Car dealers must daily decide which vehicles to purchase from the manufacturer to replenish their stock. This is an integrated sales and operations planning problem. On the sales side, dealers must anticipate customer choices. Operational costs include inventory and lot-sizing costs.We introduce a Markov Decision Process (MDP) that models this car dealer inventory replenishment problem.

Four aspects make this problem particularly challenging. First, the problem has a combi natorial nature. Any vehicle that can be produced can be ordered, leading to a catalog of over 1030 possible configurations from different option combinations. Second, the uncertainty is en dogenous. We do not know what customers would have purchased if different vehicles had been offered. Third, the historical data for demand estimation is censored, which further complicates the problem. Finally, the problem is an MDP with combinatorial state and action spaces, a class of problems known to be difficult to solve.

The core contribution is a novel policy based on Combinatorial-Optimization Augmented Machine Learning (COAML),. Numerical experiments show the performance of the approach.