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

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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

Zhenwei Luo ^1, and Jinting Wang ^2,

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

Abstract
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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.

Keywords: minimum quantity., group buying, price discount, optimization, order quantity, Newsvendor model.

Mathematics Subject Classification: Primary: 90B05; Secondary: 90B5.

Citation: Zhenwei Luo, Jinting Wang. The optimal price discount, order quantity and minimum quantity in newsvendor model with group purchase. Journal of Industrial and Management Optimization, 2015, 11 (1) : 1-11. doi: 10.3934/jimo.2015.11.1

References:

[1]	S. K. Anand and R. Aron, Group buying on the Web: A comparison of price-discovery mechanisms, Management Sci., 49 (2003), 1546-1562.
[2]	Y. K. Che and I. Gale, Buyer alliances and managed competition, Journal of Economics & Management Strategy, 6 (1997), 175-200.
[3]	F. Y. Chen, J. Chen and Y. B. Xiao, Optimal control of selling channels for an online retailer with cost-per-click payments and seasonal products, Production Oper. Management, 16 (2007), 292-305. doi: 10.1111/j.1937-5956.2007.tb00260.x.
[4]	R. R. Chen and P. Roma, Group buying of competing retailers, Production Oper. Management, 20 (2011), 181-197. doi: 10.1111/j.1937-5956.2010.01173.x.
[5]	Y. Chen and X. Li, Group Buying Commitment and Sellers' Competitive Advantage, Working paper, Kellogg School of Management, Northwestern University, Evanston, IL, 2011.
[6]	T. Chipty, Horizontal integration for bargaining power: Evidence from the cable television industry, J. Econ. Manage. Strategy, 4 (1995), 375-397. doi: 10.1111/j.1430-9134.1995.00375.x.
[7]	J. Dana, Buyer groups as strategic commitment, Games and Economic Behavior, 74 (2012), 470-485. doi: 10.1016/j.geb.2011.08.014.
[8]	R. J. Dolan, Quantity discounts: Managerial issues and research opportunities, Marketing Sci., 6 (1987), 1-22. doi: 10.1287/mksc.6.1.1.
[9]	Q. Hu, L. B. Schwarz and N. A. Uhan, The impact of GPOs on healthcare-product supply chains, Manufacturing & Service Operations Management, 14 (2012), 7-23.
[10]	R. Inderst and C. Wey, Bargaining, mergers, and technology choice in bilaterally oligopolistic industries, RAND J. Econ., 34 (2003), 1-19.
[11]	X. Jing and J. Xie, Group buying: A new mechanism for selling through social interactions, Management Science, 57 (2011), 1354-1372. doi: 10.1287/mnsc.1110.1366.
[12]	R. J. Kauffman and B. Wang, New buyers' arrival under dynamic pricing market microstructure: The scenario of group-buying discounts on the Internet, In Proceedings of the 34th Hawaii International Conference on System Sciences, R. Sprague (ed.), Maui, HI, Los Alamitos, CA: IEEE Computing Society Press, 2001.
[13]	A. H. Lau and H. S. Lau, The Newsboy problem with price-dependent demand distribution, IIE Transactions, 20 (1988), 168-175. doi: 10.1080/07408178808966166.
[14]	H. P. Marvel and H. Yang, Group purchasing, nonlinear tariffs and oligopoly, Int. J. Ind. Organ., 26 (2008), 1090-1105. doi: 10.1016/j.ijindorg.2007.10.002.
[15]	N. C. Petruzzi and M. Dada, Pricing and the newsvendor problem: A review with extensions, Operations Research, 47 (1999), 183-194. doi: 10.1287/opre.47.2.183.
[16]	Y. Zhou and S. Wang, Inventory Control: Theory and Methodology, Beijing: Science Press, 2008.

show all references

References:

[1]	S. K. Anand and R. Aron, Group buying on the Web: A comparison of price-discovery mechanisms, Management Sci., 49 (2003), 1546-1562.
[2]	Y. K. Che and I. Gale, Buyer alliances and managed competition, Journal of Economics & Management Strategy, 6 (1997), 175-200.
[3]	F. Y. Chen, J. Chen and Y. B. Xiao, Optimal control of selling channels for an online retailer with cost-per-click payments and seasonal products, Production Oper. Management, 16 (2007), 292-305. doi: 10.1111/j.1937-5956.2007.tb00260.x.
[4]	R. R. Chen and P. Roma, Group buying of competing retailers, Production Oper. Management, 20 (2011), 181-197. doi: 10.1111/j.1937-5956.2010.01173.x.
[5]	Y. Chen and X. Li, Group Buying Commitment and Sellers' Competitive Advantage, Working paper, Kellogg School of Management, Northwestern University, Evanston, IL, 2011.
[6]	T. Chipty, Horizontal integration for bargaining power: Evidence from the cable television industry, J. Econ. Manage. Strategy, 4 (1995), 375-397. doi: 10.1111/j.1430-9134.1995.00375.x.
[7]	J. Dana, Buyer groups as strategic commitment, Games and Economic Behavior, 74 (2012), 470-485. doi: 10.1016/j.geb.2011.08.014.
[8]	R. J. Dolan, Quantity discounts: Managerial issues and research opportunities, Marketing Sci., 6 (1987), 1-22. doi: 10.1287/mksc.6.1.1.
[9]	Q. Hu, L. B. Schwarz and N. A. Uhan, The impact of GPOs on healthcare-product supply chains, Manufacturing & Service Operations Management, 14 (2012), 7-23.
[10]	R. Inderst and C. Wey, Bargaining, mergers, and technology choice in bilaterally oligopolistic industries, RAND J. Econ., 34 (2003), 1-19.
[11]	X. Jing and J. Xie, Group buying: A new mechanism for selling through social interactions, Management Science, 57 (2011), 1354-1372. doi: 10.1287/mnsc.1110.1366.
[12]	R. J. Kauffman and B. Wang, New buyers' arrival under dynamic pricing market microstructure: The scenario of group-buying discounts on the Internet, In Proceedings of the 34th Hawaii International Conference on System Sciences, R. Sprague (ed.), Maui, HI, Los Alamitos, CA: IEEE Computing Society Press, 2001.
[13]	A. H. Lau and H. S. Lau, The Newsboy problem with price-dependent demand distribution, IIE Transactions, 20 (1988), 168-175. doi: 10.1080/07408178808966166.
[14]	H. P. Marvel and H. Yang, Group purchasing, nonlinear tariffs and oligopoly, Int. J. Ind. Organ., 26 (2008), 1090-1105. doi: 10.1016/j.ijindorg.2007.10.002.
[15]	N. C. Petruzzi and M. Dada, Pricing and the newsvendor problem: A review with extensions, Operations Research, 47 (1999), 183-194. doi: 10.1287/opre.47.2.183.
[16]	Y. Zhou and S. Wang, Inventory Control: Theory and Methodology, Beijing: Science Press, 2008.

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