This paper addresses the problem of scheduling independent jobs on identical parallel machines with a single server to minimise the makespan. We propose mixed integer programming (MIP) formulations to solve this problem. Each formulation reflects a specific concept on how the decision variables are defined. Moreover, we present inequalities that can be used to improve those formulations. A computational study is performed on benchmark instances from the literature to compare the proposed MIP formulations with other known formulations from the literature. It turns out that our proposed time-indexed variables formulation outperforms by far the other formulations. In addition, we propose a very efficient MIP formulation to solve a particular case of the problem with a regular job set. This formulation is able to solve all regular instances for the case of 500 jobs and 5 machines in less than 5.27 min, where all other formulations are not able to produce a feasible solution within 1 h.

本文解决了在具有一台服务器的同一台并行计算机上调度独立作业以最大程度地缩短工期的问题。我们提出混合整数编程（MIP）公式来解决此问题。每个表述都反映了有关如何定义决策变量的特定概念。此外，我们提出了可用于改善这些公式的不平等现象。对文献中的基准实例进行了计算研究，以将建议的MIP配方与文献中的其他已知配方进行比较。事实证明，我们提出的时间索引变量公式的性能远远优于其他公式。另外，我们提出了一种非常有效的MIP公式，以解决常规作业集的特殊情况。