Advertising meets assortment planning: joint advertising and assortment optimization under multinomial logit model

Despite the assortment optimization problem has been widely studied in the past decades, the interplay between advertising and its implications for this issue remains under-explored. This study seeks to bridge this research gap by tackling the combined challenge of advertising and assortment optimization. We assume that advertising can increase the awareness of specific products, and the magnitude of this effect is jointly depends on the product-specific effectiveness of advertising and the allocated advertising budget. For this joint problem, our objective is to maximize the expected revenue by finding the optimal advertising strategy and the displayed assortment. In this work, we analyze the structure of this problem and propose efficient approaches to solve it across different scenarios. In the unconstrained setting, we demonstrate that the optimal assortment includes products whose revenue exceeds a certain threshold. When there is a cardinality constraint for the assortment, we consider a relaxed problem and propose an efficient method to identify a near-optimal solution. We also examine the joint assortment, pricing, and advertising problem in both unconstrained and cardinality-constrained settings, incorporating the fairness constraint for the advertising strategy and extending our findings to account for consumer sequential decision-making patterns. Through a series of numerical tests, we confirm the validity of our methods and demonstrate that they outperform existing heuristic approaches.