A robust optimization approach to budget optimization in online marketing campaigns

Abstract This paper presents a novel approach to strategic budget allocation in online marketing campaigns using robust optimization techniques. We develop a linear programming model that specifically addresses uncertainties in conversion cost coefficients, a critical challenge in digital marketing performance measurement. The model's distinctive feature lies in its combination of robust optimization with fuzzy linguistic scales, which enables marketing professionals to express uncertainty levels in their expert estimations qualitatively. Using real campaign data obtained from advertising platform management tools, we demonstrate how the proposed robust counterpart transforms traditional deterministic optimization into a more resilient decision-making framework. Our comparative analysis between deterministic and robust approaches reveals that while the robust solution may sacrifice nominal optimality, it provides protection against cost coefficient fluctuations typically encountered in online marketing. The key contribution is a practical decision support tool that allows marketers to systematically incorporate their risk preferences and uncertainty expectations into budget allocation decisions. Case study demonstrates the model's ability to optimize performance while managing risks in digital advertising markets with volatile conversion costs.