A net present value approach in developing optimal replenishment policies for a product life cycle

In this paper, a net present value approach is developed for a decision maker to determine the optimal number of inventory replenishments and the corresponding optimal inventory replenishment time points in the finite planning horizon. Also, the demand function considered in this paper follows the product-life-cycle shape to characterize more practical and realistic situation. The objective function of the net present value for the total relevant costs considered in our model is mathematically formulated as a mixed-integer nonlinear programming problem. A complete search procedure is provided to find the optimal solution by employing the properties derived in this paper and the Nelder–Mead algorithm. Moreover, several numerical examples and the corresponding sensitivity analyses are carried out to illustrate the features of our model by utilizing the search procedure developed in this paper.