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Minimizing the makespan on a single machine subject to modular setups
Journal of Scheduling ( IF 2 ) Pub Date : 2021-09-14 , DOI: 10.1007/s10951-021-00704-8
Dirk Briskorn 1 , Konrad Stephan 2 , Nils Boysen 2
Affiliation  

Single machine scheduling with sequence-dependent setup times is one of the classical problems of production planning with widespread applications in many industries. Solving this problem under the min-makespan objective is well known to be strongly NP-hard. We consider a special case of the problem arising from products having a modular design. This means that product characteristics, (mass-)customizable by customers, are realized by separate components that can freely be combined. If consecutive products differ by a component, then a setup is necessary. This results in a specially structured setup matrix that depends on the similarities of product characteristics. We differentiate alternative problem cases where, for instance, the setup operations for multiple components either have to be executed sequentially or are allowed to be conducted in parallel. We analyze the computational complexity of various problem settings. Our findings reveal some special cases that are solvable in polynomial time, whereas most problem settings are shown to remain strongly NP-hard.



中文翻译:

通过模块化设置最大限度地减少单台机器的制造时间

具有顺序相关设置时间的单机调度是生产计划的经典问题之一,在许多行业中得到广泛应用。在 min-makespan 目标下解决这个问题是众所周知的强 NP-hard。我们考虑由具有模块化设计的产品引起的问题的特殊情况。这意味着客户可(大规模)定制的产品特性是通过可以自由组合的单独组件实现的。如果连续产品因组件而异,则需要进行设置。这会产生一个特殊结构的设置矩阵,该矩阵取决于产品特性的相似性。我们区分替代问题案例,例如,多个组件的设置操作要么必须顺序执行,要么允许并行执行。我们分析了各种问题设置的计算复杂性。我们的研究结果揭示了一些可以在多项式时间内解决的特殊情况,而大多数问题设置都表现出强烈的 NP-hard 问题。

更新日期:2021-09-15
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