In the modern catering business model, restaurants usually use established platforms to promote their food and use two channels to sell their food: online and offline sales. We construct demand functions for online and offline, considering promotion and substitution relationships by a revised Bertrand model. We first consider three classic models: the decentralized decision model, the equilibrium decision model, and the centralized decision model. In the decentralized decision model, the platform decides both the promotional effort and the online discount; in the equilibrium decision model, the platform decides the online discount, while the food service provider decides the promotional effort. In the centralized decision model, the takeaway platform and the food service provider have maximized the overall profit as the decisive goal. We find that the online discount decreases in price when the impact factor of the online promotion is high but increases in price when the impact factor of the online promotion is low. Then, we analyze and compare the results under three models. We find that when the substitution factor is low enough, or the impactor factor of online promotion is low enough, the global optimal platform discount is higher than the equilibrium platform discount and the decentralized online discount; otherwise, the results are the opposite. In addition, the global optimal promotional effort is always higher than the optimal promotional effort in the decentralized model. When the substitution factor is low enough, or the impactor factor of online promotion is low enough, the global optimal promotional effort is higher than the equilibrium optimal promotional effort; otherwise, the result is the opposite.