This study examines assortment and inventory optimization in a two-warehouse e-commerce system that aims to balance delivery speed and cost efficiency. The system consists of a front-end warehouse, strategically located near customers to support rapid order fulfillment but constrained in inventory capacity, and a back-end warehouse, which holds a larger inventory but incurs higher fulfillment costs and longer shipping times. We model this setting as a joint assortment and inventory optimization problem, where initial assortment and inventory decisions are made for the front-end warehouse before demand is realized. Once orders are placed, the e-commerce firm determines the quantity of each order type to fulfill from the front-end warehouse. The marginal distributions of each order type are known, while the correlation structure of the joint distribution is unknown. We formulate the problem using the Marginal Distribution Model (MDM). As MDM is not directly tractable, we propose an approximation that relies solely on marginal distributions and provides valid lower and upper bounds for the original problem. We further investigate conditions under which these bounds are tight. Additionally, we show that the joint assortment and inventory optimization problem is NP-hard, even under simplified settings with deterministic demand and single-item order types. To address this computational complexity, we develop a heuristic algorithm to facilitate efficient assortment decisions. Numerical experiments based on simulated data demonstrate that our proposed policies achieve a favorable balance between optimality and computational efficiency.

Wu Kexin is a Ph.D. candidate in the Department of Industrial Systems Engineering and Management at the National University of Singapore, advised by Prof. Yuan Xue-Ming and Prof. Li Xiaobo. Her research focuses on optimization, algorithm design, and e-commerce operations. She received her master’s degree from Georgia Institute of Technology and her bachelor’s degree from Jilin University.