一个具有单件订货量折扣和非递增价格的O(n log n)算法
An $O(n\log n)$ Algorithm for Single-Item Lot Sizing with a One-Breakpoint All-Units Discount and Non-Increasing Prices
AI总结：
本文提出一个O(n log n)算法，解决具有单件订货量折扣和非递增价格的单件订货问题，改进了传统算法的时间复杂度。
摘要：
本文研究了在单调环境下具有1折全部单位数量折扣的单件订货问题，其中购买价格在规划时间范围内非递增。针对这种情况，我们建立了最优解的若干新性质，并开发了一种混合动态规划方法，通过只存储关于状态的必要信息来保持解决方案空间的紧凑表示，并使用线性方程处理中间值。我们的算法运行时间为O(n log n)，其中n表示时期数。我们的结果优于之前最先进的算法，其时间复杂度为O(n²)。
英文摘要：
This paper addresses the single-item lot sizing problem with a 1-breakpoint all-units quantity discount in a monotonic setting where the purchase prices are non-increasing over the planning horizon. For this case, we establish several novel properties of the optimal solution and develop a hybrid dynamic programming approach that maintains a compact representation of the solution space by storing only essential information about the states and using linear equations for intermediate values. Our algorithm runs in \(O(n\log n)\) time, where \(n\) denotes the number of periods. Our result is an improvement over the previous state-of-the-art algorithm, which has an \(O(n^2)\) time complexity.
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。
