Stochastic optimal budget decision for advertising considering uncertain sales responses

Firms are faced with uncertain sales responses even though they advertise appropriately. To help marketing managers make optimal budget decisions in this situation, we develop a stochastic model, depicting the problem of advertising budget decision as a special Markov decision process where a new objective, maximizing expected market utility, is proposed. In the model we introduce a two-dimension state variable including accumulative sales, which vary randomly with advertising budget, and the predicted probability that an advertising campaign obtains a full sales response. We make an analysis of the model on the premise of growing infinite market potential, deriving the property of optimal policies and that of optimal value function. These results are successfully used to make advertising budget decisions for a private university in Xi’an, China.