Objective: This study aims to determine the optimal advertising budget allocation policy between customer acquisition and retention activities in Iran’s dairy industry, focusing on five major brands across milk and cheese markets, and to evaluate strategic differences among large, medium, and small brands under competitive conditions and resource constraints.

Method: The study employs the classical dynamic optimal control theory framework (Pontryagin’s principle) and the generalized Vidale–Wolfe model to capture the relationship between advertising and market share. The market share state equation incorporates two types of advertising effort: acquisition and retention. The optimization problem is formulated as maximizing total discounted profit subject to state differential equations, initial conditions, and boundary conditions. Using Pontryagin’s maximum principle, the Hamiltonian is constructed and first-order optimality conditions are derived. Data include monthly sales, advertising expenditures, prices, and profit margins for the three-year period 2022–2024.

Findings: Results indicate that the optimal budget allocation ratio for market-leading brands is approximately 70% for acquisition and 30% for retention, whereas follower brands required a ratio close to 50–50. The advertising return on investment index ranges from 1.65 to 3.12. The customer lifetime value-to-acquisition cost ratio ranges from 33.6 for Brand 5 to 134.7 for Brand 1 in cheese. The payback period is estimated at 9 months for cheese Brand 1 and 36 months for milk Brand 5. The shadow value of one percentage point of market share for cheese Brand 1 was 20.5 billion rials at the beginning of the period and 14.2 billion rials for milk.

Conclusion: By extending the Vidale–Wolfe optimal control model to a multi-brand competitive setting, calibrating competitive shock parameters based on the Dorfman–Steiner framework and GARCH estimates (rather than the empirically unsupported assumptions common in the literature), and fitting the model to real data from Iran’s dairy industry, this study provides a practical decision rule for advertising budget allocation. The findings indicate that optimal advertising budget allocation is strongly dependent on brand strength, competitive position, and product category.