The discrete parallel machine makespan scheduling location (ScheLoc) problem is an integrated combinatorial optimization problem that combines facility location and job scheduling. The problem consists in choosing the locations of multiple machines among a finite set of candidates and scheduling a set of jobs on these machines, aiming to minimize the makespan. Depending on the machine location, the jobs may have different release dates, and thus the location decisions have a direct impact on the scheduling decisions. To solve the problem, it is proposed a new arc-flow formulation, a column generation and three heuristic procedures that are evaluated through extensive computational experiments. By embedding the proposed procedures into a framework algorithm, we are able to find proven optimal solutions for all benchmark instances from the related literature and to obtain small percentage gaps for a new set of challenging instances.

离散并行机器的制造期调度位置（ScheLoc）问题是一个综合的组合优化问题，它结合了设备位置和作业调度。问题在于，在有限的一组候选者中选择多台机器的位置，并在这些机器上安排一组作业，以最大程度地减少工期。根据机器的位置，作业可能具有不同的发布日期，因此位置决策对调度决策有直接影响。为了解决该问题，提出了一种新的电弧流公式，一个色谱柱生成方法和三种启发式程序，并通过大量的计算实验对其进行了评估。通过将建议的过程嵌入到框架算法中，