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Integrated Supply Chain Management via Randomized Rounding

  • Lehilton L. C. Pedrosa
  • Maxim Sviridenko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

Abstract

We consider the supply chain problem of minimizing ordering, distribution and inventory holding costs of a supply chain formed by a set of warehouses and retailers over a finite time horizon, that we call Production and Distribution Problem (PDP). This is a common generalization of the classical Metric Facility Location Problem and Joint Replenishment Problem, that coordinates the network design and inventory management decisions in an integrated manner. This coordination can represent significant economy for many applications, where network design and operational costs are normally considered separately. This problem is considered when the instances satisfy assumptions such as metric space of warehouse and retailer locations, and monotonic increasing inventory holding costs. In this work, we give a 2.77-approximation based on the randomized rounding of the natural mixed integer programming relaxation. Also, we give a 5-approximation for the case that objective function includes retailer ordering costs.

Keywords

Cluster Center Mixed Integer Programming Service Cost Facility Location Problem Demand Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Boudia, M., Prins, C.: A memetic algorithm with dynamic population management for an integrated production–distribution problem. European J. Oper. Research 195(3), 703–715 (2009)CrossRefzbMATHGoogle Scholar
  2. 2.
    Byrka, J., Aardal, K.: An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem. SIAM J. on Comp. 39, 2212–2231 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Chan, F.T.S., Chung, S.H., Wadhwa, S.: A hybrid genetic algorithm for production and distribution. Omega 33(4), 345–355 (2005)CrossRefGoogle Scholar
  4. 4.
    Chudak, F.A., Shmoys, D.B.: Improved Approximation Algorithms for the Uncapacitated Facility Location Problem. SIAM J. on Comp. 33(1), 1–25 (2004)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Daskin, M.S., Coullard, C.R., Shen, Z.-J.: An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results. Annals of Oper. Research 110(1-4), 83–106 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Levi, R., Roundy, R., Shmoys, D.B., Sviridenko, M.: A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem. Management Science 54(4), 763–776 (2008)CrossRefzbMATHGoogle Scholar
  7. 7.
    Li, S.: A 1.488 Approximation Algorithm for the Uncapacitated Facility Location Problem. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 77–88. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Li, Y., Shu, J., Wang, X., Xiu, N., Xu, D., Zhang, J.: Approximation Algorithms for Integrated Distribution Network Design Problems. In: INFORMS J. Comp. (2012)Google Scholar
  9. 9.
    Lin, J.-H., Vitter, J.S.: ε-approximations with minimum packing constraint violation (extended abstract). In: Proc. of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, pp. 771–782 (1992)Google Scholar
  10. 10.
    Melo, M.T., Nickel, S., Saldanha-da Gama, F.: Facility location and supply chain management – A review. European J. Oper. Research 196(2), 401–412 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Pochet, Y., Wolsey, L.A.: Production planning by mixed integer programming. Springer series in operations research and financial engineering. Springer, New York (2006)zbMATHGoogle Scholar
  12. 12.
    Shen, Z.-J.: Integrated Stochastic Supply-Chain Design Models. Computing in Science Engineering 9(2), 50–59 (2007)CrossRefGoogle Scholar
  13. 13.
    Shen, Z.-J., Coullard, C., Daskin, M.S.: A Joint Location-Inventory Model. Transportation Science 37(1), 40–55 (2003)CrossRefGoogle Scholar
  14. 14.
    Shu, J., Teo, C.-P., Shen, Z.-J.: Stochastic Transportation-Inventory Network Design Problem. Oper. Research 53(1), 48–60 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Sviridenko, M.: An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem. In: Cook, W.J., Schulz, A.S. (eds.) IPCO 2002. LNCS, vol. 2337, pp. 240–257. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Teo, C.-P., Shu, J.: Warehouse-Retailer Network Design Problem. Oper. Research 52(3), 396–408 (2004)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Lehilton L. C. Pedrosa
    • 1
  • Maxim Sviridenko
    • 2
  1. 1.Institute of ComputingUniversity of CampinasBrazil
  2. 2.Department of Computer ScienceUniversity of WarwickUK

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