We consider the cyclic job shop problem with no-wait constraints which consists in minimizing the cycle time. We assume that a single product is produced on a few machines. A job is processed by performing a given set of operations in a predetermined sequence. Each operation can be performed on exactly one machine. We consider the problem of minimization the cycle time with no-wait constraints between some pairs of sequential operations and investigate the complexity of the problem and some of its subproblems. In general, the problem is proved to be strongly NP-hard. In the case when the job is processed without downtime between operations, polynomial solvability is proved and the two algorithms are proposed. Also we develop an algorithm for the general case which is pseudopolynomial if the number of admissible downtime is fixed. The case of a single no-wait constraint is polynomially solvable. The problem with two no-wait constraints becomes NP-hard. We found effectively solvable cases and propose the corresponding algorithms.

中文翻译：

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具有无等待约束的相同作业的循环作业车间调度问题的复杂性

我们考虑具有无等待约束的周期性作业车间问题，该问题在于最大程度地缩短周期时间。我们假设单个产品是在几台机器上生产的。通过以预定顺序执行给定的一组操作来处理作业。每个操作都可以在一台机器上执行。我们考虑在几对顺序操作之间使用无等待约束来最大程度地缩短周期时间的问题，并研究问题的复杂性及其子问题。通常，该问题被证明是强烈的NP难题。在处理作业而没有两次操作之间的停机时间的情况下，证明了多项式可解性，并提出了两种算法。如果允许的停机时间是固定的，我们还将开发一种针对一般情况的伪多项式算法。单个无等待约束的情况是多项式可解的。具有两个无等待约束的问题变得难以解决。我们找到了有效可解决的情况，并提出了相应的算法。