Approximation Algorithms for Dynamic Assortment Optimization Models
36 Pages Posted: 8 Aug 2015 Last revised: 6 Nov 2016
Date Written: August 8, 2015
We consider the single-period joint assortment and inventory planning problem with stochastic demand and dynamic substitution across products, motivated by applications in highly differentiated markets, such as online retailing and airlines. This class of problems is known to be computationally prohibitive. In fact, prior to the present paper, only a handful of modeling approaches were known to admit provably-good algorithms, at the cost of strong restrictions on customers' choice outcomes. Our main contribution is to provide the first efficient algorithms with provable performance guarantees for a broad class of dynamic assortment optimization models. Under general random-utility choice models, our approximation guarantee is order optimal with respect to the price parameters. We obtain improved guarantees under more specialized choice models, where customers' purchasing behaviors are elicited by price and quality cues. Our algorithms are myopic in nature, faster than existing heuristics by an order of magnitude and substantially increase revenue in extensive synthetic experiments. Technically speaking, we introduce a number of novel algorithmic ideas of independent interest, and unravel hidden relations to submodular maximization.
Keywords: Assortment Planning, Inventory Management, Choice Models, Dynamic Optimization, Approximation Algorithms, Submodularity
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