数学与统计学院知识库

本文在工件加工时间是所得到资源的函数(p_j =b_j-a_ju_j )的前提下对目标函数是最小化完工时间方差(CTV )的排序问题进行了研究.对于问题 ,通过实验和数据分析得到较优的位置分配方式是使具有最小加工时间的工件尽可能位于排序的中间,较优的资源分配方式是优先分配资源给a_j 较大的工件.当m为定值时, n越大,排序问题Pm|unres|CTV 与Pm|res|CTV  的目标函数值比值越靠近m ,并得到了三个相应的推论.针对 M_j给出了三种工件和机器的分派方式.对一台处理机和多台同速机的CTV 问题分别构造了复杂度为O(n²) 的ASMH算法和复杂度为 O(mlogm+n²)的MJ算法.

Based on the processing time of a job is a function of the resources it requires(p_j =b_j-a_ju_j  ), the article studies the scheduling problem of minimizing completion time variance . To  , we obtain the better way of position distribution is to make the job with the smallest processing time in the middle position of scheduling as far as possible , the better method of resourrce allocation is allocate resource firstly to job with the largest a_j through experiment and data analysis . Then , we give three matching types between jobs and machines for M_j  . When m  is a definite value , we obtain the larger the n , the objective function value ratio of Pm|unres|CTV and Pm|res|CTV is close to  and prove three corresponding corollaries . What’s more , this article propose the ASMH algorithm with complexity is O(n²) for single processor and the MJ algorithm with complexity is O(mlogm+n²)  for multiple identical processor .