We propose a Boolean Linear Programming model for the preemptive single machine scheduling problem with equal processing times, arbitrary release dates and weights(priorities) minimizing the total weighted completion time. Almost always an optimal solution of the Linear Programming relaxation is integral and can be straightforwardly converted into an optimal schedule. To deal with the fractional solutions we present two heuristics. Very often our heuristics find solutions with objective function values equal to the lower bound found by the Linear Programming relaxation. For the cases when upper bound returned by our heuristics differs from the lower bound we embed the bounds into a Branch and Bound algorithm, which solves the problem to optimality. Exhaustive computational study showed that the algorithm substantially surpasses state-of-the-art methods.

翻译：我们为先发制人的单一机器排期问题提出了一个布尔兰线性编程模式,处理时间相同,任意发布日期和重量(优先)最大限度地减少总加权完成时间,几乎总是线性编程放松的最佳解决办法是不可分割的,可以直接转换为最佳时间表。为了处理分数解决方案,我们提出了两种休眠法。我们的休眠法往往会找到与线性编程放松的较低约束值相等的客观功能值解决方案。对于由我们的超重调返回的上限值与我们将界限嵌入分支和伯德算法的较低约束值不同的情况,而后者能解决问题,使其达到最佳性。精度计算研究表明,算法大大超过最先进的方法。