Assortment Planning and Inventory Management Under Dynamic Stockout-based Substitution Preliminary Draft

We consider the problem of a monopolist retailer choosing the optimal assortment and in-ventory levels for a discrete set of products with varying prices and costs in order to maximize expected profit in a single-period setting. Customer preferences are modeled through the defi-nition of consumer types, where a type is a ranking of the products by order of preference. A customer buys the highest ranked product available (if any) in the assortment at the time of his visit to the store (dynamic substitution). We first solve the case where all the customers have the same consumer type, and show that it may be optimal to stock multiple products because of differences in their implied risk-return tradeoffs. The solution is obtained using an efficient dynamic programming algorithm. We then show that this algorithm gives the optimal solution for more general preference structures when customers are partitioned into different types in fixed proportions. When the number of customers of each type is random, we use the algorithm to construct two heuristics and an upper bound, and numerically evaluate the performance of the heuristics