Combinatorial Assortment Optimization
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 -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.
Cite
@article{arxiv.1711.02601,
title = {Combinatorial Assortment Optimization},
author = {Nicole Immorlica and Brendan Lucier and Jieming Mao and Vasilis Syrgkanis and Christos Tzamos},
journal= {arXiv preprint arXiv:1711.02601},
year = {2017}
}