Luis Augusto San-José

In this work, a production-inventory system for items with a time-dependent demand pattern is studied. Shortages are allowed and these are met with the arrival of the next production run. Fluctuations of the net inventory level are analysed and the costs related with the production and inventory management are calculated. The aim is to maximise the profit per unit time. That profit is equal to the difference between sale revenue and production-inventory costs. In the analysis of this system, different scenarios can occur. All these possible cases are studied in detail and, for each scenario, the optimal production-inventory policy and the maximum profit per unit time are determined. Moreover, several numerical examples to illustrate the solution methodology are presented. Finally, a sensitivity analysis of the optimal inventory policy with respect to several parameters of the system and some useful managerial insights derived from the results are given.

A model for inventory systems with multiple products is studied. Demands of items are time-dependent and follow power patterns. Shortages are allowed and fully backlogged. For this inventory system, our findings provide the efficient inventory policy that helps decision-makers to obtain the initial inventory levels and the reorder points that maximize the profit per unit time. Moreover, when it is assumed that the warehouse used for the storage of products has a limited capacity, the optimal inventory policy is also developed. The model presented here extends some inventory systems studied by other authors. Numerical examples are introduced to illustrate the applicability of the theoretical results presented.

In this paper, we address an inventory system where the demand rate multiplicatively combines the effects of time and selling price. It is assumed that the demand rate is the product of two power functions, one depending on the selling price and the other on the time elapsed since the last inventory replenishment. Shortages are allowed and fully backlogged. The aim is to obtain the lot sizing, the inventory cycle and the unit selling price that maximize the profit per unit time. To achieve this, two efficient algorithms are proposed to obtain the optimal solution to the inventory problem for all possible parameter values of the system. We solve several numerical examples to illustrate the theoretical results and the solution methodology. We also develop a numerical sensitivity analysis of the optimal inventory policy and the maximum profit with respect to the parameters of the demand function.

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