Optimal advertising pulsation policies: a dynamic programming approach

This study formulates and solves an advertising pulsation problem for a monopolistic firm using dynamic programming (DP). The firm aims at maximising profit through an optimal allocation of the advertising budget in terms of rectangular pulses over a finite planning horizon. Aggregate sales response to the advertising effort is assumed to be governed by a modified version of the Vidale–Wolfe model in continuous time proposed by Little. Using a numerical example in which a planning horizon of one year is divided into one, two through ten equal time periods, computing routines are developed to solve 150 DP problems. Computational results show among other findings that the performance yielded by the DP policy dominates the uniform advertising policy (constant spending) for a concave advertising response function and the advertising pulsing policy (turning advertising on and off) for a linear or convex response function.