Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimality gap of constant-order policies decays exponentially in the
  lead time for lost sales models   Inventory models with lost sales and large lead times have traditionally been
considered intractable due to the curse of dimensionality. Recently, Goldberg
and co-authors laid the foundations for a new approach to solving these models,
by proving that as the lead time grows large, a simple constant-order policy is
asymptotically optimal. However, the bounds proven there require the lead time
to be very large before the constant-order policy becomes effective, in
contrast to the good numerical performance demonstrated by Zipkin even for
small lead time values. In this work, we prove that for the infinite-horizon
variant of the same lost sales problem, the optimality gap of the same
constant-order policy actually converges \emph{exponentially fast} to zero,
with the optimality gap decaying to zero at least as fast as the exponential
rate of convergence of the expected waiting time in a related single-server
queue to its steady-state value. We also derive simple and explicit bounds for
the optimality gap, and demonstrate good numerical performance across a wide
range of parameter values for the special case of exponentially distributed
demand. Our main proof technique combines convexity arguments with ideas from
queueing theory.

19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph