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GAME MODEL FOR ONLINE AND OFFLINE RETAILERS UNDER BUY-ONLINE AND PICK-UP-IN-STORE MODE WITH DELIVERY COST AND RANDOM DEMAND

Part of: Game theory Operations research and management science

Published online by Cambridge University Press:  03 July 2020

YING OUYANG Open the ORCID record for YING OUYANG [Opens in a new window] ,
ZHAOMAN WAN Open the ORCID record for ZHAOMAN WAN [Opens in a new window]  and
ZHONG WAN Open the ORCID record for ZHONG WAN [Opens in a new window]
YING OUYANG
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email ouyangying@csu.edu.cn, 0302170220@csu.edu.cn, wanmath@csu.edu.cn
ZHAOMAN WAN*
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email ouyangying@csu.edu.cn, 0302170220@csu.edu.cn, wanmath@csu.edu.cn
ZHONG WAN
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email ouyangying@csu.edu.cn, 0302170220@csu.edu.cn, wanmath@csu.edu.cn
*
✉0302170220@csu.edu.cn
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Abstract

Online retailers are increasingly adding buy-online and pick-up-in-store (BOPS) modes to order fulfilment. In this paper, we study a system of BOPS by developing a stochastic Nash equilibrium model with incentive compatibility constraints, where the online retailer seeks optimal online sale prices and an optimal delivery schedule in an order cycle, and the offline retailer pursues a maximal rate of sharing the profit owing to the consignment from the online retailer. By an expectation method and optimality conditions, the equilibrium model is first transformed into a system of constrained nonlinear equations. Then, by a case study and sensitivity analysis, the model is validated and the following practical insights are revealed. (I) Our method can reliably provide an equilibrium strategy for the online and offline retailers under BOPS mode, including the optimal online selling price, the optimal delivery schedule, the optimal inventory and the optimal allocation of profits. (II) Different model parameters, such as operational cost, price sensitivity coefficient, cross-sale factor, opportunity loss ratio and loss ratio of unsold goods, generate distinct impacts on the equilibrium solution and the profits of the BOPS system. (III) Optimization of the delivery schedule can generate greater consumer surplus, and makes the offline retailer share less sale profit from the online retailer, even if the total profit of the BOPS system becomes higher. (IV) Inventory subsidy is an indispensable factor to improve the applicability of the game model in BOPS mode.

Keywords

online saledelivery planbuy-online and pick-up-in-store modegame model

MSC classification

Primary: 90B36: Scheduling theory, stochastic
Secondary: 91A35: Decision theory for games
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 1 , January 2020 , pp. 62 - 88
Copyright
© 2020 Australian Mathematical Society

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