Many practical productions are full of significant uncertainties. For example, the working environment may change, machines may breakdown, workers may become unstable, etc. In such an environment, job processing times should not be fixed numbers. In light of this situation, we investigate a single-machine problem with two-scenario-based processing times, where the goal is to minimize the maximum total completion times over two scenarios. When the uncertainty of the job processing times is confronted, the robust version of this problem is NP-hard, even for very restricted cases. To solve this problem, we derive some dominance rules and a lower bound for developing branch-and-bound algorithms to find optimal solutions. As for determining approximate solutions, we propose five heuristics, adopting combined two-scenario-based dependent processing times, to produce initial solutions and then improve each with a pairwise interchange. Further, we propose a simulated annealing hyper-heuristic incorporating the proposed seven low level heuristics to solve this problem as well. Finally, the performances of all proposed algorithms are tested and reported.

许多实际生产充满了重大的不确定性。例如，工作环境可能会改变，机器可能会故障，工人可能会变得不稳定等。在这种环境下，工作处理时间不应为固定数字。鉴于这种情况，我们研究了基于两个方案的处理时间的单机问题，目的是最大程度地减少两种方案的最大总完成时间。当面对工作处理时间的不确定性时，即使对于非常有限的情况，此问题的可靠版本也是NP-hard。为了解决这个问题，我们导出了一些支配规则和一个下界，用于开发分支定界算法以找到最佳解决方案。至于确定近似解，我们提出了五种启发式方法，采用基于两种情况的组合相依处理时间来生成初始解，然后通过成对互换来改进每个解。此外，我们提出了一种模拟退火超启发式方法，并结合了所提出的七个低级启发式方法来解决该问题。最后，对所有提出的算法的性能进行了测试和报告。