Skip to main content
SpringerLink
Log in

An Efficient Polynomial-Time Approximation Scheme for the Joint Replenishment Problem

  • Conference paper
Integer Programming and Combinatorial Optimization (IPCO 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7801))

Abstract

We give an efficient polynomial-time approximation scheme (EPTAS) for the Joint Replenishment Problem (JRP) with stationary demand. Moreover, using a similar technique, we give a PTAS for the capacitated JRP with non-stationary demand but constant size capacities.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adelman, D., Klabjan, D.: Duality and existence of optimal policies in generalized joint replenishment. Mathematics of Operations Research 30(1), 28–50 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aggarwal, A., Park, J.K.: Improved algorithms for economic lot size problems. Oper. Res. 41(3), 549–571 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Arkin, E., Joneja, D., Roundy, R.: Computational complexity of uncapacitated multi-echelon production planning problems. Operations Research Letters 8(2), 61–66 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Federgruen, A., Tzur, M.: A simple forward algorithm to solve general dynamic lot sizing models with n periods in O(n logn) or O(n) time. Management Science 37(8), 909–925 (1991)

    Article  MATH  Google Scholar 

  5. Harris, F.W.: Operations cost. Factory Management Series. A. W. Shaw Co., Chicago (1915)

    Google Scholar 

  6. Jackson, P., Maxwell, W., Muckstadt, J.: The joint replenishment problem with power-of-two restriction. AIIE Trans. 17, 25–32 (1985)

    Google Scholar 

  7. Levi, R., Roundy, R., Shmoys, D.B.: Primal-dual algorithms for deterministic inventory problems. Mathematics of Operations Research 31, 267–284 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Levi, R., Roundy, R., Shmoys, D.B., Sviridenko, M.: A constant approximation algorithm for the one-warehouse multi-retailer problem. Management Science 54, 763–776 (2008)

    Article  MATH  Google Scholar 

  9. Roundy, R., Muckstadt, J.: Handbooks in Operations Research and Management Science: Analysis in Multi-Stage Production Systems, pp. 59–131. Elsevier (1993)

    Google Scholar 

  10. Naddor, E., Saltzman, S.: Optimal reorder periods for an inventory system with variable costs of ordering. Operations Research 6, 676–685

    Google Scholar 

  11. Nonner, T., Souza, A.: Approximating the joint replenishment problem with deadlines. Discrete Mathematics, Algorithms and Applications 1(2), 153–173 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Roundy, R.: 98%-effective integer-ratio lot-sizing for one-warehouse multi-retailer systems. Management Science 31(11), 1416–1430 (1985)

    Article  MATH  Google Scholar 

  13. Schulz, A.S., Telha, C.: Approximation Algorithms and Hardness Results for the Joint Replenishment Problem with Constant Demands. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 628–639. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  14. Segev, D.: An approximate dynamic-programming approach to the joint replenishment problem (2012) (manuscript)

    Google Scholar 

  15. Stauffer, G., Massonnet, G., Rapine, C., Gayon, J.-P.: A simple and fast 2-approximation algorithm for the one-warehouse multi-retailers problem. In: Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, pp. 67–79 (2011)

    Google Scholar 

  16. Teo, C.-P., Bertsimas, D.: Multistage lot sizing problems via randomized rounding. Operations Research 49(4), 599–608 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IBM Research, Zurich, Switzerland

    Tim Nonner

  2. University of Warwick, UK

    Maxim Sviridenko

Authors
  1. Tim Nonner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maxim Sviridenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Massachusetts Institute of Technology, 77 Massachusetts Ave., 02139, Cambridge, MA, USA

    Michel Goemans

  2. Universidad de Chile, Santiago, Chile

    José Correa

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nonner, T., Sviridenko, M. (2013). An Efficient Polynomial-Time Approximation Scheme for the Joint Replenishment Problem. In: Goemans, M., Correa, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2013. Lecture Notes in Computer Science, vol 7801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36694-9_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36694-9_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36693-2

  • Online ISBN: 978-3-642-36694-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation