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MixedInteger Linear Programming and Constraint Programming Models for the Online Printing Shop Scheduling Problem
Computers & Operations Research ( IF 4.1 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.cor.2020.105020
Willian T. Lunardi , Ernesto G. Birgin , Philippe Laborie , Débora P. Ronconi , Holger Voos

Abstract In this work, the online printing shop scheduling problem is considered. This challenging real problem, that appears in the nowadays printing industry, can be seen as a flexible job shop scheduling problem with sequence flexibility in which precedence constraints among operations of a job are given by an arbitrary directed acyclic graph. In addition, several complicating particularities such as periods of unavailability of the machines, resumable operations, sequence-dependent setup times, partial overlapping among operations with precedence constraints, release times, and fixed operations are also present in the addressed problem. In the present work, mixed integer linear programming and constraint programming models for the minimization of the makespan are presented. Modeling the problem is twofold. On the one hand, the problem is precisely defined. On the other hand, the capabilities and limitations of a commercial software for solving the models are analyzed. Extensive numerical experiments with small-, medium-, and large-sized instances are presented. Numerical experiments show that the commercial solver is able to optimally solve only a fraction of the small-sized instances when considering the mixed integer linear programming model; while all small-sized and a fraction of the medium-sized instances are optimally solved when considering the constraint programming formulation of the problem. Moreover, the commercial solver is able to deliver feasible solutions for the large-sized instances that are of the size of the instances that appear in practice.

中文翻译:

在线印刷车间调度问题的混合整数线性规划和约束规划模型

摘要 在这项工作中,考虑了在线印刷厂调度问题。这个出现在当今印刷行业中的具有挑战性的实际问题可以被视为具有序列灵活性的灵活作业车间调度问题,其中作业操作之间的优先约束由任意有向无环图给出。此外,在解决的问题中还存在一些复杂的特殊性,例如机器不可用的时期、可恢复的操作、依赖于序列的设置时间、具有优先约束的操作之间的部分重叠、发布时间和固定操作。在目前的工作中,提出了用于最小化完工时间的混合整数线性规划和约束规划模型。对问题建模是双重的。一方面,这个问题是精确定义的。另一方面,分析了用于求解模型的商业软件的能力和局限性。介绍了具有小型、中型和大型实例的大量数值实验。数值实验表明,商业求解器在考虑混合整数线性规划模型时,只能最优求解一小部分小实例;而在考虑问题的约束规划公式时,所有小型和一小部分中型实例都得到了最佳解决。此外,商业求解器能够为实际出现的实例大小的大型实例提供可行的解决方案。分析了用于求解模型的商业软件的能力和局限性。介绍了具有小型、中型和大型实例的大量数值实验。数值实验表明,商业求解器在考虑混合整数线性规划模型时,只能最优求解一小部分小实例;而在考虑问题的约束规划公式时,所有小型和一小部分中型实例都得到了最佳解决。此外,商业求解器能够为实际出现的实例大小的大型实例提供可行的解决方案。分析了用于求解模型的商业软件的能力和局限性。介绍了具有小型、中型和大型实例的大量数值实验。数值实验表明,商业求解器在考虑混合整数线性规划模型时,只能最优求解一小部分小实例;而在考虑问题的约束规划公式时,所有小型和一小部分中型实例都得到了最佳解决。此外,商业求解器能够为实际出现的实例大小的大型实例提供可行的解决方案。数值实验表明,商业求解器在考虑混合整数线性规划模型时,只能最优求解一小部分小实例;而在考虑问题的约束规划公式时,所有小型和一小部分中型实例都得到了最佳解决。此外,商业求解器能够为实际出现的实例大小的大型实例提供可行的解决方案。数值实验表明,商业求解器在考虑混合整数线性规划模型时,只能最优求解一小部分小实例;而在考虑问题的约束规划公式时,所有小型和一小部分中型实例都得到了最佳解决。此外,商业求解器能够为实际出现的实例大小的大型实例提供可行的解决方案。
更新日期:2020-11-01
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