  We introduce the refined assortment optimization problem where a firm may
decide to make some of its products harder to get instead of making them
unavailable as in the traditional assortment optimization problem. Airlines,
for example, offer fares with severe restrictions rather than making them
unavailable. This is a more subtle way of handling the trade-off between demand
induction and demand cannibalization. For the latent class MNL model, a firm
that engages in refined assortment optimization can make up to $\min(n,m)$
times more than one that insists on traditional assortment optimization, where
$n$ is the number of products and $m$ the number of customer types.
Surprisingly, the revenue-ordered assortment heuristic has the same performance
guarantees relative to {\em personalized} refined assortment optimization as it
does to traditional assortment optimization. Based on this finding, we
construct refinements of the revenue-order heuristic and measure their improved
performance relative to the revenue-ordered assortment and the optimal
traditional assortment optimization problem. We also provide tight bounds on
the ratio of the expected revenues for the refined versus the traditional
assortment optimization for some well known discrete choice models.
