Abstract

The paired job scheduling problem seeks to schedule n jobs on a single machine, each job consisting of two tasks for which there is a mandatory minimum waiting time between the completion of the first task and the start of the second task. We provide complexity results for problems defined by three commonly used objective functions. We propose an integer programming formulation based on a decision diagram decomposition that models the objective function and some of the challenging constraints in the space of the flow variables stemming from the diagrams while enforcing the simpler constraints in the space of the original scheduling variables. We then show how to simplify our reformulation by projecting out a subset of the flow variables, resulting in a lifted reformulation for the problem that can be obtained without building the decision diagrams. Computational results show that our proposed model performs considerably better than a standard time-indexed formulation over a set of randomly generated instances.

摘要

配对作业调度问题寻求调度n单台计算机上的多个作业，每个作业由两个任务组成，在第一个任务完成与第二​​个任务开始之间必须有最短的强制等待时间。对于三个常用目标函数定义的问题，我们提供了复杂性结果。我们基于决策图分解提出一种整数规划公式，该模型对目标函数和源自图的流量变量空间中的一些具有挑战性的约束建模，同时在原始调度变量的空间中实施更简单的约束。然后，我们展示了如何通过投影流变量的子集来简化重构，从而提高了无需构建决策图即可获得的问题的重构。