Within the framework of continuous-review \((S-1, S)\) inventory systems with rationing and backorders, there are two streams of studies in the literature that involve optimization models. In the first stream, service level optimizations are studied for which exact optimization routines are provided. The second stream of studies involves cost optimization models, which relies on optimizing approximate cost models rather than the original cost model. Our main contribution in this study is to fill this research gap by providing a computationally efficient and exact optimization algorithm for determining the optimal policy parameters which minimizes the expected cost rate per unit time. One important aspect of our method is that, as the base-stock level is increased by 1 as the iteration continues, the steady-state probabilities need to be calculated only once in our optimization routine (for which the rationing level equals to zero). For the given base-stock level, the cost measures of all other policy parameters can be computed immediately through the knowledge of the probabilities computed in previous iterations. This result significantly reduces the computational complexity of the optimization routine. In the numerical study section, we show the efficiency of the proposed optimization routine under varying system parameters. We also compare the performance of our approach with the existing heuristic in the literature and show that savings up to \(34.75 \%\) can be achieved.

在连续审核的框架内（（S-1，S）\）具有配给和延期交货的库存系统，文献中有两个涉及优化模型的研究流。在第一个流中，研究了服务级别的优化，为其提供了精确的优化例程。第二类研究涉及成本优化模型，该模型依赖于优化近似成本模型而不是原始成本模型。我们在这项研究中的主要贡献是通过提供一种计算有效且精确的优化算法来确定最佳政策参数，从而将单位时间的预期成本率降至最低，从而填补了这一研究空白。我们方法的一个重要方面是，随着迭代的进行，基础库存水平将增加1，稳态概率仅需在我们的优化例程中计算一次（对于该概率而言，配给级别等于0）。对于给定的基本库存水平，可以通过了解先前迭代中计算的概率，立即计算所有其他策略参数的成本度量。该结果显着降低了优化例程的计算复杂度。在数值研究部分，我们显示了在变化的系统参数下提出的优化程序的效率。我们还将我们的方法的性能与文献中现有的启发式方法进行了比较，并表明节省了多达 通过了解先前迭代中计算出的概率，可以立即计算出所有其他策略参数的成本测度。该结果显着降低了优化例程的计算复杂度。在数值研究部分，我们显示了在变化的系统参数下提出的优化程序的效率。我们还将我们的方法的性能与文献中现有的启发式方法进行了比较，并表明节省了多达 通过了解先前迭代中计算出的概率，可以立即计算出所有其他策略参数的成本测度。该结果显着降低了优化例程的计算复杂度。在数值研究部分，我们显示了在变化的系统参数下提出的优化程序的效率。我们还将我们的方法的性能与文献中现有的启发式方法进行了比较，并表明节省了多达\（34.75 \％\）即可实现。