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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 578280, 6 pages
Research Article

Optimal Order Strategy in Uncertain Demands with Free Shipping Option

1School of Management, Shandong University, Jinan, Shandong 250100, China
2School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Received 10 March 2014; Accepted 8 May 2014; Published 25 May 2014

Academic Editor: Xiang Li

Copyright © 2014 Qing-Chun Meng 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.


Free shipping with conditions has become one of the most effective marketing tools; more and more companies especially e-business companies prefer to offer free shipping to buyers whenever their orders exceed the minimum quantity specified by them. But in practice, the demands of buyers are uncertain, which are affected by weather, season, and many other factors. Firstly, we model the centralization ordering problem of retailers who face stochastic demands when suppliers offer free shipping, in which limited distributional information such as known mean, support, and some deviation measures of the random data is needed only. Then, based on the linear decision rule mainly for stochastic programming, we analyze the optimal order strategies of retailers and discuss the approximate solution. Further, we present the core allocation between all retailers via dual and cooperative game theory. The existence of core shows that each retailer is pleased to cooperate with others in the centralization problem. Finally, a numerical example is implemented to discuss how uncertain data and parameters affect the optimal solution.