An inventory system with time-dependent demand and partial backordering under return on inventory investment maximization
研究了需求呈幂函数模式且允许缺货的库存系统，以库存投资回报率最大化为目标，给出了最优库存策略，并与最小化总成本策略进行了对比。
In this article, we study an inventory system for items that have a power demand pattern and where shortages are allowed. We suppose that only a fixed proportion of demand during the stock-out period is backordered. The decision variables are the inventory cycle and the ratio between the initial stock and the total quantity demanded throughout the inventory cycle. The objective is to maximize the Return on Inventory Investment (ROII) defined as the ratio of the profit per unit time over the average inventory cost. After analysing the objective function, the optimal global solutions for all the possible cases of the inventory problem are determined. These optimal policies that maximize the ROII are, in general, different from those that minimize the total inventory cost per unit time. Finally, a numerical sensitivity analysis of the optimal inventory policy with respect to the system input parameters and some useful managerial insights derived from the results are presented.