误工工件个数和最大费用函数的单机双代理KS公平定价问题  

Kalai-Smorodinsky Price of Fairness in Two-Agent Single-Machine Scheduling Problem to Minimize the Number of Tardy Jobs and Maximum Cost Function

作　　者：张新功 刘甲玉[2] 崔同欣 ZHANG Xingong;LIU Jiayu;CUI Tongxin(College of Mathematics Sciences,Chongqing Normal University,Chongqing 401331;Henan College of Transportation,Zhengzhou 450000,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]河南交通职业技术学院,郑州450000

出　　处：《重庆师范大学学报（自然科学版）》2020年第1期16-21,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11571321,No.715610007);重庆市研究生教育教学改革研究重点项目(No.yjg182019);重庆市科学技术委员会基础研究与前沿探索项目(No.cstc2018jcyjAX0631)。

摘　　要：【目的】考虑把资源分配的公平价格问题应用到单机双代理排序中,这里的双代理就是两个代理具有各自的工件集,公平竞争的安排在单台机器上加工自己的工件。【方法】第一个代理的目标函数为在共同工期的前提下最小化总权误工工件个数,第二个代理的目标是为最小化最大费用函数。【结果】给出公平效用的概念和KS公平定价的概念,进而给出了一般情况下KS的价格公平结构性之和紧界分析。【结论】推广了已有文献的结果。[Purposes]It solves Kalai-Smorodinsky fairness on a two-agent single machine.[Methods]It presents a definition of utility function of each agent,and the convex combination of system utility function:u^A+αu^B,where u^A and u^B are the utility of agent A and agent B,α>0.It defines Kalai-Smorodinsky fair solutions and shows two results of price of fairness by analyzing the relation between the processing time of agent B and the common due date of agent A.It considers the situation where one agent aims at minimizing the number of tardy jobs with respect to a common due date for her jobs,while the other seeks to minimize the maximum cost function.[Findings]Kalai-Smorodinsky fair solutions are α/1+α or 1/1+α.Furthermore,Kalai Smorodinsky fair solution is 1/2 if α=1.[Conclusions]It shows two results of price of fairness.

关 键 词：排序 双代理 公平定价 效用函数 

分 类 号：O223[理学—运筹学与控制论]