Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T10:45:58.387Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Operations research and management science Game theory

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 [email protected], [email protected], [email protected]
ZHAOMAN WAN*
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email [email protected], [email protected], [email protected]
ZHONG WAN
Affiliation:
School of Mathematics and Statistics, Central South University, Hunan Changsha, China email [email protected], [email protected], [email protected]
*
✉[email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adida, E. and Ratisoontorn, N., “Consignment contracts with retail competition”, European J. Oper. Res. 215 (2011) 136–148; doi:10.1016/j.ejor.2011.05.059.CrossRefGoogle Scholar
Cao, J., So, K. C. and Yin, S., “Impact of an ‘online-to-store’ channel on demand allocation, pricing and profitability”, European J. Oper. Res. 248 (2016) 234–245; doi:10.1016/j.ejor.2015.07.014.CrossRefGoogle Scholar
Cao, L. and Li, L., “The impact of cross-channel integration on retailers’ sales growth”, J. Retail. 91 (2015) 198–216; doi:10.1016/j.jretai.2014.12.005.CrossRefGoogle Scholar
Chen, X. R., Liu, Y. and Wan, Z., “Optimal decision making for online and offline retailers under BOPS mode”, ANZIAM J. 58 (2016) 187–208; doi:10.1017/S1446181116000201.CrossRefGoogle Scholar
Chopra, S., “The evolution of omni-channel retailing and its impact on supply chains”, Transp. Res. Proc. 30 (2018) 4–13; doi:10.1016/j.trpro.2018.09.002.CrossRefGoogle Scholar
Deng, S. H. and Wan, Z., “A three-term conjugate gradient algorithm for large-scale unconstrained optimization problems”, Appl. Numer. Math. 92 (2015) 70–81; doi:10.1016/j.apnum.2015.01.008.CrossRefGoogle Scholar
Di, C., Dimitrov, S. and He, Q. M., “Incentive compatibility in prediction markets: costly actions and external incentives”, Int. J. Forecast. 35 (2019) 351–370; doi:10.1016/j.ijforecast.2018.07.005.CrossRefGoogle Scholar
Gallino, S. and Moreno, A., “Integration of online and offline channels in retail: the impact of sharing reliable inventory availability information”, Mark. Sci. 60 (2014) 1434–1451; doi:10.2139/ssrn.2149095.Google Scholar
“Gap between online and offline commerce is shrinking”, Retail & Ecommerce (10 October 2016),https://www.emarketer.com/Article/Gap-Between-Online-Offline-Commerce-Shrinking/1014575.Google Scholar
Hariga, M., Gumus, M. and Daghfous, A., “Storage constrained vendor managed inventory models with unequal shipment frequencies”, Omega 48 (2014) 94–106; doi:10.1016/j.omega.2013.11.003.CrossRefGoogle Scholar
Huang, S., Wan, Z. and Zhang, J., “An extended nonmonotone line search technique for large-scale unconstrained optimization”, J. Comput. Appl. Math. 330 (2018) 586–604; doi:10.1016/j.cam.2017.09.026.CrossRefGoogle Scholar
Ishfaq, R. and Raja, U., “Evaluation of order fulfillment options in retail supply chains”, Decis. Sci. 49 (2017) 487–521; doi:10.1111/deci.12277.CrossRefGoogle Scholar
Jin, M., Li, G. and Cheng, T. C., “Buy online and pick up in-store: design of the service area”, European J. Oper. Res. 268 (2018) 613–623; doi:10.1016/j.ejor.2018.02.002.CrossRefGoogle Scholar
Keser, C. and Willinger, M., “Principals’ principles when agents’ actions are hidden”, Int. J. Ind. Organ. 360 (2000) 163–185; doi:10.1016/S0167-7187(99)00038-7.CrossRefGoogle Scholar
Kim, E., Park, M. C. and Lee, J., “Determinants of the intention to use buy-online, pickup in-store (BOPS): the moderating effects of situational factors and product type”, Telemat. Inform. 34 (2017) 1721–1735; doi:10.1016/j.tele.2017.08.006.CrossRefGoogle Scholar
Lee, Y. C. E., Chan, C. K. and Langevin, A., “Integrated inventory–transportation model by synchronizing delivery and production cycles”, Transp. Res. Part E: Logist. Transp. Rev. 91 (2016) 68–89; doi:10.1016/j.tre.2016.03.017.CrossRefGoogle Scholar
Levitt, S. D., “Incentive compatibility constraints as an explanation for the use of prison sentences instead of fines”, Int. Rev. Law Econ. 17 (1997) 179–192; doi:10.1016/S0144-8188(97)00002-1.CrossRefGoogle Scholar
Li, T. and Wan, Z., “New adaptive Barzilar–Borwein step size and its application in solving large scale optimization problems”, ANZIAM J. 61 (2019) 76–98; doi:10.1017/S1446181118000263.Google Scholar
Li, Y. X., Wan, Z. and Liu, J. J., “Bi-level programming approach to optimal strategy for vendor-managed inventory problems under random demand”, ANZIAM J. 59 (2017) 247–270; doi:10.1017/S1446181117000384.CrossRefGoogle Scholar
Liu, Y. M. and Zhou, D., “Is it always beneficial to implement BOPS? A comparative research with traditional dual channel”, Oper. Res. Manag. Sci. 2268 (2018) 613–623; http://en.cnki.com.cn/Article_en/CJFDTotal-YCGL201802023.htm.Google Scholar
MacCarthy, B. L., Zhang, L. and Muyldermans, L., “Best performance frontiers for buy-online-pickup-in-store order fulfilment”, Int. J. Prod. Econ. 211 (2019) 251–264; doi:10.1016/j.ijpe.2019.01.037.CrossRefGoogle Scholar
Ofek, E., Katona, Z. and Sarvary, M., “‘Bricks and clicks’: the impact of product returns on the strategies of multichannel retailers”, Mark. Sci. 360 (2011) 42–60; doi:10.1287/mksc.1100.0588.CrossRefGoogle Scholar
Rapp, A., Baker, T. L. and Bachrach, D. G., “Perceived customer showrooming behavior and the effect on retail salesperson self-efficacy and performance”, J. Retail. 91 (2015) 358–369; doi:10.1016/j.jretai.2014.12.007.CrossRefGoogle Scholar
Sadigh, A. N., Mozafari, M. and Karimi, B., “Manufacturer–retailer supply chain coordination: a bi-level programming approach”, Adv. Eng. Softw. 45 (2012) 144–152; doi:10.1016/j.advengsoft.2011.09.008.CrossRefGoogle Scholar
Saghiri, S., Wilding, R., Mena, C. and Bourlakis, M., “Toward a three-dimensional framework for omni-channel”, J. Bus. Res. 77 (2017) 53–67; doi:10.1016/j.jbusres.2017.03.025.CrossRefGoogle Scholar
Shi, X. T., Dong, C. W. and Cheng, T. C. E., “Does the buy-online-and-pick-up-in-store strategy with pre-orders benefit a retailer with the consideration of returns?”, Int. J. Prod. Econ. 206 (2018) 134–145; doi:10.1016/j.ijpe.2018.09.030.CrossRefGoogle Scholar
Wan, Z., Tang, J. Y., Ren, L., Xiao, Y. and Liu, S., “Optimization techniques to deeply mine the transcriptomic profile of the sub-genomes in hybrid fish lineage”, Front. Genet. 10 (2019) 1–17; doi:10.3389/fgene.2019.00911.CrossRefGoogle ScholarPubMed