Optimization of an inventory system with partial backlogging from a financial investment perspective

In some real inventory systems, item sales can be adjusted to a stable demand rate along the cycle. For instance, home appliances, electrical products, lounge furniture, water supply, etc., are items with rate. this work, we analyze an system for of type, where is constant. Shortages allowed, and it assumed that fraction during stock-out period backlogged. It supposed shortage costs (backorder cost lost cost) have affine structure: fixed plus linear depends on time shortages exist. paper, instead maximization profit per unit time, or minimization average objective return investment, which quotient defined as divided by cost. The optimal policy obtained in closed form under new perspective. Moreover, shown maximizes investment is, general, different from one time. addition, perspective offers advantages. does not depend selling price. Therefore, manager need change his/her if price changes. These advantages usually present when Numerical examples provided illustrate theoretical results developed work. A sensitivity analysis respect input parameters also developed.