American Institute of Mathematical Sciences

Advanced
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

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 & 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. Google Scholar

[2]

Y. K. Che and I. Gale, Buyer alliances and managed competition, Journal of Economics & Management Strategy, 6 (1997), 175-200. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

Y. Chen and X. Li, Group Buying Commitment and Sellers' Competitive Advantage, Working paper, Kellogg School of Management, Northwestern University, Evanston, IL, 2011. Google Scholar

[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.  Google Scholar

[7]

J. Dana, Buyer groups as strategic commitment, Games and Economic Behavior, 74 (2012), 470-485. doi: 10.1016/j.geb.2011.08.014.  Google Scholar

[8]

R. J. Dolan, Quantity discounts: Managerial issues and research opportunities, Marketing Sci., 6 (1987), 1-22. doi: 10.1287/mksc.6.1.1.  Google Scholar

[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. Google Scholar

[10]

R. Inderst and C. Wey, Bargaining, mergers, and technology choice in bilaterally oligopolistic industries, RAND J. Econ., 34 (2003), 1-19. Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[16]

Y. Zhou and S. Wang, Inventory Control: Theory and Methodology, Beijing: Science Press, 2008. Google Scholar

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. Google Scholar

[2]

Y. K. Che and I. Gale, Buyer alliances and managed competition, Journal of Economics & Management Strategy, 6 (1997), 175-200. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

Y. Chen and X. Li, Group Buying Commitment and Sellers' Competitive Advantage, Working paper, Kellogg School of Management, Northwestern University, Evanston, IL, 2011. Google Scholar

[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.  Google Scholar

[7]

J. Dana, Buyer groups as strategic commitment, Games and Economic Behavior, 74 (2012), 470-485. doi: 10.1016/j.geb.2011.08.014.  Google Scholar

[8]

R. J. Dolan, Quantity discounts: Managerial issues and research opportunities, Marketing Sci., 6 (1987), 1-22. doi: 10.1287/mksc.6.1.1.  Google Scholar

[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. Google Scholar

[10]

R. Inderst and C. Wey, Bargaining, mergers, and technology choice in bilaterally oligopolistic industries, RAND J. Econ., 34 (2003), 1-19. Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[16]

Y. Zhou and S. Wang, Inventory Control: Theory and Methodology, Beijing: Science Press, 2008. Google Scholar

[1]

Jian Chen, Lei Guan, Xiaoqiang Cai. Analysis on Buyers' cooperative strategy under group-buying price mechanism. Journal of Industrial & Management Optimization, 2013, 9 (2) : 291-304. doi: 10.3934/jimo.2013.9.291
[2]

Chui-Yu Chiu, Ming-Feng Yang, Chung-Jung Tang, Yi Lin. Integrated imperfect production inventory model under permissible delay in payments depending on the order quantity. Journal of Industrial & Management Optimization, 2013, 9 (4) : 945-965. doi: 10.3934/jimo.2013.9.945
[3]

Chuan Ding, Kaihong Wang, Shaoyong Lai. Channel coordination mechanism with retailers having fairness preference ---An improved quantity discount mechanism. Journal of Industrial & Management Optimization, 2013, 9 (4) : 967-982. doi: 10.3934/jimo.2013.9.967
[4]

Wei Liu, Shiji Song, Ying Qiao, Han Zhao, Huachang Wang. The loss-averse newsvendor problem with quantity-oriented reference point under CVaR criterion. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021085
[5]

Tien-Yu Lin, Bhaba R. Sarker, Chien-Jui Lin. An optimal setup cost reduction and lot size for economic production quantity model with imperfect quality and quantity discounts. Journal of Industrial & Management Optimization, 2021, 17 (1) : 467-484. doi: 10.3934/jimo.2020043
[6]

Mahdi Karimi, Seyed Jafar Sadjadi, Alireza Ghasemi Bijaghini. An economic order quantity for deteriorating items with allowable rework of deteriorated products. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1857-1879. doi: 10.3934/jimo.2018126
[7]

Hao Sun, Shihua Li, Xuming Wang. Output feedback based sliding mode control for fuel quantity actuator system using a reduced-order GPIO. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1447-1464. doi: 10.3934/dcdss.2020375
[8]

Tien-Yu Lin, Ming-Te Chen, Kuo-Lung Hou. An inventory model for items with imperfect quality and quantity discounts under adjusted screening rate and earned interest. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1333-1347. doi: 10.3934/jimo.2016.12.1333
[9]

Caichun Chai, Tiaojun Xiao, Eilin Francis. Is social responsibility for firms competing on quantity evolutionary stable?. Journal of Industrial & Management Optimization, 2018, 14 (1) : 325-347. doi: 10.3934/jimo.2017049
[10]

Mohsen Lashgari, Ata Allah Taleizadeh, Shib Sankar Sana. An inventory control problem for deteriorating items with back-ordering and financial considerations under two levels of trade credit linked to order quantity. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1091-1119. doi: 10.3934/jimo.2016.12.1091
[11]

M. M. Ali, L. Masinga. A nonlinear optimization model for optimal order quantities with stochastic demand rate and price change. Journal of Industrial & Management Optimization, 2007, 3 (1) : 139-154. doi: 10.3934/jimo.2007.3.139
[12]

Sankar Kumar Roy, Magfura Pervin, Gerhard Wilhelm Weber. A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy. Journal of Industrial & Management Optimization, 2020, 16 (2) : 553-578. doi: 10.3934/jimo.2018167
[13]

Ata Allah Taleizadeh, Biswajit Sarkar, Mohammad Hasani. Delayed payment policy in multi-product single-machine economic production quantity model with repair failure and partial backordering. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1273-1296. doi: 10.3934/jimo.2019002
[14]

Songhai Deng, Zhong Wan, Yanjiu Zhou. Optimization model and solution method for dynamically correlated two-product newsvendor problems based on Copula. Discrete & Continuous Dynamical Systems - S, 2020, 13 (6) : 1637-1652. doi: 10.3934/dcdss.2020096
[15]

Chong Wang, Xu Chen. Fresh produce price-setting newsvendor with bidirectional option contracts. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021052
[16]

Tien-Yu Lin. Effect of warranty and quantity discounts on a deteriorating production system with a Markovian production process and allowable shortages. Journal of Industrial & Management Optimization, 2021, 17 (3) : 1101-1118. doi: 10.3934/jimo.2020013
[17]

Miriam Kiessling, Sascha Kurz, Jörg Rambau. The integrated size and price optimization problem. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 669-693. doi: 10.3934/naco.2012.2.669
[18]

Alain Bensoussan, Metin Çakanyildirim, Suresh P. Sethi. Censored newsvendor model revisited with unnormalized probabilities. Journal of Industrial & Management Optimization, 2009, 5 (2) : 391-402. doi: 10.3934/jimo.2009.5.391
[19]

Yang Shen, Tak Kuen Siu. Consumption-portfolio optimization and filtering in a hidden Markov-modulated asset price model. Journal of Industrial & Management Optimization, 2017, 13 (1) : 23-46. doi: 10.3934/jimo.2016002
[20]

Yiju Wang, Wei Xing, Hengxia Gao. Optimal ordering policy for inventory mechanism with a stochastic short-term price discount. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1187-1202. doi: 10.3934/jimo.2018199

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (281)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy