Marketing effort within the newsvendor problem framework: A systematic review and extensions of demand-effort and cost-effort formulations

Abstract

This study deals with a generalization of the newsvendor problem with marketing efforts. Combining inventory and marketing decisions is currently a topic that has been widely studied. Various formulations of marketing efforts and their costs have been applied in the literature. Therefore, a systematic review was performed to identify existing formulations, especially those that deal with mathematical modeling and optimization. The findings observed on a wide set of marketing effort formulations are summarized, generalized, and applied in the newsvendor problem framework. It was found that the optimal marketing effort decision does not depend on the uncertainty involved in the model for the additive demand case under commonly used assumptions. Optimal marketing is equal to its deterministic equivalent, contrary to the multiplicative form, where the decision directly depends on uncertainty. Formulations of the demand-effort response function and the cost of marketing effort are generalized (to concave and convex functions, respectively) and extended to an S-shaped demand-effort response function. Assumptions and theorems that guarantee the uniqueness of optimal marketing efforts are established. Finally, the effects of price and cost parameter changes on optimal marketing effort decisions were analyzed.