solve the optimal scheduling is designed.