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OPTIMAL DECISION MAKING FOR ONLINE AND OFFLINE RETAILERS UNDER BOPS MODE

Part of: Artificial intelligence (68Txx) Design of experiments

Published online by Cambridge University Press:  20 October 2016

XINGRAN CHEN ,
YONGMEI LIU  and
ZHONG WAN
XINGRAN CHEN
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email xran_chen_666792@163.com, wanmath@csu.edu.cn
YONGMEI LIU
Affiliation:
School of Business, Central South University, Hunan Changsha, China email liuyongmeicn@163.com
ZHONG WAN*
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email xran_chen_666792@163.com, wanmath@csu.edu.cn
*
✉wanmath@csu.edu.cn
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Abstract

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As a new business form, the buy-online and pick-up-in-store (BOPS) mode allows consumers to pay for goods online and pick them up in a physical store. In this paper, an equilibrium model is constructed to formulate an optimal decision-making problem for online and offline retailers under the BOPS mode, where the online retailer determines the retail price of the goods and the consignment quantity in a physical store, while the offline retailer chooses the revenue share of profit by a consignment contract. Different to the existing models, the cost of overstocking and loss of understocking are incorporated into the profit function of the online retailer due to the randomness of demand. For the objective function of the offline retailer, the cross-sale quantity generated by the BOPS mode is taken into account. Then the game between the online and offline retailers is expressed as a stochastic Nash equilibrium model. Based on the analytic properties of the model, necessary conditions for the equilibrium solution are obtained. A case study and sensitivity analysis are employed to reveal the managerial implications of the model, which can provide a number of valuable suggestions on optimizing the strategies for the online and offline retailers under the BOPS mode.

Keywords

BOPSoptimization modelNash gamestochastic optimization

MSC classification

Primary: 90C30: Nonlinear programming
Secondary: 62K05: Optimal designs 68T37: Reasoning under uncertainty
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 2 , October 2016 , pp. 187 - 208
Copyright
© 2016 Australian Mathematical Society 

