Optimal replenishment policies for the case of a demand function with product-life-cycle shape in a finite planning horizon

In this paper, we explore the demand function follows the product-life-cycle shape for the decision maker to determine the optimal number of inventory replenishments and the corresponding optimal inventory replenishment time points in the finite planning horizon. The objective function of 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. Also, based on the search procedure developed in this paper, a decision support system is implemented on a personal computer to solve the proposed problem.