Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation Algorithms for the Joint Replenishment Problem with
  Deadlines   The Joint Replenishment Problem (JRP) is a fundamental optimization problem
in supply-chain management, concerned with optimizing the flow of goods from a
supplier to retailers. Over time, in response to demands at the retailers, the
supplier ships orders, via a warehouse, to the retailers. The objective is to
schedule these orders to minimize the sum of ordering costs and retailers'
waiting costs.
  We study the approximability of JRP-D, the version of JRP with deadlines,
where instead of waiting costs the retailers impose strict deadlines. We study
the integrality gap of the standard linear-program (LP) relaxation, giving a
lower bound of 1.207, a stronger, computer-assisted lower bound of 1.245, as
well as an upper bound and approximation ratio of 1.574. The best previous
upper bound and approximation ratio was 1.667; no lower bound was previously
published. For the special case when all demand periods are of equal length we
give an upper bound of 1.5, a lower bound of 1.2, and show APX-hardness.

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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol