Skip to main content
Log in

A cost-sharing method for the multi-level economic lot-sizing game

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

Multi-level economic lot-sizing models have been extensively investigated under different multi-level structure assumptions. In this paper, we consider the cooperative game associated with the multi-level economic lot-sizing problem. We present a cost-sharing method for the multi-level economic lot-sizing game, under a mild condition, which is cross-monotonic, competitive, and approximate cost recovery.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Jeunet J, Jonard N. Single-point stochastic search algorithms for the multi-level lot-sizing problem. Comput Oper Res, 2005, 32: 985–1006

    Article  MATH  MathSciNet  Google Scholar 

  2. Lambrecht M, Vander Eecken J, Vanderveken H. Review of optimal and heuristic methods for a class of facilities in series dynamic lot-size problems. In: Schwarz L B, ed. Multi-Level Production Inventory Control Systems. Amsterdam: North-Holland Publishing Company, 1981. 69–94

    Google Scholar 

  3. Zangwill W I. A backlogging model and a multi-echelon model of a dynamic economic lot size production system-a network approach. Manage Sci, 1969, 15: 506–527

    Article  MATH  MathSciNet  Google Scholar 

  4. Moulin H, Shenker S. Strategyproof sharing of submodular cost: budget balance versus efficiency. J Econ Theor, 2001, 18: 511–533

    Article  MATH  MathSciNet  Google Scholar 

  5. Pál M, Tardos É. Group strategyproof mechanisms via primal-dual algorithms. In: Proceedings of FOCS. Cambridge: IEEE Conference Publications, 2003. 584–593

    Google Scholar 

  6. van den Heuvel W, Borm P, Hamers H. Economic lot-sizing games. Eur J Oper Res, 2005, 176: 1117–1130

    Article  Google Scholar 

  7. Chen X, Zhang J. Duality approaches to economic lot-sizing games. Working Paper. New York: Stern School of Business, New York University, 2009. NYU Working Paper No. OM-2006-01

    Google Scholar 

  8. Pochet Y, Wolsey L A. Lot-size models with backlogging: strong reformulations and cutting planes. Math Program, 1988, 40: 317–335

    Article  MATH  MathSciNet  Google Scholar 

  9. Xu D, Yang R. A cost-sharing method for an economic lot-sizing game. Oper Res Lett, 2009, 37: 107–110

    Article  MATH  MathSciNet  Google Scholar 

  10. Yang R, Wang Z, Xu D. A cost-sharing method for the soft-capacitated economic lot-sizing game. In: Du D, Hu X, Pardols P, eds. Proceedings of COCOA. Berlin/Heidelberg: Springer-Verlag, 2009. 166–173

    Google Scholar 

  11. Aardal K I, Chudak F A, Shmoys D B. A 3-approximation algorithm for the k-level uncapacitated facility location problem. Inform Process Lett, 1999, 72: 161–167

    Article  MATH  MathSciNet  Google Scholar 

  12. Zhang J. Approximating the two-level facility location problem via a quasi-greedy approach. Math Program, 2006, 108: 159–176

    Article  MATH  MathSciNet  Google Scholar 

  13. Ageev A, Ye Y, Zhang J. Improved combinatorial approximation algorithms for the k-level facility location problem. SIAM J Discrete Math, 2005, 18: 207–217

    Article  MathSciNet  Google Scholar 

  14. Xu D, Du D. The k-level facility location game. Oper Res Lett, 2006, 34: 421–426

    Article  MATH  MathSciNet  Google Scholar 

  15. Chen X, Chen B. Approximation algorithms for soft-capacitated facility location in capacitated network design. Algorithmica, 2009, 53: 263–297

    Article  MATH  MathSciNet  Google Scholar 

  16. Du D, Lu R, Xu D. A primal-dual approximation algorithm for the facility location problem with submodular penalties. Algorithmica, 2012, 63: 191–200

    Article  MATH  MathSciNet  Google Scholar 

  17. Li S. A 1.488-approximation algorithm for the uncapacitated facility location problem. In: Aceto L, Henzinger M, Sgall J, eds. Proceedings of ICALP, Part II. Berlin/Heidelberg: Springer-Verlag, 2011. 77–88

    Google Scholar 

  18. Mahdian M, Ye Y, Zhang J. Improved approximation algorithms for metric facility location problems. SIAM J Comput, 2006, 36: 411–432

    Article  MATH  MathSciNet  Google Scholar 

  19. Shu J. An efficient greedy heuristic for warehouse-retailer network design optimization. Transport Sci, 2010, 44: 183–192

    Article  Google Scholar 

  20. Shu J, Teo C P, Max S Z J. Stochastic transportation-inventory network design problem. Oper Res, 2005, 53: 48–60

    Article  MATH  MathSciNet  Google Scholar 

  21. Zhang J, Chen B, Ye Y. A multiexchange local search algorithm for the capacitated facility location problem. Math Oper Res, 2005, 30: 389–403

    Article  MATH  MathSciNet  Google Scholar 

  22. Zhang P. A new approximation algorithm for the k-facility location problem. Theor Comput Sci, 2007, 384: 126–135

    Article  MATH  Google Scholar 

  23. Lu K, Chen G, Feng Y, et al. Approximation algorithm for minimizing relay node placement in wireless sensor networks. Sci China Inf Sci, 2010, 53: 2332–2342

    Article  Google Scholar 

  24. Jiang H, Zhu D. A 14/11-approximation algorithm for sorting by short block-move. Sci China Inf Sci, 2011, 54: 279–292

    Article  MATH  MathSciNet  Google Scholar 

  25. Li G, Du D, Xu D, et al. The multi-level economic lot-sizing game. In: Zhang X, ed. Operations Research and its Applications, ISORA. 2011. 100–106

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to DaChuan Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, G., Du, D., Xu, D. et al. A cost-sharing method for the multi-level economic lot-sizing game. Sci. China Inf. Sci. 57, 1–9 (2014). https://doi.org/10.1007/s11432-012-4694-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-012-4694-4

Keywords

Navigation