Computers and Industrial Engineering
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
Pricing and lot-sizing policies for deteriorating items with partial backlogging under inflation
Expert Systems with Applications: An International Journal
Computers & Mathematics with Applications
Computers and Industrial Engineering
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In this paper, we investigate replenishment policies with allowable shortages by considering a general, time-varying, continuous, and deterministic demand function for a product life cycle. The objective is to optimally determine the number of inventory replenishments, the inventory replenishment time points, and the beginning time points of shortages within the product life cycle by minimizing the total relevant costs of the inventory replenishment system. The proposed problem is mathematically formulated as a mixed-integer nonlinear programming model. A complete search procedure is developed to find the optimal solution by employing the properties derived in this paper and the well-known Nelder-Mead algorithm. Also, 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.