# American Institute of Mathematical Sciences

January  2015, 11(1): 1-11. doi: 10.3934/jimo.2015.11.1

## The optimal price discount, order quantity and minimum quantity in newsvendor model with group purchase

 1 Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China 2 Department of Mathematics, Beijing Jiaotong University, 100044 Beijing

Received  December 2012 Revised  February 2014 Published  May 2014

Based on the feature of small profits but quick turnover, group-buying, an emerging e-commerce model, benefits both retailers and customers. In this paper, we explore the optimal price discount, order quantity and minimum quantity with a fixed selling price of the product to maximize the sellers' profit. The traditional newsvendor model framework is used in view of the shortened life cycle of most products. The demand of customers is assumed to be in addition form and product form, respectively, and the impacts of demand parameters are examined numerically. It is revealed that in some cases the profit cannot be improved significantly through price discount because of unconspicuous increase in demand. However, when the demand changes obviously with price discount, group-buying can bring more profit through price discount and inspire vendors to order more goods. Through numerical results, it is shown that the influence of demand in the product form is more evident than that in the addition form under the strategy of group-buying. Furthermore, the profit-based minimum quantity and the probability of selling nothing during the group time are also shown in this paper.
Citation: Zhenwei Luo, Jinting Wang. The optimal price discount, order quantity and minimum quantity in newsvendor model with group purchase. Journal of Industrial & Management Optimization, 2015, 11 (1) : 1-11. doi: 10.3934/jimo.2015.11.1
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