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OPTIMAL DECISION MAKING FOR ONLINE AND OFFLINE RETAILERS UNDER BOPS MODE

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

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 

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