When Advertising meets Assortment Planning: Joint Advertising and Assortment Optimization under Multinomial Logit Model

Abstract

Although assortment optimization has been extensively studied in the literature, there is lack of studies on exploring the impact of advertising on the output of assortment planning. In this article, we fill this gap by considering a novel joint advertising budget strategy and assortment optimization problem, where the platforms must jointly decide (1) the optimal advertising effort allocated to each product and (2) an assortment of products displayed to consumers. We assume that the purchase behavior of a consumer is governed by the classic multinomial logit choice model, where each product is associated with a preference weight and the purchase probability of a product in an assortment is proportional to its preference weight. To capture the advertising effect in the context of assortment planning, we assume that one can increase the preference weight of a product through advertising that product, and the degree of improvement is decided by a response function in terms of the amount of advertising efforts allocated to that product. Given a budget constraint on advertising, our objective is to find a solution, which is composed of an advertising strategy and an assortment of products, to maximize the expected revenue. We analyze the structural properties of this problem and derive effective solutions under different settings. If there is no capacity constraint on the number of products displayed to consumers, we show that the revenue-ordered assortments still maintain optimality, and we leverage this result to derive an optimal solution. For the capacity constrained case, it is hard to solve the optimization problem directly, we overcome this challenge by proposing an efficient iterative scheme to find the optimal solution.