Skip to main content
SpringerLink
Log in

Algorithms for the two-stage production-capacitated lot-sizing problem

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

We model the two-stage production-capacitated lot-sizing problem as a concave minimum cost network flow problem and characterize the possible patterns of flow between successive periods in which transportation occurs. We demonstrate that production and transportation decisions can be made based only on the local state of transportation patterns between successive transportation periods. Utilizing this observation together with the insight that it is not necessary to consider transportation decisions between transportation periods, we provide a novel improved \(O(T^6)\) algorithm (where T is the length of the planning horizon). We extend this approach to special cases, and develop an \(O(T^5)\) algorithm for the case with non-speculative costs, and an \(O(T^4)\) algorithm for the case with linear costs.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Florian, M., Klein, M.: Deterministic production planning with concave costs and capacity constraints. Manag. Sci. 18, 12–20 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  2. He, Q., Ahmed, S., Nemhauser, G.L.: Minimum concave cost flow over a grid network. Math. Program. 150, 79–98 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hwang, H.-C., Ahn, H., Kaminsky, P.: Basis paths and a polynomial algorithm for the multi-level production-capacitated lot-sizing problem. Oper. Res. 61, 469–482 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kaminsky, P., Simchi-Levi, D.: Production and distribution lot sizing in a two stage supply chain. IIE Trans. 35, 1065–1075 (2003)

    Article  Google Scholar 

  5. Melo, R., Wolsey, L.A.: Uncapacitated two-level lot-sizing. Oper. Res. Lett. 38, 241–245 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Sargut, F.Z., Romeijn, H.E.: Capacitated production and subcontracting in a serial supply chain. IIE Trans. 39, 1031–1043 (2007)

    Article  Google Scholar 

  7. Van Vyve, M., Wolsey, L.A., Yaman, H.: Relaxations for two-level multi-item lot-sizing problems. Math. Program. 146, 495–523 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Van den Heuvel, W., Wagelmans, A.P.M.: An efficient dynamic programming algorithm for a special case of the capacitated lot-sizing problem. Comput. Oper. Res. 33, 3583–3599 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Van Hoesel, S., Romeijn, H.E., Morales, D.R., Wagelmans, A.P.M.: Integrated lot-sizing in serial supply chains with production capacities. Manag. Sci. 51, 1706–1719 (2005)

    Article  MATH  Google Scholar 

  10. Wagner, H.M., Whitin, T.M.: Dynamic version of the economic lot-size model. Manag. Sci. 5, 89–96 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zangwill, W.I.: A backlogging model and a multi-echelon model of a dynamic economic lot size transportation system-a network approach. Manag. Sci. 15, 506–527 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhang, M., Küçükyavuz, S., Yaman, H.: A polyhedral study of multi-echelon lot sizing with intermediate demands. Oper. Res. 60, 918–935 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

We thank an Associate Editor for the constructive comments to improve the paper. This work was supported by a grant from Kyung Hee University in 2014 (KHU-20140686) and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0021551).

Author information

Authors and Affiliations

  1. School of Management, Kyung Hee University, 26 Kyunghee-daero, Dongdaemun-gu, Seoul, 130-701, Republic of Korea

    Hark-Chin Hwang

  2. Department of Operations and Management Science, Ross School of Business, University of Michigan, Ann Arbor, MI, 48109, USA

    Hyun-Soo Ahn

  3. Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, 94720, USA

    Philip Kaminsky

Authors
  1. Hark-Chin Hwang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hyun-Soo Ahn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Philip Kaminsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hark-Chin Hwang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hwang, HC., Ahn, HS. & Kaminsky, P. Algorithms for the two-stage production-capacitated lot-sizing problem. J Glob Optim 65, 777–799 (2016). https://doi.org/10.1007/s10898-015-0392-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-015-0392-2

Keywords

Search

Navigation