具有通用机的多组工件的Q//C_(max)问题的近似算法

研究的目的在于解决实践中对多组任务的优化排序问题,即在最短的时间内完成所有给定的任务。由于这类问题往往都是NP完全问题,人们通常寻求其近似算法。提出了一种改进的LPT算法,利用"最大相对加工时间"准则和"首先空闲"准则,讨论了将n组工件安排在n台速度不同的专用机,一台速度小于专用机的通用机上的Cmax问题,得到了利用该近似算法所得的解T与最优解T*的一个估计:T/T*≤1+1/∑i∈Isi,其中I表示在最后完工的工件完工之前,在通用机上至少安排了一个工件的工件组的下标集合。由此得出采用该近似算法对工件排序,在最差情况下要比最优排序多出1/∑i∈Isi的时间。

Heuristic Algorithm of the Q//C_(max) Problem on Multi-Tasks with Uniform Processors

To study the Cmax problem on many group jobs with one general purpose machinery and n special purpose machineries that they are with the different speeds. This problem is always NP C problem, so the approximate method is usually to be found. An improved LPT algorithm and the upper bound performance are given. The ratio of the approximate solution and the best way is T/T*≤1+1/∑〖DD(X〗i∈I〖DD)〗si, it means that the complete time using this approximate method is 1/∑〖DD(X〗i∈I〖DD)〗si more than the best in worst condition.