总完工时间排序两人合作博弈的纳什博弈解 (运筹学与控制论)

研究合作加工一批工件,加工成本由最小的总完工时间决定的两台机器合作博弈问题。每一方都有一台机器用于加工工件,每个工件只需在两台机器中任何一台加工一次,而且加工时间都相等。要确定这批工件的一个划分以把这些工件分给这两台机器加工,使得相应的合作(加工)收益分配合理、能够被双方接受。本文研究在相同工件的情况下,以最小完工时间作为加工成本的两人合作博弈问题,并给出此合作博弈问题的纳什博弈解。

The Nash Bargaining Solution(s) of Two-Person Cooperative Games on Total Completion Time Scheduling

This paper considers a(two-party) Nash bargaining problem involving job scheduling.In this problem,each party can only offer one machine to process jobs so that the cooperation between them is necessary.It implies two parties should first negotiate a reasonable partition of all the jobs to make the corresponding cooperative(processing) profit allocation scheme,i.e.the bargaining solution,acceptable to each party.This paper derives the Nash bargaining solution(s) of the case where the processing time of each job is the same and each party’s processing cost is determined by his total completion time.