An inventory system with time-dependent demand and partial backordering under return on inventory investment maximization

In this article, we study an inventory system for items that have a power demand pattern and where shortages are allowed. We suppose only fixed proportion of during the stock-out period is backordered. The decision variables cycle ratio between initial stock total quantity demanded throughout cycle. objective to maximize Return on Inventory Investment (ROII) defined as profit per unit time over average cost. After analysing function, optimal global solutions all possible cases problem determined. These policies ROII are, in general, different from those minimize cost time. Finally, numerical sensitivity analysis policy with respect input parameters some useful managerial insights derived results presented. • An time-dependent partial backlogging analysed. On (ROII). obtained.