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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 2017253, 11 pages
Research Article

The Distribution-Free Newsboy Problem with Multiple Discounts and Upgrades

1Department of Industrial Engineering, Seoul National University, Seoul 08826, Republic of Korea
2Quality Management Department, LG Electronics, Seoul 07336, Republic of Korea

Received 28 March 2016; Accepted 26 July 2016

Academic Editor: Paolo Crippa

Copyright © 2016 Ilkyeong Moon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Most papers on the newsboy problem assume that excess inventory is either sold after discount or discarded. In the real world, overstocks are handled with multiple discounts, upgrades, or a combination of these measures. For example, a seller may offer a series of progressively increasing discounts for units that remain on the shelf, or the seller may use incrementally applied innovations aimed at stimulating greater product sophistication. Moreover, the normal distribution does not provide better protection than other distributions with the same mean and variance. In this paper, we find the differences between normal distribution approaches and distribution-free approaches in four scenarios with mean and variance of demand as the only available data to decision-makers. First, we solve the newsboy problem by considering multiple discounts. Second, we formulate and solve the newsboy problem by considering multiple upgrades. Third, we formulate and solve a mixed newsboy problem characterized with multiple discounts and upgrades. Finally, we extend the model to solve a multiproduct newsboy problem with a storage or a budget constraint and develop an algorithm to find the solutions of the models. Concavity of the models is proved analytically. Extensive computational experiments are presented to verify the robustness of the distribution-free approach. The results show that the distribution-free approach is robust.