In this paper we consider a resource-constrained scheduling problem on two parallel dedicated machines with given fixed processing sequences of jobs assigned to each one of the machines. The problem is to determine the starting times of all jobs, subject to the resource constraint, in order to minimize some given performance measure. Lin et al. (J Sched 19(2):153–163, 2016) showed that the problem is NP-hard in the ordinary sense under the performance measures of weighted total tardiness and weighted number of tardy jobs, and questioned the existence of approximation schemes. In this paper we answer their question in the affirmative by designing fully polynomial time approximation schemes.

在本文中，我们考虑了两台并行专用机器上的资源受限调度问题，其中给定分配给每台机器的作业的固定处理序列。问题是在资源约束下确定所有作业的开始时间，以最小化某些给定的性能度量。林等人。(J Sched 19(2):153–163, 2016) 表明，在加权总延迟和加权延迟作业数的性能度量下，该问题是普通意义上的 NP-hard，并质疑近似方案的存在。在本文中，我们通过设计完全多项式时间近似方案来肯定地回答他们的问题。