Skip to main content
SpringerLink
Log in

Lagrangian Relaxation Bounds for a Production-Inventory-Routing Problem

  • Conference paper
  • First Online:
Machine Learning, Optimization, and Big Data (MOD 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10122))

Included in the following conference series:

Abstract

We consider a single item Production-Inventory-Routing problem with a single producer/supplier and multiple retailers. Inventory management constraints are considered both at the producer and at the retailers, following a vendor managed inventory approach, where the supplier monitors the inventory at retailers and decides on the replenishment policy for each retailer. We assume a constant production capacity. Based on the mathematical formulation we discuss a classical Lagrangian relaxation which allows to decompose the problem into four subproblems, and a new Lagrangian decomposition which decomposes the problem into just a production-inventory subproblem and a routing subproblem. The new decomposition is enhanced with valid inequalities. A computational study is reported to compare the bounds from the two approaches.

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

Access this chapter

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and 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

References

  1. Adulyasak, Y., Cordeau, J., Jans, R.: The production routing problem: a review of formulations and solution algorithms. Comput. Oper. Res. 55, 141–152 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Adulyasak, Y., Cordeau, J., Jans, R.: Formulations and branch and cut algorithms for multi-vehicle production and inventory routing problems. Inf. J. Comput. 26(1), 103–120 (2014)

    Article  MathSciNet  Google Scholar 

  3. Agra, A., Andersson, H., Christiansen, M., Wolsey, L.: A maritime inventory routing problem: discrete time formulations and valid inequalities. Networks 62, 297–314 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Agra, A., Christiansen, M., Delgado, A.: Mixed integer formulations for a short sea fuel oil distribution problem. Transp. Sci. 47, 108–124 (2013)

    Article  Google Scholar 

  5. Agra, A., Christiansen, M., Delgado, A., Simonetti, L.: Hybrid heuristics for a short sea inventory routing problem. Eur. J. Oper. Res. 236, 924–935 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Agra, A., Christiansen, M., Ivarsoy, K., Solhaug, I., Tomasgard, A.: Combined ship routing and inventory management in the salmon farming industry. Ann. Oper. Res. (in press)

    Google Scholar 

  7. Andersson, H., Hoff, A., Christiansen, M., Hasle, G., Løkketangen, A.: Industrial aspects and literature survey: combined inventory management and routing. Comput. Oper. Res. 37(9), 1515–1536 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Archetti, C., Bertazzi, L., Laporte, G., Speranza, M.G.: A branch-and-cut algorithm for a vendor-managed inventory-routing problem. Transp. Sci. 41(3), 382–391 (2007)

    Article  Google Scholar 

  9. Bell, W.J., Dalberto, L.M., Fisher, M.L., Greenfield, A.J., Jaikumar, R., Kedia, P.: Improving the distribution of industrial gases with an on-line computerized routing and scheduling optimizer. Interfaces 13(6), 4–23 (1983)

    Article  Google Scholar 

  10. Christiansen, M.: Decomposition of a combined inventory and time constrained ship routing problem. Transp. Sci. 33(1), 3–16 (1999)

    Article  MATH  Google Scholar 

  11. Christiansen, M., Fagerholt, K.: Maritime Inventory Routing Problems. In: Floudas, C., Pardalos, P. (eds.) Encyclopedia of Optimization, 2nd edn, pp. 1947–1955. