Joint promotional effort and assortment optimization under the multinomial logit model

Promotional effort is a common strategy to induce sales and broaden the market scope by enhancing the products' utility to customers. In this article, we incorporate promotional effort into the customer choice model and study the joint promotional effort and assortment optimization problems, where the customer's choice behavior follows the widely used multinomial‐logit (MNL) model. Motivated by various marketing scenarios, we introduce two distinct models that address the allocation of promotional effort: (1) differentiated promotional effort—the retailer can arbitrarily allocate promotional resources to each offered product; (2) uniform promotional effort—the retailer can determine a promotional level, and the promotional effort is equally distributed to each offered product. In the first model, the revenue‐ordered assortment strategy is optimal, and we can efficiently determine the optimal promotional effort level. In the second model, the revenue‐ordered assortment is no longer optimal. We develop a polynomial time algorithm to solve the joint optimization problem under this model. Using the algorithmic results, we conduct comparative analyses between the assortment optimization problem under the proposed models and the classic MNL model, which does not exert any promotional effort. We show that the assortment size shrinks when the retailer makes the promotional effort in the decision, which indicates that product variety and promotional effort are strategic substitutes. Moreover, the retailer and customers can be better off in the presence of promotional efforts, irrespective of the format. Additionally, we conduct extensive numerical experiments to demonstrate our analytical results and gain more managerial insights.