This paper proposes a novel extension to Media Mix Modeling (MMM) that introduces a multiplicative interaction between marketing activity and underlying consumer demand. Unlike standard MMM frameworks that assume additive and independent effects of media and baseline demand drivers, our specification allows marketing effectiveness to vary with prevailing demand conditions. However, the proposed structure introduces significant statistical challenges, particularly identifiability issues that can lead to unstable and biased parameter estimates. Using comprehensive simulation studies, we analyze the nature and severity of these identification issues through bias assessment and their implications for statistical inference. To address these issues, we develop a constrained genetic algorithm optimization approach which facilitates robust estimation that simultaneously mitigates biases arising from the aforementioned issues. The proposed approach also offers flexibility to incorporate economically meaningful parameter constraints. Finally, the proposed methodology is applied to real-world data to demonstrate its effectiveness in enhancing estimation accuracy while taking into account additional commercial constraints, facilitating budget allocation decisions.

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