工件加工时间是开工时间线性函数的排序博弈问题

The Bargaining Problem on Scheduling with Linear Processing Time of Its Start Time

工件加工过程中存在这样的情况:一个工件加工者无法独自完成一整批工件的加工任务,于是在排序研究中考虑多人合作共同加工一批工件的问题就应运而生了。讨论两人合作加工一批工件,每人提供一台机器用于加工,工件的加工时间是其开工时间的简单线性函数,以最小的最大完工时间为加工成本。给出最优工件划分,将工件分配给两人进行加工,让每个参与者都能获得合理的收益,从而愿意合作。

There is such a situation in workpiece processing:a processor is not able to undertake all processing jobs alone.So the new scheduling problems come into being,where many people work together to process a batch of workpieces.In this paper,we discuss the problem where two persons process a batch of workpieces by cooperation.Each person is offered a single machine and does each job with linear processing time of its start time,and his processing cost is defined as the smaller maximum makespan.An optimal division of those jobs is proposed and assigned to the two persons respectively so that each participant can get a satisfactory return and be willing to cooperate.