Skip to main content
SpringerLink
Log in

On discrete lot-sizing and scheduling on identical parallel machines

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

We consider the multi-item discrete lot-sizing and scheduling problem on identical parallel machines. Based on the fact that the machines are identical, we introduce aggregate integer variables instead of individual variables for each machine. For the problem with start-up costs, we show that the inequalities based on a unit flow formulation for each machine can be replaced by a single integer flow formulation without any change in the resulting LP bound. For the resulting integer lot-sizing with start-ups subproblem, we show how inequalities for the unit demand case can be generalized and how an approximate version of the extended formulation of Eppen and Martin can be constructed. The results of some computational experiments carried out to compare the effectiveness of the various mixed-integer programming formulations are presented.

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

Similar content being viewed by others

References

  1. Belvaux G., Wolsey L.A.: Modelling practical lot-sizing problems as mixed-integer programs. Manag. Sci. 47, 993–1007 (2001)

    Article  MATH  Google Scholar 

  2. Constantino, M.: A polyhedral approach to production planning models: startup costs and times and lower bounds on production. PhD thesis, Université catholique de Louvain, Belgique (1995)

  3. Eppen G.D, Martin R.K.: Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper. Res. 35, 832–848 (1987)

    Article  MATH  Google Scholar 

  4. Gicquel, C., Minoux, M., Dallery, Y.: A tight MIP formulation for the discrete lot sizing and scheduling problem with parallel resources, International Conference on Computers and Industrial Engineering. Université Technologique de Troyes, Troyes, France (2009)

  5. Jans R., Degraeve Z.: An industrial extension of the discrete lot-sizing and scheduling problem. IIE Trans. 36, 47–58 (2004)

    Article  Google Scholar 

  6. Lasdon L.S.: Optimization theory for large systems. Macmillan, New York (1970)

    MATH  Google Scholar 

  7. Lasdon L.S., Terjung R.C.: An efficient algorithm for multi-item scheduling. Oper. Res. 19, 946–969 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  8. Salomon M., Solomon M., van Wassenhove L.N., Dumas Y., Dauzère-Peres S.: Solving the discrete lotsizing and scheduling problem with sequence dependent set-up costs and set-up times using the travelling salesman problem with time windows. Eur. J. Oper. Res. 100, 494–513 (1997)

    Article  MATH  Google Scholar 

  9. Vanderbeck F., Wolsey L.A.: Valid inequalities for the Lasdon-Terjung production model. J. Oper. Res. Soc. 43, 435–441 (1992)

    MATH  Google Scholar 

  10. Van Eijl C.A., van Hoesel C.P.M.: On the discrete lot-sizing and scheduling problem with Wagner-Whitin costs. Oper. Res. Lett. 20, 7–13 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. van Hoesel C.P.M., Kolen A.: A linear description of the discrete lot-sizing and scheduling problem. Eur. J. Oper. Res. 75, 342–353 (1994)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire Génie Industriel, Ecole Centrale, Grande Voie des Vignes, 92290, Chatenay-Malabry, France

    C. Gicquel

  2. Center of Operations Research and Econometrics (CORE), Université catholique de Louvain, 34 Voie du Roman Pays, 1348, Louvain-la-Neuve, Belgium

    L. A. Wolsey

  3. Laboratoire d’Informatique de Paris 6, 5 place Jussieu, 75005, Paris, France

    M. Minoux

Authors
  1. C. Gicquel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. A. Wolsey
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Minoux
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. A. Wolsey.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gicquel, C., Wolsey, L.A. & Minoux, M. On discrete lot-sizing and scheduling on identical parallel machines. Optim Lett 6, 545–557 (2012). https://doi.org/10.1007/s11590-011-0280-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-011-0280-8

Keywords

Search

Navigation