# American Institute of Mathematical Sciences

July 2019, 15(3): 1455-1472. doi: 10.3934/jimo.2018104

## Online and offline cooperation under buy-online, pick-up-in-store: Pricing and inventory decisions

 School of Business, Central South University, Changsha 410083, China

* Corresponding author: liuyongmeicn@163.com

Received  November 2017 Revised  March 2018 Published  July 2018

Fund Project: This work is supported by the National Natural Science Foundation in China (Grant No. 71271219, 71071164 and 71431006), by Major Program of National Social Science Foundation of China (Grant No. 15ZDB169), and by Innovation-Driven Programme of Central South University (Grant No. 2015CX010)

This study considered the problem of pricing and inventory decision-making where an online retailer and an offline retailer cooperate in a setting where buy-online, pick-up-in-store (BOPS) is implemented. Given the extra revenue generated from additional sales by BOPS customers who purchase additional products at the offline outlet, we considered revenue sharing, service subsidy, and inventory subsidy contracts among the coordinating supply chain partners. Optimization models under centralized and decentralized decision-making structures were established, and the solution was found for the equilibrium states of these optimization models. The results from numerical experiments were examined. We found that (1) the optimal stocking factor had different variation trends with the increase in additional sales under a centralized structure and under the three contracts in decentralized scenarios; (2) the revenue sharing contract was the most effective among the three contracts for coordinating online and offline retailers, and it was optimal for both retailers if the additional sales parameter was relatively low and offline cost share was small; and (3) an inventory subsidy contract had strong operability and steadiness under different product characteristics.

