Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-stage and Multi-customer Assortment Optimization with Inventory
  Constraints   We consider an assortment optimization problem where a customer chooses a
single item from a sequence of sets shown to her, while limited inventories
constrain the items offered to customers over time. In the special case where
all of the assortments have size one, our problem captures the online
stochastic matching with timeouts problem. For this problem, we derive a
polynomial-time approximation algorithm which earns at least 1-ln(2-1/e), or
0.51, of the optimum. This improves upon the previous-best approximation ratio
of 0.46, and furthermore, we show that it is tight. For the general assortment
problem, we establish the first constant-factor approximation ratio of 0.09 for
the case that different types of customers value items differently, and an
approximation ratio of 0.15 for the case that different customers value each
item the same. Our algorithms are based on rounding an LP relaxation for
multi-stage assortment optimization, and improve upon previous randomized
rounding schemes to derive the tight ratio of 1-ln(2-1/e).

7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat