Abstract This paper addresses the problem of scheduling a set of jobs that are released over the time on a set of identical parallel machines, aiming at the minimization of the total weighted completion time. This problem, referred to as P | r j | ∑ w j C j , is of great importance in practice, because it models a variety of real-life applications. Despite its importance, the P | r j | ∑ w j C j has not received much attention in the recent literature. In this work, we fill this gap by proposing mixed integer linear programs and a tailored branch-and-price algorithm. Our branch-and-price relies on the decomposition of an arc-flow formulation and on the use of efficient exact and heuristic methods for solving the pricing subproblem. Computational experiments carried out on a set of randomly generated instances prove that the proposed methods can solve to the proven optimality instances with up to 200 jobs and 10 machines, and provide very low gaps for larger instances.

中文翻译：

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通过最小化总加权完成时间，在相同的并行机上安排具有发布日期的作业

摘要 本文解决了在一组相同的并行机上调度随时间释放的一组作业的问题，旨在最小化总加权完成时间。这个问题，简称P| rj | ∑ wj C j 在实践中非常重要，因为它模拟了各种现实生活中的应用。尽管它很重要，P | rj | ∑ wj C j 在最近的文献中没有受到太多关注。在这项工作中，我们通过提出混合整数线性程序和定制的分支和价格算法来填补这一空白。我们的分支和价格依赖于弧流公式的分解以及使用有效的精确和启发式方法来解决定价子问题。