The newsvendor problem with advertising: an overview with extensions

The effect of advertising on sales has been the subject of recent studies as an important aspect in many demand-based problems. Herein, we deal with the newsvendor problem, due to its simple structure, as a suitable tool for illustrating how facets of marketing may affect decision-making concerning operational problems. In the setting presented, the newsvendor is faced with advertising-sensitive stochastic demand, where a demand-related random element comprises an advertising decision of the multiplicative or additive form. We assume that a suitable advertising strategy results in increased sales. Two advertising response functions are considered, these being concave downward and S-shaped. We review and extend the existing results relating to the newsvendor problem with marketing effects, which mostly pertain to the concave function. These are generalized by defining the S-shaped function, and some original insights into the effect of advertising are given. We establish that the optimal advertising expenditure for the multiplicative case is always less than or equal to the optimal amount in the equivalent deterministic model while it is always equal in the additive case. We finally illustrate the results that are obtained by providing numerical examples involving various advertising response functions, as well as management-related interpretations.