预算不确定性下的鲁棒排列流水车间
Robust Permutation Flowshops Under Budgeted Uncertainty
AI总结：
本文研究预算不确定性模型下的鲁棒排列流水车间问题，通过将问题简化为多项式个名义问题实例，证明了该问题在双机时可多项式时间求解，在固定机器数时可多项式时间近似，并改进了运行时间对数因子。
摘要：
我们考虑预算不确定性模型下的鲁棒排列流水车间问题，其中每台机器上最多有给定数量的作业加工时间可能偏离。我们表明，该问题的解可以通过求解相应名义问题的多项式多个实例来确定。直接结果是，我们的结果意味着该鲁棒流水车间问题在双机情况下可以在多项式时间内求解，并且在任意固定机器数情况下可以在多项式时间内近似。我们的主要结果归约来自类似于Bertsimas和Sim（2003）的分析，但不同的是，对偶化应用于min-max目标的项而不是线性目标函数。考虑到文献中已经开发了用于求解双机流水车间问题的启发式和基于整数规划的方法，我们的结果可能令人惊讶。接下来，我们展示了在双机和三机情况下，通过简单归约到名义问题所隐含的整体运行时间的对数因子改进。最后，我们指出，我们的归约似乎对具有类似形式的预算不确定性下的鲁棒优化问题具有更一般的意义。
英文摘要：
We consider the robust permutation flowshop problem under the budgeted uncertainty model, where at most a given number of job processing times may deviate on each machine. We show that solutions for this problem can be determined by solving polynomially many instances of the corresponding nominal problem. As a direct consequence, our result implies that this robust flowshop problem can be solved in polynomial time for two machines, and can be approximated in polynomial time for any fixed number of machines. The reduction that is our main result follows from an analysis similar to Bertsimas and Sim (2003) except that dualization is applied to the terms of a min-max objective rather than to a linear objective function. Our result may be surprising considering that heuristic and exact integer programming based methods have been developed in the literature for solving the two-machine flowshop problem. Next, we show a logarithmic factor improvement in the overall running time implied by a naive reduction to nominal problems in the case of two machines and three machines. We conclude by noting that our reduction appears to have more general consequences for robust optimization problems under budgeted uncertainty having a similar form.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
