Approximation Algorithms for the Joint Replenishment Problem with Deadlines

  • Marcin Bienkowski
  • Jaroslaw Byrka
  • Marek Chrobak
  • Neil Dobbs
  • Tomasz Nowicki
  • Maxim Sviridenko
  • Grzegorz Świrszcz
  • Neal E. Young
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7965)

Abstract

The Joint Replenishment Problem (JRP) is a fundamental optimization problem in supply-chain management, concerned with optimizing the flow of goods over time from a supplier to retailers. Over time, in response to demands at the retailers, the supplier sends shipments, via a warehouse, to the retailers. The objective is to schedule shipments to minimize the sum of shipping costs and retailers’ waiting costs.

We study the approximability 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, and 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.

Keywords

Joint replenishment problem with deadlines inventory theory linear programming integrality gap randomized rounding approximation algorithm 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Marcin Bienkowski
    • 1
  • Jaroslaw Byrka
    • 1
  • Marek Chrobak
    • 2
  • Neil Dobbs
    • 3
  • Tomasz Nowicki
    • 3
  • Maxim Sviridenko
    • 4
  • Grzegorz Świrszcz
    • 4
  • Neal E. Young
    • 2
  1. 1.Institute of Computer ScienceUniversity of WrocławPoland
  2. 2.Department of Computer ScienceUniversity of California at RiversideUSA
  3. 3.IBM T.J. Watson Research CenterYorktown HeightsUSA
  4. 4.Department of Computer ScienceUniversity of WarwickUK

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