Abstract
This work presents an inventory model for a single item where the demand rate is stock-dependent. Three fixed costs are considered in the model: purchasing cost, ordering cost and holding cost. A new approach focused on maximizing the return on investment (ROI) is used to determine the optimal policy. It is proved that maximizing profitability is equivalent to minimizing the average inventory cost per item. The global optimum of the objective function is obtained, proving that the zero ending policy at the final of a cycle is optimal. Closed expressions for the lot size and the maximum ROI are determined. The optimal policy for minimizing the inventory cost per unit time is also obtained with a zero-order point, but the optimal lot size is different. Both solutions are not equal to the one that provides the maximum profit per unit time. The optimal lot size for the maximum ROI policy does not change if the purchasing cost or the selling price vary. A sensitivity analysis for the optimal values regarding the initial parameters is performed by using partial derivatives. The maximum ROI is more sensitive regarding the selling price or the purchasing cost than regarding the other parameters. Some useful managerial insights are deduced for decision-makers. Numerical examples are solved to illustrate the obtained results.
Highlights
The traditional literature on inventory models assumes that the demand of the items is uniform on time, and independent of the levels of stock for sale in the warehouse
If the demand rate is constant, i.e., β = 0, both solutions are equal. Note that both solutions do not depend on the values p and v of the purchasing cost and the selling price. This is an interesting result for inventory managers because the optimal lot size does not change when these prices vary, as long as the objective is the maximization of the return on investment or the minimization of the inventory cost per unit of time
It is interesting for inventory managers to highlight the fact that the solution with maximum return on investment (ROI) is obtained with the zero order point, while the solution with maximum profit per unit time can lead to a non-zero order point
Summary
The traditional literature on inventory models assumes that the demand of the items is uniform on time, and independent of the levels of stock for sale in the warehouse. The optimal inventory policy for a system with stock-dependent demand rate is analyzed, where the aim is the maximization of the return on investment. Pando et al [44] found the solution that maximizes the profitability ratio in an inventory model with non-linear holding cost, but the problem with a minimum cost per unit time is not addressed and the comparison between both solutions is not studied. Other papers on this subject are Ishfaq and Bajwa [45] and Pando et al [46].
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