235 / 2024-04-23 17:13:44

The Joint Assortment-Price-Position Optimization Problem Under the Multilevel Nested Logit Model

Assortment optimization,The joint assortment-price-position optimization,Multilevel nested logit model

In many revenue management scenarios, display position of options are concerned with customers' choice probabilities, e.g. top-ranked products on a Web page tend to receive more clicks. We study the joint assortment-price-position optimization problem (APPOP), where a retailer must display a set of products at various position and set their prices to maximize expected revenue. We use the multilevel nested logit (MLNL) model to capture customers' choice behavior, which generalizes the multinomial logit (MNL) and the nested logit (NL) models by capturing product similarities across multiple dimensions. We show that APPOP under the MLNL model is NP-hard. We then focus on designing approximate algorithms for this problem. In our approach, we first decompose the original problem into an assortment-position problem and a pricing problem. We then create an auxiliary problem of the assortment-position problem, where the position biases are uniformly rounded to a specific grid on the positive axis. We prove that the optimal solution to the auxiliary problem can be obtained in polynomial time using dynamic programming and that the solution contributes to generating an \(\alpha-\)approximation of the assortment-position problem. Finally, we develop a polynomial-time approximate scheme (PTAS) to the original problem by combining the solutions to the assortment-position problem and the pricing problem.