大规模集成电路预烧作业中分批排序问题的数学模型

分批排序(Batch Scheduling)是在半导体生产过程的最后阶段提炼出来的一类重要的排序问题。单机分批排序问题就是n个工件在一台机器上加工,要将工件分批,每批最多可以同时加工B个工件,每批的加工时间等于此批工件中的最大的加工时间。Skutella^8]1998年把平行机排序的P｜｜∑ω_jC_j和R｜｜∑ω_jC_j表述成二次的0-1整数规划,得到一些令人满意的结果;国内罗守成等^9]、张倩^10]给出了单机排序问题1｜｜∑ω_jC_j的数学规划表示,对于用数学规划来研究排序问题是一个很有意义的进展。本文首先介绍总完工时间和最小的带权单机分批排序问题1｜B｜∑ω_jC_j,然后将1｜B｜∑ω_jC_j表示成数学规划的形式,并且用数学规划中的对偶理论证明了SPT序是其特殊情况1｜B=1｜∑C_j的最优解。

Formulating the Batch Scheduling in Semiconductor Burn-in Operations as a Mathematical Programming

We study the problem of minimizing total weighted completion time on single batch processing machine.It is a problem of batch scheduling which arises in the burn in stage of semiconductor manufacturing.Burn in ovens are modeled as batch processing machines which can handle up to B jobs simultaneously.The processing time of a batch is equal to the longest processing time among the jobs in the batch.In 1998,Skutella formulated the parallel machine scheduling problem P||∑ω_jC_j and R||∑ω_jC_j as 0 1 mixed integer programming.Luo and Zhang formuated the single machine scheduling problem 1||∑ω_jC_j as mathematical programming.We first formulate the problem of minimizing total weighted completion time on single batch processing machine 1|B|∑ω_jC_j and get some conclusions.