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Approximation Algorithms for Dynamic Assortment Optimization Models

We consider a single-period joint assortment and inventory planning problem with stochastic demand and dynamic substitution across products, motivated by inventory management applications in highly differentiated markets, such as retailing, airlines, and consumer electronics. In its utmost generality, this problem is extremely hard to approximate with respect to various parameters. In fact, prior to the present paper, only a handful of modeling approaches were known to admit efficient algorithms with provably-good performance guarantees.Our main contribution is to provide the first polynomial-time algorithms with provable approximation guarantees for a broad class of dynamic assortment optimization models that capture real-life purchasing behaviors. From a technical perspective, we introduce a number of novel algorithmic ideas of independent interest, possibly applicable in broader settings, and unravel hidden relations to submodular maximization. In addition, our algorithms employ a mixture of greedy procedures, efficient enumerations methods, and low-dimensional dynamic programs, that are suitable for solving instances of practical nature and scale.