Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2012, Article ID 582323, 21 pages
http://dx.doi.org/10.1155/2012/582323
Research Article

Dynamic Programming and Heuristic for Stochastic Uncapacitated Lot-Sizing Problems with Incremental Quantity Discount

1Department of Automation, TNList, Tsinghua University, Beijing 100084, China
2Industry Solutions, IBM Research-China, Beijing 100193, China

Received 30 January 2012; Revised 25 April 2012; Accepted 8 May 2012

Academic Editor: Jung-Fa Tsai

Copyright © 2012 Yuli Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Beraldi, G. Ghiani, A. Grieco, and E. Guerriero, “Fix and relax heuristic for a stochastic lot-sizing problem,” Computational Optimization and Applications, vol. 33, no. 2-3, pp. 303–318, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. H. M. Wagner and T. M. Whitin, “Dynamic version of the economic lot size model,” Management Science, vol. 5, pp. 89–96, 1958. View at Google Scholar · View at Zentralblatt MATH
  3. J. Hu and C. L. Munson, “Dynamic demand lot-sizing rules for incremental quantity discounts,” Journal of the Operational Research Society, vol. 53, no. 8, pp. 855–863, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. L. M. A. Chan, A. Muriel, Z. J. Shen, and D. S. Levi, “On the effectiveness of zero-inventory-ordering policies for the economic lot-sizing model with a class of piecewise linear cost structures,” Operations Research, vol. 50, no. 6, pp. 1058–1067, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. A. Federgruen and C. Y. Lee, “The dynamic lot size model with quantity discount,” Naval Research Logistics, vol. 37, no. 5, pp. 707–713, 1990. View at Google Scholar
  6. D. X. Shaw and A. P. M. Wagelmans, “An algorithm for single-item capacitated economic lot sizing with piecewise linear production costs and general holding costs,” Management Science, vol. 44, no. 6, pp. 831–838, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. S. Ahmed, A. J. King, and G. Parija, “A multi-stage stochastic integer programming approach for capacity expansion under uncertainty,” Journal of Global Optimization, vol. 26, no. 1, pp. 3–24, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Y. P. Guan and A. J. Miller, “Polynomial-time algorithms for stochastic uncapacitated lot-sizing problems,” Operations Research, vol. 56, no. 5, pp. 1172–1183, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. K. Huang and S. Küçükyavuz, “On stochastic lot-sizing problems with random lead times,” Operations Research Letters, vol. 36, no. 3, pp. 303–308, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. G. Lulli and S. Sen, “A branch-and-price algorithm for multistage stochastic integer programming with application to stochastic batch-sizing problems,” Management Science, vol. 50, no. 6, pp. 786–796, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. P. Beraldi, G. Ghiani, E. Guerriero, and A. Grieco, “Scenario-based planning for lot-sizing and scheduling with uncertain processing times,” International Journal of Production Economics, vol. 101, no. 1, pp. 140–149, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. D. Quadt and H. Kuhn, “Capacitated lot-sizing with extensions: a review,” A Quarterly Journal of Operations Research, vol. 6, no. 1, pp. 61–83, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. J. Raf and D. Zeger, “Modeling industrial lot sizing problems: a review,” International Journal of Production Research, vol. 46, no. 6, pp. 1619–1643, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. L. Buschkühl, F. Sahling, S. Helber, and H. Tempelmeier, “Dynamic capacitated lot-sizing problems: a classification and review of solution approaches,” OR Spectrum, vol. 32, no. 2, pp. 231–261, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. C. L. Munson and M. J. Rosenblatt, “Theories and realities of quantity discounts: an exploratory study,” Production and Operations Management, vol. 7, no. 4, pp. 352–369, 1998. View at Google Scholar · View at Scopus
  16. P. Beraldi, G. Ghiani, A. Grieco, and E. Guerriero, “Rolling-horizon and fix-and-relax heuristics for the parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs,” Computers and Operations Research, vol. 35, no. 11, pp. 3644–3656, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. D. Kim and P. M. Pardalos, “A solution approach to the fixed charge network flow problem using a dynamic slope scaling procedure,” Operations Research Letters, vol. 24, no. 4, pp. 195–203, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. S. Lawphongpanich, “Dynamic slope scaling procedure and lagrangian relaxation with subproblem approximation,” Journal of Global Optimization, vol. 35, no. 1, pp. 121–130, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH