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首页> 外文期刊>International Journal of Computer Integrated Manufacturing >Minimising the total completion time in a single machine scheduling problem under bimodal flexible periodic availability constraints
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Minimising the total completion time in a single machine scheduling problem under bimodal flexible periodic availability constraints

机译：在双峰柔性周期性可用性约束下，使单机调度问题中的总完成时间最小化

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摘要

In many scheduling problems, machines can face availability constraints and as a result, they may stop for a while. In this paper, a novel definition for single machine scheduling problem with flexible periodic availability constraints has been provided. According to this definition, in each period, the duration of unavailability corresponding to the continuous working time of the machine changes in a discrete manner and it can adopt two different values. Therefore, such availability constraints are called bimodal availability constraints. The objective has been to minimise the total completion time. By considering the complexity issues through a mathematical model, a heuristic algorithm with the time complexity of O(nlog n) and a branch- and- bound algorithm accompanied with several lemmas and efficient dominance rules are proposed in order to solve the problems optimally. Computational results for 1680 sample problems are employed to demonstrate that the branch- and- bound algorithm is able to solve problems up to 22 jobs and the mean average error for the heuristic algorithm is 1.05%.
机译：在许多调度问题中，计算机可能会遇到可用性约束，结果，它们可能会停一会儿。在本文中，为具有灵活周期可用性约束的单机调度问题提供了一种新颖的定义。根据该定义，在每个周期中，对应于机器连续工作时间的不可用持续时间以离散的方式变化，并且可以采用两个不同的值。因此，这种可用性约束称为双峰可用性约束。目的是使总的完成时间最小化。通过数学模型考虑复杂性问题，提出了一种具有时间复杂度O（nlog n）的启发式算法和带有多个引理和有效支配规则的分支定界算法，以最优地解决这些问题。通过对1680个样本问题的计算结果证明，分支定界算法能够解决多达22个工作的问题，启发式算法的平均误差为1.05％。

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