In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

在本文中，考虑了库存周期必须是已知基本周期的整数倍的库存问题。此外，每个基本周期的需求率是一个功率时间相关的函数。短缺是允许的，但考虑到客户的需要或利益，在缺货期间只有固定比例的需求在下一次补货到来时得到满足。与库存系统管理相关的成本有订货成本、采购成本、持有成本、延期交货成本和销售损失成本。问题是确定使单位时间利润最大化的最佳库存策略，即从产品销售中获得的收入与先前成本之和的差额。库存问题的建模导致整数非线性数学规划问题。针对这一问题，提出了一种计算最优库存周期和经济订货量的新型高效算法。提供了数值示例来说明该算法如何工作以确定最佳库存策略。开发了关于库存系统某些参数的最优策略的敏感性分析。最后，给出了对未来研究方向的结论和建议。开发了关于库存系统某些参数的最优策略的敏感性分析。最后，给出了对未来研究方向的结论和建议。开发了关于库存系统某些参数的最优策略的敏感性分析。最后，给出了对未来研究方向的结论和建议。