Greedy-Like Algorithms for Dynamic Assortment Planning Under Multinomial Logit Preferences
We study the joint assortment planning and inventory management problem, where stock-out events elicit dynamic substitution effects, described by the Multinomial Logit (MNL) choice model. Special cases of this setting have extensively been studied in recent literature, typically as static assortment planning problems. Nevertheless, the general formulation is not known to admit efficient algorithms with analytical performance guarantees, and most of its computational aspects are still wide open.
We devise the first provably-good approximation algorithm for dynamic assortment planning under the MNL model. Our approach relies on a combination of greedy procedures, where stocking decisions are restricted to specific classes of products, and the objective function takes modified forms. In the course of establishing our main result, we develop new algorithmic ideas that may be of independent interest. These include weaker notions of submodularity and monotonicity, shown sufficient to obtain constant-factor worst-case guarantees, despite using noisy estimates of the objective function.
This talk is based on a joint paper with Ali Aouad (MIT) and Retsef Levi (MIT).