References

Adida, E. and Ratisoontorn, N., “Consignment contracts with retail competition”, Eur. J. Oper. Res. 215 (2011) 136–148; doi:10.1016/j.ejor.2011.05.059.Google Scholar
Chen, J. M., Cheng, H. L. and Chien, M. C., “On channel coordination through revenue-sharing contracts with price and shelf-space dependent demand”, Appl. Math. Model. 35 (2011) 4886–4901; doi:10.1016/j.apm.2011.03.042.Google Scholar
Chen, Y. and Wan, Z., “A locally smoothing method for mathematical programs with complementarity constraints”, ANZIAM J. 56 (2015) 299–315; doi:10.1017/S1446181115000048.Google Scholar
Du, D., Chen, B. and Xu, D., “Quantifying the efficiency of price-only contracts in push supply chains over demand distributions of known supports”, Omega-Int. J. Manag. Sci. 42 (2014) 98–108; doi:10.1016/j.omega.2013.03.004.Google Scholar
Gallino, S. and Moreno, A., “Integration of online and offline channels in retail: the impact of sharing reliable inventory availability information”, Manag. Sci. 60 (2014) 1434–1451;doi:10.2139/ssrn.2149095.Google Scholar
Grewal, D., Janakiraman, R., Kalyanam, K., Kannan, P. K., Ratchford, B., Song, R. and Tolerico, S., “Strategic online and offline retail pricing: a review and research agenda”, J. Interact. Mark. 24 (2010) 138–154; doi:10.1016/j.intmar.2010.02.007.Google Scholar
Huang, S., Wan, Z. and Chen, X. H., “A new nonmonotone line search technique for unconstrained optimization”, Numer. Algorithms 68 (2015) 671–689; doi:10.1007/s11075-014-9866-4.Google Scholar
Lee, H. G., Lee, S. C., Kim, H. Y. and Lee, R. H., “Is the internet making retail transactions more efficient? Comparison of online and offline CD retail markets”, Electron. Commer. Res. Appl. 2 (2003) 266–277; doi:10.1016/S1567-4223(03)00030-9.Google Scholar
Li, S., Zhu, Z. and Huang, L., “Supply chain coordination and decision making under consignment contract with revenue sharing”, Int. J. Prod. Econ. 120 (2009) 88–99;doi:10.1016/j.ijpe.2008.07.015.Google Scholar
Liu, H. Y., Luo, X. X., Bi, W. J., Man, Y. M. and Teo, K. L., “Dynamic pricing of network goods in duopoly markets with boundedly rational consumers”, J. Ind. Manag. Optim. 12 (2016) 5–25; doi:10.3934/jimo.2016025.Google Scholar
de Matta, R. E., Lowe, T. J. and Zhang, D., “Consignment or wholesale: retailer and supplier preferences and incentives for compromise”, Omega-Int. J. Manag. Sci. 49 (2014) 93–106;doi:10.1016/j.omega.2014.05.011.Google Scholar
Netessine, S., Savin, S. and Xiao, W., “Revenue management through dynamic cross selling in e-commerce retailing”, Oper. Res. 54 (2006) 893–913; doi:10.1287/opre.1060.0296.Google Scholar
Pan, K., Lai, K. K., Leung, S. C. H. and Xiao, D., “Revenue-sharing versus wholesale price mechanisms under different channel power structures”, Eur. J. Oper. Res. 203 (2010) 532–538;doi:10.1016/j.ejor.2009.08.010.Google Scholar
Ru, J. and Wang, Y., “Consignment contracting: who should control inventory in the supply chain?”, Eur. J. Oper. Res. 201 (2010) 760–769; doi:10.1016/j.ejor.2009.04.006.Google Scholar
Seifert, R. W., Zequeira, R. I. and Liao, S., “A three-echelon supply chain with price-only contracts and sub-supply chain coordination”, Int. J. Prod. Econ. 138 (2012) 345–353;doi:10.1016/j.ijpe.2012.04.006.Google Scholar
Shi, J. and Xiao, T., “Service investment and consumer returns policy in a vendor-managed inventory supply chain”, J. Ind. Manag. Optim. 11 (2015) 439–459;doi:10.3934/jimo.2015.11.439.Google Scholar
Sun, J. and Debo, L., “Sustaining long-term supply chain partnerships using price-only contracts”, Eur. J. Oper. Res. 233 (2014) 557–565; doi:10.1016/j.ejor.2013.09.020.Google Scholar
Wan, Z., Chen, Y., Huang, S. and Feng, D. D., “A modified nonmonotone BFGS algorithm for solving smooth nonlinear equations”, Optim. Lett. 8 (2014) 1845–1860;doi:10.1007/s11590-013-0678-6.Google Scholar
Wan, Z., Yuan, M. and Wang, C., “A partially smoothing Jacobian method for nonlinear complementarity problems with P-0 function”, J. Comput. Appl. Math. 286 (2015) 158–171;doi:10.1016/j.cam.2015.03.015.Google Scholar
Wan, Z., Zhang, S. J. and Teo, K. L., “Polymorphic uncertain nonlinear programming approach for maximizing the capacity of V-belt driving”, Optim. Eng. 15 (2014) 267–292;doi:10.1007/s11081-012-9205-3.Google Scholar
Wang, Y., Jiang, L. and Shen, Z. J., “Channel performance under consignment contract with revenue sharing”, Manage. Sci. 50 (2014) 34–47; doi:10.1287/mnsc.1030.0168.Google Scholar
Wu, C. and Mallik, S., “Cross sales in supply chains: an equilibrium analysis”, Int. J. Prod. Econ. 126 (2010) 158–167; doi:10.1016/j.ijpe.2010.03.003.Google Scholar
Xie, G., Yue, W. Y. and Wang, S. Y., “Optimal selection of cleaner products in a green supply chain with risk aversion”, J. Ind. Manag. Optim. 11 (2015) 515–528; doi:10.3934/jimo.2015.11.515.Google Scholar
Xu, G., Dan, B., Zhang, X. and Liu, C., “Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contract”, Int. J. Prod. Econ. 147 (2014) 171–179;doi:10.1016/j.ijpe.2013.09.012.Google Scholar
Yao, Z., Leung, S. C. H. and Lai, K. K., “Manufacturer’s revenue-sharing contract and retail competition”, Eur. J. Oper. Res. 186 (2008) 637–651; doi:10.1016/j.ejor.2007.01.049.Google Scholar
Zhang, D., De Matta, R. and Lowe, T. J., “Channel coordination in a consignment contract”, Eur. J. Oper. Res. 207 (2010) 897–905; doi:10.1016/j.ejor.2010.05.027.Google Scholar
Zhang, S. J. and Wan, Z., “Polymorphic uncertain nonlinear programming model and algorithm for maximizing the fatigue life of V-belt drive”, J. Ind. Manag. Optim. 8 (2012) 493–505;doi:10.3934/jimo.2012.8.493.Google Scholar
Zhang, R. Q., Zhang, L. K., Zhou, W. H., Saigal, R. and Wang, H. W., “The multi-item newsvendor model with cross-selling and the solution when demand is jointly normally distributed”, Eur. J. Oper. Res. 236 (2014) 147–159; doi:10.1016/j.ejor.2014.01.006.Google Scholar