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中文摘要：
考虑带有拒绝工件和机器维修区间的单机排序问题。目标是最小化被加工工件的总完工时间与被拒绝工件的总惩罚（被拒绝加工的工件需要支付拒绝惩罚）的和。这个问题是一般意义下NP难的，因此需要快速寻找满足指定精确度要求的近似解。为了能在较少的运行时间内得到该问题的较好的近似解，利用削减状态空间方法得到了一个全多项式时间近似方案（FPTAS）。该FPTAS是一个具有强多项式运行时间的较优近似方案，其时间复杂性为O（n2/e2），其中”为输入工件的个数，e〉O为任意小的实数。
英文摘要：
This paper considers a single machine scheduling problem with rejection jobs and a fixed non-availability interval. The objective is to minimize the sum of the total completion times of the scheduled jobs and the total rejection penalty of the rejected jobs（A job is rejected, in which case a rejection penalty has to be paid）. The problem is NP-hard in the ordinary sense. There- fore, we need to find an approximate solution that fulfills the required error bound. To get a better approximation solution in a polynomial running time, we propose a fully polynomial-time approximation scheme（FPTAS） by cutting states space. This FPTAS is a better approximation algorithm and its running time is strongly polynomial, which running time is O（n2/e2 ）.
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