Citation: Chen Fan, Yongmei Liu, Xuehua Yang, Xiaohong Chen, Junhua Hu. Online and offline cooperation under buy-online, pick-up-in-store: Pricing and inventory decisions. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1455-1472. doi: 10.3934/jimo.2018104
##### References:
 [1] R. E. Barlow and F. Proschan, Mathematical Theory of Reliability, John Wiley and Sons, New York, 1965. [2] D. R. Bell, S. Gallino and A. Moreno, Offline Showrooms in Omni-Channel Retail: Demand and Operational Benefits, Available at SSRN 2370535, December 24, 2016. [3] R. Bhalla, The omni-channel customer experience: Driving engagement through digitisation, Journal of Digital and Social Media Marketing, 1 (2014), 365-372. [4] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 51 (2005), 30-44. doi: 10.1287/mnsc.1040.0215. [5] G. G. Cai, Channel selection and coordination in dual-channel supply chains, Journal of Retailing, 86 (2010), 22-36. doi: 10.1016/j.jretai.2009.11.002. [6] G. G. Cai, Z. G. Zhang and M. Zhang, Game theoretical perspectives on dual-channel supply chain competition with price discounts and pricing schemes, International Journal of Production Economics, 117 (2009), 80-96. doi: 10.1016/j.ijpe.2008.08.053. [7] P. Chatterjee, Causes and consequences of 'order online pick up in-store' shopping behavior, The International Review of Retail, Distribution and Consumer Research, 20 (2010), 431-448. doi: 10.1080/09593969.2010.504009. [8] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. doi: 10.1016/j.omega.2011.11.005. [9] X. Chen, Y. Liu and Z. Wan, Optimal Decision Making for Online and Offline Retailers under BOPS Mode, Anziam Journal, 58 (2016), 187-208. doi: 10.1017/S1446181116000201. [10] W. K. Chiang, D. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Management science, 49 (2003), 1-20. doi: 10.1287/mnsc.49.1.1.12749. [11] C. H. Chiu, T. M. Choi and C. S. Tang, Price, rebate, and returns supply contracts for coordinating supply chains with price - dependent demands, Production and Operations Management, 20 (2011), 81-91. doi: 10.1111/j.1937-5956.2010.01159.x. [12] S. Gallino and A. Moreno, Integration of online and offline channels in retail: The impact of sharing reliable inventory availability information, Management Science, 60 (2014), 1434-1451. [13] F. Gao and X. Su, Omnichannel retail operations with buy-online-and-pickup-in-store, Management Science, 63 (2016), 2478-2492. [14] L. Langegger and R. Sjölander, Multi-channel Sales Distribution–Should Online Retailers Expand Offline?, Master thesis, University of Borȧs, 2013. [15] Y. Liu, C. Ding, C. Fan and X. Chen, Pricing decision under dual-channel structure considering fairness and free-riding behavior, Discrete Dynamics in Nature and Society, 2014 (2014), Art. ID 536576, 10 pp. doi: 10.1155/2014/536576. [16] S. Mahar, P. D. Wright, K. M. Bretthauer and R. P. Hill, Optimizing marketer costs and consumer benefits across "clicks" and "bricks", Journal of the Academy of Marketing Science, 42 (2014), 619-641. doi: 10.1007/s11747-014-0367-8. [17] L. B. Oh, H. H. Teo and V. Sambamurthy, The effects of retail channel integration through the use of information technologies on firm performance, Journal of Operations Management, 30 (2012), 368-381. doi: 10.1016/j.jom.2012.03.001. [18] C. Patel, Successful service retail channel expansions: The roles of technical and brand integration, Industrial Marketing Management, 43 (2014), 102-112. doi: 10.1016/j.indmarman.2013.07.020. [19] K. Pauwels, P. S. Leeflang, M. L. Teerling and K. E. Huizingh, Does online information drive offline revenues?: Only for specific products and consumer segments!, Journal of Retailing, 87 (2011), 1-17. doi: 10.1016/j.jretai.2010.10.001. [20] A. Payne and P. Frow, The role of multichannel integration in customer relationship management, Industrial Marketing Management, 33 (2004), 527-538. doi: 10.1016/j.indmarman.2004.02.002. [21] 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. [22] A. A. Tsay and N. Agrawal, Channel conflict and coordination in the e - commerce age, Production and Operations Management, 13 (2004), 93-110. doi: 10.1111/j.1937-5956.2004.tb00147.x. [23] Y. Wang, L. Jiang and Z. J. Shen, Channel performance under consignment contract with revenue sharing, Management Science, 50 (2004), 34-47. doi: 10.1287/mnsc.1030.0168. [24] D. Xing and T. Liu, Sales effort free riding and coordination with price match and channel rebate, European Journal of Operational Research, 219 (2012), 264-271. doi: 10.1016/j.ejor.2011.11.029. [25] G. Xu, B. Dan, X. Zhang and C. Liu, Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contract, International Journal of Production Economics, 147 (2014), 171-179. [26] E. Zabel, Monopoly and uncertainty, The Review of Economic Studies, 37 (1970), 205-219. doi: 10.2307/2296413. [27] P. Zhang, Y. Xiong and Z. Xiong, Coordination of a dual-channel supply chain after demand or production cost disruptions, International Journal of Production Research, 53 (2015), 3141-3160. doi: 10.1080/00207543.2014.975853.

