Skip to main content
SpringerLink
Log in
Book cover

International Conference on Variable Neighborhood Search

ICVNS 2018: Variable Neighborhood Search pp 41–51Cite as

A VNS Approach to Solve Multi-level Capacitated Lotsizing Problem with Backlogging

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11328))

Abstract

In this paper a multi-level capacitated lotsizing problem with machine-capacity-constraint and backlogging is studied. The main objective is to minimize the total cost which includes the inventory and delaying costs of produced items. Since the problem under study is NP-hard, a variable neighborhood search (VNS) combined with CPLEX solver is proposed as a solution approach. Neighborhood is changed according to VNS scheme employing four different functions and is locally optimized for a set of partial MIP problems that can be easily solved.

Finally, extensive computational tests demonstrate that the proposed search algorithm can find good quality solutions for all examined problems. The objective values obtained by the proposed algorithm are comparable to the results of state-of-the art, much more complicated algorithms.

This work is supported by AGH UST statutory research no. 11/11.200.327.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
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

Learn about institutional subscriptions

References

  1. Akartunali, K., Miller, A.J.: A heuristic approach for big bucket multi-level production planning problems. Eur. J. Oper. Res. 193(2), 396–411 (2009)

    Article  MathSciNet  Google Scholar 

  2. Billington, P., McClain, J., Thomas, L.: Mathematical programming approaches to capacity-constrained MRP systems: review, formulation and problem reduction. Manag. Sci. 29(10), 1126–1141 (1983)

    Article  Google Scholar 

  3. Buschkuehl, L., Sahling, F., Helber, S., Tempelmeier, H.: Dynamic capacitated lot-sizing problems: a classification and review of solution approaches. OR Spectr. 32(2), 231–261 (2010)

    Article  MathSciNet  Google Scholar 

  4. Chen, H.: Fix-and-optimize and variable neighborhood search approaches for multi-level capacitated lot sizing problems. Omega 56, 25–36 (2015)

    Article  Google Scholar 

  5. Duda, J., Stawowy, A.: A variable neighborhood search for multi-family capacitated lot-sizing problem. Electron. Notes Discrete Math. 66, 119–126 (2018)

    Article  MathSciNet  Google Scholar 

  6. Erromdhani, R., Jarboui, B., Eddaly, M., Rebai, A., Mladenovic, N.: Variable neighborhood formulation search approach for the multi-item capacitated lot-sizing problem with time windows and setup times. Yugoslav J. Oper. Res. 27(3), 301–322 (2017)

    Article  MathSciNet  Google Scholar 

  7. Jans, R., Degraeve, Z.: Meta-heuristics for dynamic lot sizing: a review and comparison of solution approaches. Eur. J. Oper. Res. 177(3), 1855–1875 (2007)

    Article  Google Scholar 

  8. Lazic, J., Hanafi, S., Mladenovic, N., Urosevic, D.: Variable neighbourhood decomposition search for 0–1 mixed integer programs. Comput. Oper. Res. 37(6), 1055–1067 (2010)

    Article  MathSciNet  Google Scholar 

  9. Seeanner, F., Almada-Lobo, B., Meyr, H.: Combining the principles of variable neighborhood decomposition search and the fix and optimize heuristic to solve multi-level lot-sizing and scheduling problems. Comput. Oper. Res. 40(1), 303–317 (2013)

    Article  MathSciNet  Google Scholar 

  10. Sifaleras, A., Konstantaras, I.: General variable neighborhood search for the multi-product dynamic lot sizing problem in closed-loop supply chain. Electron. Notes Discrete Math. 47, 69–76 (2015)

    Article  MathSciNet  Google Scholar 

  11. Sifaleras, A., Konstantaras, I.: Variable neighborhood descent heuristic for solving reverse logistics multi-item dynamic lot-sizing problems. Comput. Oper. Res. 78, 385–392 (2017)

    Article  MathSciNet  Google Scholar 

  12. Simpson, N., Erengue, S.: Modeling multiple stage manufacturing systems with generalized costs and capacity issues. Nav. Res. Logist. 52(6), 560–570 (2005)

    Article  MathSciNet  Google Scholar 

  13. Toledo, C., de Oliveira, R., Franca, P.: A hybrid multi-population genetic algorithm applied to solve the multi-level capacitated lot sizing problem with backlogging. Comput. Oper. Res. 40(4), 910–919 (2013)

    Article  MathSciNet  Google Scholar 

  14. Wu, T., Shi, L., Geunes, J., Akartunali, K.: An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging. Eur. J. Oper. Res. 214(2), 428–441 (2011)

    Article  MathSciNet  Google Scholar 

  15. Zhao, Q., Xie, C., Xiao, Y.: A variable neighborhood decomposition search algorithm for multilevel capacitated lot-sizing problem. Electron. Notes Discrete Math. 39, 129–135 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Computer Science, Faculty of Management, AGH University of Science and Technology, Gramatyka St. 10, 30-067, Krakow, Poland

    Jerzy Duda & Adam Stawowy

Authors
  1. Jerzy Duda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adam Stawowy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jerzy Duda .

Editor information

Editors and Affiliations

  1. University of Macedonia, Thessaloniki, Greece

    Angelo Sifaleras

  2. University of Kent, Canterbury, UK

    Said Salhi

  3. Royal Military College of Canada, Kingston, ON, Canada

    Jack Brimberg

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Duda, J., Stawowy, A. (2019). A VNS Approach to Solve Multi-level Capacitated Lotsizing Problem with Backlogging. In: Sifaleras, A., Salhi, S., Brimberg, J. (eds) Variable Neighborhood Search. ICVNS 2018. Lecture Notes in Computer Science(), vol 11328. Springer, Cham. https://doi.org/10.1007/978-3-030-15843-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-15843-9_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-15842-2

  • Online ISBN: 978-3-030-15843-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation