含释放时间的单机模糊调度问题  

Single machine fuzzy scheduling problem with release dates

作　　者：李凯[1,2] 张勋[1] 孙秋景[1] 王明星[1] 

机构地区：[1]合肥工业大学管理学院,安徽合肥230009 [2]合肥工业大学过程优化与智能决策教育部重点实验室,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2015年第10期1410-1416,共7页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(71471052;71101040;71131002)

摘　　要：文章研究了作业释放时间与加工时间其中一者或二者同时为区间模糊数的单机模糊调度问题,调度的目标是最小化最大完工时间。释放时间的引入,使得仅采用模糊数的加法运算无法实现对问题的求解,为此定义了区间模糊数的max运算。对于仅加工时间为区间模糊数情形,证明了ERD算法能够获得最优调度方案。若释放时间为区间模糊数,无论加工时间是否模糊,问题均无法构建ERD算法,因此基于决策者的不同偏好构建了乐观算法OERD和悲观算法PERD。证明了OERD获得的最大完工时间具有较大模糊程度,并覆盖了PERD最大完工时间的模糊区间。通过数值算例验证了理论分析的正确性,并采用事后评价的方式对各种决策方案进行了比较。This paper studies single machine scheduling problems with fuzzy release dates and/or fuzzy processing time, in which the goal is to minimize the makespan and the fuzzy numbers are described as interval fuzzy numbers. When the release dates are considered, they can not be solved only by using the fuzzy number＇s addition operation, so the max operation of interval fuzzy number is defined. It is proved that the Earliest Release Date firstly （ERD） algorithm can receive the optimal scheduling scheme under the condition that only the processing time is fuzzy. However, no matter whether the processing time is fuzzy or not, the ERD algorithm can not be constructed when the release dates are fuzzy. Therefore, Optimistic Earliest Release Date firstly（OERD） algorithm and Pessimistic Earliest Release Date firstly（PERD） algorithm are constructed according to the decision maker＇s preferences. It is proved that the fuzzy degree of the makespan of the same problem gotten by OERD is not lower than that of PERD, and covers the makespan of PERD. The validity of the theoretical analysis is veri- fied by numerical examples, and various decisions are compared with each other by the way of ex-post evaluation.

关 键 词：模糊释放时间 区间模糊数 单机 模糊调度 

分 类 号：TP301[自动化与计算机技术—计算机系统结构] O223[自动化与计算机技术—计算机科学与技术]