This paper presents a profound analysis of the robust job scheduling problem with uncertain release dates on unrelated machines. Our model involves minimizing the worst-case makespan and interval uncertainty where each release date belongs to a well-defined interval. Robust optimization requires scenario-based decision-making. A finite subset of feasible scenarios to determine the worst-case regret (a deviation from the optimal makespan) for a particular schedule is indicated. We formulate a mixed-integer nonlinear programming model to solve the underlying problem via three (constructive) greedy algorithms. Polynomial-time solvable cases are also discussed in detail. The algorithms solve the robust combinatorial problem using the makespan criterion and its non-deterministic counterpart. Computational testing compares both robust solutions and different decomposition strategies. Finally, the results confirm that a decomposition strategy applied to the makespan criterion is enough to create a competitive robust schedule.

中文翻译：

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具有间隔发布日期的鲁棒无关并行机调度问题

本文深入分析了在无关机器上发布日期不确定的鲁棒作业调度问题。我们的模型涉及最小化最坏情况下的完工时间和间隔不确定性，其中每个发布日期属于明确定义的间隔。稳健的优化需要基于场景的决策。指示了用于确定特定时间表的最坏情况遗憾（与最佳制造期的偏差）的可行方案的有限子集。我们制定了一个混合整数非线性规划模型，以通过三种（构造性）贪婪算法解决潜在问题。多项式时间可解的情况也被详细讨论。这些算法使用 makespan 标准及其非确定性对应物来解决稳健组合问题。计算测试比较了稳健的解决方案和不同的分解策略。最后，结果证实，应用于完工标准的分解策略足以创建具有竞争力的稳健进度表。