Online Joint Assortment-Inventory Optimization Under MNL Choices

Learning to Optimize Assortment and Inventory Decisions with Unknown Demand How should a retailer coordinate product assortment and inventory when customer preferences need to be learned on the fly and stockouts dynamically reshape demand? In the paper “Online Joint Assortment-Inventory Optimization under MNL Choices,” the authors study an online learning setting where customers follow a multinomial logit choice model with unknown parameters. The retailer repeatedly selects assortments and inventory levels across sales cycles, using observed choice data to update decisions, aiming to maximize the cumulative profit. Because stochastic stockouts induce complex substitution patterns, preference learning and decision making are intrinsically difficult. The paper introduces a new exploration–exploitation algorithm that combines a novel estimator for customer preferences, an adaptive mechanism that promotes informative experimentation, and an optimization oracle for inventory and assortment planning. The authors establish nearly optimal regret bounds and show that the algorithm remains effective when practical approximate optimization methods are used. They also extend the framework to incorporate inventory carryover and unknown arrival processes, with numerical studies confirming the strong performance of the proposed approach.