The mixed no-idle flowshop scheduling problem arises in modern industries including integrated circuits, ceramic frit and steel production, among others, and where some machines are not allowed to remain idle between jobs. This paper describes an exact algorithm that uses Benders decomposition with a simple yet effective enhancement mechanism that entails the generation of additional cuts by using a referenced local search to help speed up convergence. Using only a single additional optimality cut at each iteration, and combined with combinatorial cuts, the algorithm can optimally solve instances with up to 500 jobs and 15 machines that are otherwise not within the reach of off-the-shelf optimization software, and can easily surpass ad-hoc existing metaheuristics. To the best of the authors’ knowledge, the algorithm described here is the only exact method for solving the mixed no-idle permutation flowshop scheduling problem.

中文翻译：

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混合无空闲置换流水车间调度问题的 Benders 分解

混合无空闲流水车间调度问题出现在包括集成电路、陶瓷熔块和钢铁生产等在内的现代工业中，并且不允许某些机器在作业之间保持空闲状态。本文描述了一种精确算法，该算法使用 Benders 分解和简单而有效的增强机制，该机制需要通过使用参考局部搜索来生成额外的切割来帮助加速收敛。在每次迭代中仅使用一个额外的优化切割，并结合组合切割，该算法可以优化解决多达 500 个作业和 15 台机器的实例，否则这些实例是现成的优化软件无法实现的，并且可以轻松地超越临时现有的元启发式。据作者所知，