Combinatorial Assortment Optimization

Assortment optimization refers to the problem of designing a slate products offer potential customers, such as stocking shelves in convenience store. The price each product is fixed advance, and probabilistic choice function describes which customer will choose from any given subset. We introduce combinatorial assortment problem, where may select bundle products. consider model consumer selects utility-maximizing subject private valuation function, study complexity resulting problem. Our main result an exact algorithm for additive k -demand valuations, under vertical differentiation customers agree on relative value pair items but differ their absolute willingness pay. For valuations that are vertically differentiated not necessarily -demand, we show how obtain constant approximations “well-priced” condition, product’s sufficiently high. further even single with known valuation, sub-polynomial approximation requires exponentially many demand queries when XOS no FPTAS exists succinctly representable.