This research work deals with the single-item dynamic lot size problem under (i) age-dependent inventory deterioration rates and inventory costs and (ii) stockouts (or lost sales, that is, the demands do not have to be satisfied). Two equivalent forward dynamic programming (DP) algorithms are devised to solve this problem in $O\left(T^3\right)$ time based on several properties of the optimal solution, where $T$ denotes the length of the problem horizon. Moreover, a special case with no speculative motive cost structures is investigated. Compared to the general time-variant case, two equivalent algorithms for efficient forward DP in $O\left(T^2\right)$ time are developed. Furthermore, we study the problem under storage capacity constraint and develop a forward DP algorithm to solve this problem. Finally, we offer two useful managerial insights by using a comprehensive test bed of instance: (i) the stockout policy can reduce the total costs when stockout costs are relatively small, and (ii) prolonging the product's lifetime or extending the storage capacity at great financial costs under smaller setup costs and higher holding costs for the firm is not needed.

这项研究工作涉及（i）与年龄有关的库存恶化率和库存成本以及（ii）缺货（或销售损失，即不必满足需求）下的单项动态批量问题。设计了两种等效的前向动态编程（DP）算法来解决该问题。$Ø（{Ť}^3）$ 时间基于最佳解决方案的几个属性，其中 $Ť$表示问题范围的长度。此外，研究了一种没有投机动机成本结构的特殊情况。与一般时变情况相比，两种等效算法可以有效地实现前向DP。$Ø（{Ť}^{\mathrm{2个}}）$时间发展了。此外，我们研究了存储容量约束下的问题，并开发了一种正向DP算法来解决该问题。最后，我们通过使用全面的测试平台来提供两个有用的管理见解：（i）缺货策略可以在缺货成本相对较小时降低总成本，并且（ii）延长产品的使用寿命或极大地扩展存储容量不需要较小的设置成本和较高的控股成本下的财务成本。