Implications of Advertising Lag on the Dynamic Optimal Decisions in an O2O Supply Chain

The advertising lag effect and the reference quality effect are intrinsic properties of the market that influence supply chain performance. In this paper, we use the differential game theory considering the above two effects under an O2O (online to offline) environment. We investigate how these two effects impact supply chain performance. By the extended maximum principle, the optimal analytical solutions of the decision variables in two different game scenarios are obtained, i.e., with and without advertising cooperation. We conclude that the optimal wholesale price (advertising effort level, product quality level, and retail price) increases or decreases exponentially to its steady state, which depends on whether the initial goodwill is lower than the static goodwill or not. The analysis shows that the advertising lag effect has a negative impact on the supply chain, while the reference quality effect is positive. The vertical advertising cooperation strategy is effective in facilitating the channel performance. From a comparison analysis, we obtain that the manufacturer concentrates more effort on quality improvement if the advertising lag time is larger or if consumers are more sensitive to quality, and the manufacturer pays more attention to advertising relative to quality improvements with a higher advertising cost sharing ratio.