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Mathematical Problems in Engineering
Volume 2014, Article ID 307935, 10 pages
http://dx.doi.org/10.1155/2014/307935
Research Article

Impacts of Transportation Cost on Distribution-Free Newsboy Problems

1Department of Industrial Engineering & Management, National Kaohsiung University of Applied Sciences, 415 Chien Kung Road, Kaohsiung 80778, Taiwan
2Department of Information Management, Kun Shan University, 195 Kunda Road, Yongkang District, Tainan 71003, Taiwan
3Department of Industrial and Information Management, National Cheng Kung University, 1 University Road, Tainan 70101, Taiwan

Received 27 June 2014; Revised 3 September 2014; Accepted 13 September 2014; Published 30 September 2014

Academic Editor: Vikas Kumar

Copyright © 2014 Ming-Hung Shu 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.

Abstract

A distribution-free newsboy problem (DFNP) has been launched for a vendor to decide a product’s stock quantity in a single-period inventory system to sustain its least maximum-expected profits when combating fierce and diverse market circumstances. Nowadays, impacts of transportation cost on determination of optimal inventory quantity have become attentive, where its influence on the DFNP has not been fully investigated. By borrowing an economic theory from transportation disciplines, in this paper the DFNP is tackled in consideration of the transportation cost formulated as a function of shipping quantity and modeled as a nonlinear regression form from UPS’s on-site shipping-rate data. An optimal solution of the order quantity is computed on the basis of Newton’s approach to ameliorating its complexity of computation. As a result of comparative studies, lower bounds of the maximal expected profit of our proposed methodologies surpass those of existing work. Finally, we extend the analysis to several practical inventory cases including fixed ordering cost, random yield, and a multiproduct condition.