运筹学学报 ›› 2010, Vol. 14 ›› Issue (4): 112-120.

• 运筹学 • 上一篇    下一篇

带任意个松弛量的四元行偶最优化决策

王晶, 李星梅, 乞建勋   

  • 出版日期:2010-12-15 发布日期:2010-12-15

 The Optimization of Four Ordinal Activities Pairs with Random Slack

WANG Jing, LI Xing-Mei, QI Jian-Xun   

  • Online:2010-12-15 Published:2010-12-15

摘要: 从\emph{n}个平行工序中选出2\emph{m}个工序调整为对总工期影响最小的\emph{n}个顺序工序对是一类典型的资源限制项目排序问题. 为了给该类问题的解决提供理论依据和方法,本文针对如何从\emph{n}个平行工序中选出八个工序调整为四个顺序工序对的最优化决策问题,结合序偶亏值定理、行偶亏值定理、标准行偶定理和规范行偶定理给出最佳行偶定理,并以此为基础提出标准规范法,分析其正确性. 最后,通过算例实现对算法的应用.

Abstract: It is one of resource constrained project scheduling problems, which selecting 2\emph{m} activities from \emph{n} parallel activities to make \emph{m} ordinal activities pairs and minimize the affection on the project duration. In order to provide theories and methods for such problem, in this paper, we study the optimization problem that how to select eight parallel activities from \emph{n} ones to make four ordinal activities pairs. Based on present theory, optimal row-mate theorem is given, and founded on them, standard-criterion algorithm is designed and proved theoretically. Finally, an example is given to illustrate the feasibility of the algorithm.