In this paper, we are interested in minimizing the maximal or total cost of jobs in a permutation flowshop. This problem is known to be strongly NP-hard and exact algorithms of practical interest to solve it have very high, often factorial, worst-case complexity bounds. From a more theoretical point of view, we describe an Inclusion–Exclusion-based exact algorithm with a moderate exponential time and a pseudopolynomial space worst-case complexity bound for a fixed number of machines. We discuss extensions of this algorithm for job precedence constraints, with moderate exponential space and time bounds.

中文翻译：

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使用包含 - 排除的置换流水车间调度问题的中等最坏情况复杂性界限

在本文中，我们感兴趣的是最小化排列流水车间中工作的最大或总成本。众所周知，这个问题具有很强的 NP-hard 和实际意义的精确算法来解决它具有非常高的、通常是阶乘的、最坏情况的复杂性界限。从更理论的角度来看，我们描述了一种基于包含-排除的精确算法，它具有适中的指数时间和伪多项式空间最坏情况复杂度，适用于固定数量的机器。我们讨论了该算法对工作优先约束的扩展，具有适度的指数空间和时间界限。