Integrating Predictive and Prescriptive Analytics for Assortment Optimization – A Machine Learning Approach Using Conjoint Data

The assortment optimization (AO) problem seeks to determine the optimal product set that maximizes profit while incorporating customer preferences. Traditional methods follow a sequential predict-then-optimize approach, where demand estimation and optimization are performed separately, often leading to suboptimal decisions due to prediction errors. We develop an integrated optimization model that simultaneously estimates parameters of a multinomial logit (MNL) choice model from conjoint data and optimizes the assortment to enhance both profit and empirical fit, measured by maximum likelihood or hit rate. By aligning estimation with decision-making, our approach mitigates the impact of prediction errors on optimization outcomes, leading to more robust decisions. Our formulation results in a mixed-integer linear program for hit-rate maximization and a mixed-integer convex optimization problem for maximum likelihood, both solvable with commercial solvers. For larger instances, we propose heuristic methods for computational efficiency. Our preliminary numerical experiments demonstrate that integration significantly improves assortment decisions, achieving revenue gains of 39.2% (hit rate) and 15.8% (maximum likelihood). We analyze trade-offs between statistical fit, solution quality, and computational complexity, providing insights into when and to what extent integration outperforms traditional methods.