Abstract: Both traditional manufacturers and online retailers have been implementing omnichannel strategies such as Buy-Online-and-Pick-up-in-Store (BOPS). By introducing interval grey numbers to represent consumer preference, which depicts uncertain consumer valuation, and the wholesale price and selling price constitute the profit function, we develop a basic dual-channel and three omnichannel grey models. Compared with the traditional online or offline dual-channel supply chain, the construction of the omnichannel model considers agency selling agreements and spillover effects as well. Four propositions have been proposed and proven through the analysis of the position degree analysis of the grey game model. Equilibrium analysis indicates that there is no option of [BOPS, No BOPS] in the equilibrium strategy of the grey game. Finally, a case study and numerical simulation are given to verify the model and reveal the relationship between the profit function and BOPS channel agency fees when reaching an equilibrium strategy.

Key words: BOPS, Consumer Valuation, Grey Model, Omnichannel