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arXiv · 1711.02601

Combinatorial Assortment Optimization

Nicole Immorlica·Brendan Lucier·Jieming Mao·Vasilis Syrgkanis·Christos Tzamos
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Abstract

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a model of consumer choice where the relative value of different bundles is described by a valuation function, while individual customers may differ in their absolute willingness to pay, and study the complexity of the resulting optimization problem. We show that any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS, and that no FPTAS exists even for succinctly-representable submodular valuations. On the positive side, we show how to obtain constant approximations under a "well-priced" condition, where each product's price is sufficiently high. We also provide an exact algorithm for $k$-additive valuations, and show how to extend our results to a learning setting where the seller must infer the customers' preferences from their purchasing behavior.

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Nicole Immorlica, Brendan Lucier, Jieming Mao, Vasilis Syrgkanis, Christos Tzamos. 2017-11-07. Combinatorial Assortment Optimization. https://arxiv.org/abs/1711.02601

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