Skip to main content

A Matheuristic Approach for the Total Completion Time Two-Machines Permutation Flow Shop Problem

  • Conference paper
Book cover Evolutionary Computation in Combinatorial Optimization (EvoCOP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6622))

Abstract

This paper deals with the total completion time 2-machines flow shop problem. We present a so-called matheuristic post processing procedure that improves the objective function value with respect to the solutions provided by state of the art procedures. The proposed procedure is based on the positional completion times integer programming formulation of the problem with O(n 2) variables and O(n) constraints.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akkan, C., Karabati, S.: The two-machine flowshop total completion time problem: Improved lower bounds and a branch-and-bound algorithm. European Journal of Operational Research 159, 420–429 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bansal, S.P.: Minimizing the sum of completion times of n-jobs over M-machines in a flowshop. AIIE Transactions on a Branch and Bound Approach 9, 306–311 (1977)

    Article  Google Scholar 

  3. Della Croce, F., Ghirardi, M., Tadei, R.: An improved branch-and-bound algorithm for the two machine total completion time flow shop problem. European Journal of Operational Research 139, 293–301 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Della Croce, F., Ghirardi, M., Tadei, R.: Recovering Beam Search: enhancing the beam search approach for combinatorial optimization problems. Journal of Heuristics 10, 89–104 (2004)

    Article  MATH  Google Scholar 

  5. Della Croce, F., Narayan, V., Tadei, R.: The two-machine total completion time flow shop problem. European Journal of Operational Research 90, 227–237 (1996)

    Article  MATH  Google Scholar 

  6. Della Croce, F., Salassa, F.: A Variable Neighborhood Search Based Matheuristic for Nurse Rostering Problems. In: Proceedings of 8th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2010, Belfast, UK, August 10-13 (2010)

    Google Scholar 

  7. Dong, X., Huang, H., Chen, P.: An iterated local search algorithm for the permutation flowshop problem with total flowtime criterion. Computers & Operations Research 36, 1664–1669 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fischetti, M., Lodi, A.: Local Branching. Mathematical Programming B 98, 23–47 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Garey, M.R., Johnson, D.S., Sethi, R.: The complexity of flowshop and jobshop scheduling. Mathematics of Operations Research 1, 117–129 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  10. Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Operations Research 5, 287–326 (1979)

    MathSciNet  MATH  Google Scholar 

  11. Hansen, P., Mladenovic, N.: Variable neighborhood search: Principles and applications. European Journal of Operational Research 130, 449–467 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hoogeveen, H., van Norden, L., van de Velde, S.: Lower bounds for minimizing total completion time in a two-machine flow shop. Journal of Scheduling 9, 559–568 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hoogeveen, J.A., Van de Velde, S.L.: Stronger Lagrangian bounds by use of slack variables: applications to machine scheduling problems. Mathematical Programming 70, 173–190 (1995)

    MathSciNet  MATH  Google Scholar 

  14. Ladhari, T., Rakrouki, M.A.: Heuristics and lower bounds for minimizing the total completion time in a two-machine flowshop. International Journal of Production Economics 122, 678–691 (2009)

    Article  Google Scholar 

  15. Lasserre, J.B., Queyranne, M.: Generic scheduling polyhedral and a new mixed integer formulation for single machine scheduling. In: Proceedings of the IPCO Conference (1992)

    Google Scholar 

  16. Maniezzo, V., Stutzle, T., Voss, S.: Matheuristics: Hybridizing Metaheuristics and Mathematical Programming. Annals of Information Systems 10 (2009)

    Google Scholar 

  17. Ruiz, R., Maroto, C.: A comprehensive review and evaluation of permutation flowshop heuristics. European Journal of Operational Research 165, 479–494 (2005)

    Article  MATH  Google Scholar 

  18. Taillard, E.: Some efficient heuristic methods for the flow shop sequencing problem. European Journal of Operational Research 47, 65–74 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  19. T’kindt, V., Monmarché, N., Laugt, D., Tercinet, F.: An Ant Colony Optimization Algorithm to Solve a 2-Machine Bicriteria Flowshop Scheduling Problem. European Journal of Operational Research 142, 250–257 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  20. Stafford, E.F.: On the development of a mixed integer linear programming model for the flowshop sequencing problem. Journal of the Operational Research Society 39, 1163–1174 (1988)

    Article  MATH  Google Scholar 

  21. Van de Velde, S.: Minimizing the sum of job completion times in the two-machine flowshop by Lagrangean relaxation. Annals of Operations Research 26, 257–268 (1990)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Della Croce, F., Grosso, A., Salassa, F. (2011). A Matheuristic Approach for the Total Completion Time Two-Machines Permutation Flow Shop Problem. In: Merz, P., Hao, JK. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2011. Lecture Notes in Computer Science, vol 6622. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20364-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-20364-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20363-3

  • Online ISBN: 978-3-642-20364-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics