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运筹学学报 ›› 2010, Vol. 14 ›› Issue (1): 31-36.

• 运筹学 • 上一篇    下一篇

单可变资源最小化加权完工时间和排序问题的强NP-困难性

原晋江, 王勤   

  • 出版日期:2010-03-15 发布日期:2010-03-15

Strong NP-hardness of the Single-variable-resource Scheduling Problem to Minimize the Total Weighted Completion Time

Yuan-Jin-Jiang, WANG Qin   

  • Online:2010-03-15 Published:2010-03-15

摘要： Baker和Nuttle提出了下述单可变资源排序问题：n个工件利用某个单资源进行加工使得工件的完工时间的某个函数达到最小，而资源的可利用率是随着时间而变化的.当最小化的目标函数是工件的加权完工时间和时，Baker和Nuttle猜测该问题是NP-困难的.最近，Yuan、Cheng 和 Ng 证明该问题在一般意义下是NP-困难的，但是问题的精确复杂性仍然是悬而未决的.本文我们证明了该问题是强NP-困难的.

Abstract: Baker and Nuttle studied the following single-variable-resource scheduling problem: sequencing n jobs for processing by a single resource to minimize a function of job  completion times, when the availability of the resource varies over time.  When the objective function to be minimized is the total weighted completion time,   Baker and Nuttle conjectured that the problem is NP-hard. Recently, Yuan, Cheng and Ng   showed that this problem is NP-hard in the binary sense, but the   exact complexity of the problem is still open. We show in this paper  that this problem is strongly NP-hard.