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A probabilistic model toward a permutation flowshop scheduling problem with imperfect jobs

机译：具有不完善作业的置换流水车间调度问题的概率模型

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This article addresses a permutation flowshop scheduling problem with rework activities. The concept of a reworkable job here means that a job on a machine may need more than one operation to reach a predefined quality level, stochastically. Therefore in this configuration, processing times become random variables with a known probability distribution. The objective function is the minimization of the expected makespan. The solution mechanism is based on using mathematical expectations of processing times in order to find a job sequence by solving a mixed integer mathematical model, then assessing the makespan of the obtained sequence by running several simulated trials and reporting the mean value. In other words, a flowshop scheduling problem with stochastic processing times on machines is considered in this article, and the solution approach merges a mixed integer programming model and simulation. Finally a comprehensive, randomly generated example is presented for verifying the proposed problem. According to the results, the existence of reworkable jobs in a flowshop scheduling problem can change the optimum job sequence when minimization of the makespan is assumed.
机译：本文解决了带有返工活动的置换Flowshop调度问题。可重做作业的概念在此意味着，机器上的作业可能需要多次操作才能随机达到预定的质量水平。因此，在该配置中，处理时间成为具有已知概率分布的随机变量。目标函数是最小化预期的制造期限。解决方案机制基于使用处理时间的数学期望，以便通过求解混合整数数学模型来找到作业序列，然后通过运行几次模拟试验并报告平均值来评估获得的序列的有效期。换句话说，本文考虑了在机器上具有随机处理时间的Flowshop调度问题，并且该解决方案方法将混合整数规划模型与仿真合并在一起。最后，提供了一个综合的，随机生成的示例来验证所提出的问题。根据结果​​，当假设最小化制造期时，在流水车间调度问题中可重复工作的存在可以改变最佳工作顺序。

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