在误工工件个数最少的条件下使最大延误为最小的分支定界算法

多目标排序是研究多个优化目标的排序问题，在解决经济、管理、工程、军事和社会等领域出现的复杂问题中起着越来越重要的作用。2007年有文献证明以误工工件个数最少为第l目标、使总完工时间最小或者使总延误最小的多重目标排序问题1‖（∑Cj／∑uj）或者1‖（∑Tj／∑Uj）都是NP困难的。然而，迄今为止，对于以误工工件个数最少为第1目标、使最大延误最小的多重目标排序问题1‖（Tmax／∑Uj）的计算复杂性还不清楚。给出了这个多重目标排序问题1‖（Tmax/／∑Uj）的分支定界算法，借助几个性质，得到较好的上下界，能够较快地得到最优解。

A Branch-Bound Algorithm to Minimize the Maximum Tardiness with Minimum Number Tardy

Multi-criteria scheduling problems play more and more important roles in solving complicated problems appearing in economy, management, engineering, military affairs and society etc. In 2007, a paper proved that the two multi-criteria scheduling problems 1‖（∑Cj/∑uj） or 1‖（∑Tf/∑uj） to minimize the total completion time or the total tardiness with minimum number of tardy jobs are NP hard. However, till now, the computational complexity of the multi-criteria scheduling problem 1‖（Tmax/∑Uj） have still not been known. In this paper, the authors propose a branch-bound algorithm for the problem l1‖（Tmax/∑Uj）. They find its several properties. Through them, they get good upper and lower bounds, and so get the optimal solution more quickly.