基于加权总完工时间的两人合作排序博弈  

Two-person Cooperative Scheduling Games on Weighted Total Completion Time

作　　者：邱言玲 高淑萍[1] 张宝玉[1] 

机构地区：[1]西安电子科技大学数学与统计学院,西安710071

出　　处：《重庆师范大学学报（自然科学版）》2014年第6期9-15,共7页Journal of Chongqing Normal University:Natural Science

摘　　要：现实活动中,往往存在一方无法独自完成一个项目中全部工件加工任务的情况,这就需要双方或者多方合作共同完成任务。假设每人有一台用于加工工件的机器,通过确定这批工件的一个恰当划分,把工件分配给两台机器,使得双方合作收益最大。本文研究当工件加工时间是其开工时间线性恶化函数,以最小的加权总完工时间作为加工成本,建立两人合作排序博弈模型。通过运用Matlab软件,分析不同的盈利能力和机会成本对最优解的影响,并与以总完工时间作为加工成本的模型进行比较,表明本文模型在盈利能力不强以及恶化因子小的情况下都可以求得最优解。In the real activities, there are circumstances that one party is not able to undertake all the jobs alone in a large project. This paper specifically supposes two parties, each of whom offers a single machine to process jobs, cooperate in the performance of a project. A division of those jobs should be negotiated to yield a reasonable cooperative profit allocation scheme acceptable to them. This is a two-person cooperative scheduling game. The processing time of each job is a linear deteriorating function of its start time. And the processing cost is determined by his minimized total weighted total completion time. By Matlab software, the influence of profitability and opportunity cost for optimal solution is discussed. Besides, compared with the model which processing cost is the total completion time, examples illustrate that this model is much useful when the profit ability is not strong and deterioration factor is small.

关 键 词：排序博弈 线性恶化 加权总完工时间 

分 类 号：O221.7[理学—运筹学与控制论]