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Based on a continuous version of the Lanchester advertising model for a duopoly, a mathematical model is developed to determine the optimal advertising policy of a firm responding to the advertising pulsation policy of its competitor. A Dynamic Programming (DP) approach has been employed to arrive at the optimal solution.

It has been mainly demonstrated that under a concave or linear advertising response function, the focal firm's DP policy is superior to its Uniform Advertising Policy (UAP) counterpart (constant advertising spending over time), irrespective of the advertising pulsation policy employed by its rival. Under a convex advertising response function, on the other hand, the focal firm's DP policy is superior to its Advertising/Maintenance Pulsing Policy (APMP) and Advertising Pulsing Policy (APP) counterparts (alternating advertising spending at two levels), irrespective of the advertising pulsation policy used by the competitor.