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Optimal replenishment policies with allowable shortages for a product life cycle

Authors
Journal
Computers & Mathematics with Applications
0898-1221
Publisher
Elsevier
Publication Date
Volume
53
Issue
10
Identifiers
DOI: 10.1016/j.camwa.2006.03.044
Keywords
  • Shortage
  • Replenishment
  • Time-Varying Demand
  • Nelder–Mead Algorithm
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract 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.

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