show all references

##### References:
 [1] R. E. Barlow and F. Proschan, Mathematical Theory of Reliability, John Wiley and Sons, New York, 1965. [2] D. R. Bell, S. Gallino and A. Moreno, Offline Showrooms in Omni-Channel Retail: Demand and Operational Benefits, Available at SSRN 2370535, December 24, 2016. [3] R. Bhalla, The omni-channel customer experience: Driving engagement through digitisation, Journal of Digital and Social Media Marketing, 1 (2014), 365-372. [4] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 51 (2005), 30-44. doi: 10.1287/mnsc.1040.0215. [5] G. G. Cai, Channel selection and coordination in dual-channel supply chains, Journal of Retailing, 86 (2010), 22-36. doi: 10.1016/j.jretai.2009.11.002. [6] G. G. Cai, Z. G. Zhang and M. Zhang, Game theoretical perspectives on dual-channel supply chain competition with price discounts and pricing schemes, International Journal of Production Economics, 117 (2009), 80-96. doi: 10.1016/j.ijpe.2008.08.053. [7] P. Chatterjee, Causes and consequences of 'order online pick up in-store' shopping behavior, The International Review of Retail, Distribution and Consumer Research, 20 (2010), 431-448. doi: 10.1080/09593969.2010.504009. [8] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. doi: 10.1016/j.omega.2011.11.005. [9] X. Chen, Y. Liu and Z. Wan, Optimal Decision Making for Online and Offline Retailers under BOPS Mode, Anziam Journal, 58 (2016), 187-208. doi: 10.1017/S1446181116000201. [10] W. K. Chiang, D. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Management science, 49 (2003), 1-20. doi: 10.1287/mnsc.49.1.1.12749. [11] C. H. Chiu, T. M. Choi and C. S. Tang, Price, rebate, and returns supply contracts for coordinating supply chains with price - dependent demands, Production and Operations Management, 20 (2011), 81-91. doi: 10.1111/j.1937-5956.2010.01159.x. [12] S. Gallino and A. Moreno, Integration of online and offline channels in retail: The impact of sharing reliable inventory availability information, Management Science, 60 (2014), 1434-1451. [13] F. Gao and X. Su, Omnichannel retail operations with buy-online-and-pickup-in-store, Management Science, 63 (2016), 2478-2492. [14] L. Langegger and R. Sjölander, Multi-channel Sales Distribution–Should Online Retailers Expand Offline?, Master thesis, University of Borȧs, 2013. [15] Y. Liu, C. Ding, C. Fan and X. Chen, Pricing decision under dual-channel structure considering fairness and free-riding behavior, Discrete Dynamics in Nature and Society, 2014 (2014), Art. ID 536576, 10 pp. doi: 10.1155/2014/536576. [16] S. Mahar, P. D. Wright, K. M. Bretthauer and R. P. Hill, Optimizing marketer costs and consumer benefits across "clicks" and "bricks", Journal of the Academy of Marketing Science, 42 (2014), 619-641. doi: 10.1007/s11747-014-0367-8. [17] L. B. Oh, H. H. Teo and V. Sambamurthy, The effects of retail channel integration through the use of information technologies on firm performance, Journal of Operations Management, 30 (2012), 368-381. doi: 10.1016/j.jom.2012.03.001. [18] C. Patel, Successful service retail channel expansions: The roles of technical and brand integration, Industrial Marketing Management, 43 (2014), 102-112. doi: 10.1016/j.indmarman.2013.07.020. [19] K. Pauwels, P. S. Leeflang, M. L. Teerling and K. E. Huizingh, Does online information drive offline revenues?: Only for specific products and consumer segments!, Journal of Retailing, 87 (2011), 1-17. doi: 10.1016/j.jretai.2010.10.001. [20] A. Payne and P. Frow, The role of multichannel integration in customer relationship management, Industrial Marketing Management, 33 (2004), 527-538. doi: 10.1016/j.indmarman.2004.02.002. [21] 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. [22] A. A. Tsay and N. Agrawal, Channel conflict and coordination in the e - commerce age, Production and Operations Management, 13 (2004), 93-110. doi: 10.1111/j.1937-5956.2004.tb00147.x. [23] Y. Wang, L. Jiang and Z. J. Shen, Channel performance under consignment contract with revenue sharing, Management Science, 50 (2004), 34-47. doi: 10.1287/mnsc.1030.0168. [24] D. Xing and T. Liu, Sales effort free riding and coordination with price match and channel rebate, European Journal of Operational Research, 219 (2012), 264-271. doi: 10.1016/j.ejor.2011.11.029. [25] G. Xu, B. Dan, X. Zhang and C. Liu, Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contract, International Journal of Production Economics, 147 (2014), 171-179. [26] E. Zabel, Monopoly and uncertainty, The Review of Economic Studies, 37 (1970), 205-219. doi: 10.2307/2296413. [27] P. Zhang, Y. Xiong and Z. Xiong, Coordination of a dual-channel supply chain after demand or production cost disruptions, International Journal of Production Research, 53 (2015), 3141-3160. doi: 10.1080/00207543.2014.975853.
The effect of $\alpha$ on decision variables
The effect of $\alpha$ and $\theta$ on online profits
The effect of $\alpha$ and $\theta$ on offline profits
The effect of $\alpha$ and $\theta$ on offline profits
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