Mathematical optimization problems including a time dimension abound. For example, logistics, process optimization and production planning tasks must often be optimized for a range of time periods. Usually, these problems incorporating time structure are very large and cannot be solved to global optimality by modern solvers within a reasonable period of time. Therefore, the so-called rolling-horizon approach is often adopted. This approach aims to solve the problem periodically, including additional information from proximately following periods. In this paper, we first investigate several drawbacks of this approach and develop an algorithm that compensates for these drawbacks both theoretically and practically. As a result, the rolling-horizon decomposition methodology is adjusted to enable large scale optimization problems to be solved efficiently. In addition, we introduce conditions that guarantee the quality of the solutions. We further demonstrate the applicability of the method to a variety of challenging optimization problems. We substantiate the findings with computational studies on the lot-sizing problem in production planning, as well as for large-scale real-world instances of the tail-assignment problem in aircraft management. It proves possible to solve large-scale realistic tail-assignment instances efficiently, leading to solutions that are at most a few percent away from a globally optimal solution.

包括时间维度在内的数学优化问题比比皆是。例如，物流、流程优化和生产计划任务通常必须针对一系列时间段进行优化。通常，这些包含时间结构的问题非常大，现代求解器无法在合理的时间内求解到全局最优。因此，通常采用所谓的滚动水平方法。这种方法旨在定期解决问题，包括来自最近一段时间的附加信息。在本文中，我们首先研究了这种方法的几个缺点，并开发了一种在理论上和实践上都可以弥补这些缺点的算法。因此，调整滚动水平分解方法，以有效解决大规模优化问题。此外，我们还引入了保证解决方案质量的条件。我们进一步证明了该方法对各种具有挑战性的优化问题的适用性。我们通过对生产计划中的批量问题以及飞机管理中尾部分配问题的大规模真实世界实例的计算研究来证实这些发现。事实证明，有效地解决大规模现实尾部分配实例是可能的，导致解决方案与全局最优解决方案最多相差几个百分点。我们进一步证明了该方法对各种具有挑战性的优化问题的适用性。我们通过对生产计划中的批量问题以及飞机管理中尾部分配问题的大规模真实世界实例的计算研究来证实这些发现。事实证明，有效地解决大规模现实尾部分配实例是可能的，导致解决方案与全局最优解决方案最多相差几个百分点。我们进一步证明了该方法对各种具有挑战性的优化问题的适用性。我们通过对生产计划中的批量问题以及飞机管理中尾部分配问题的大规模真实世界实例的计算研究来证实这些发现。事实证明，有效地解决大规模现实尾部分配实例是可能的，导致解决方案与全局最优解决方案最多相差几个百分点。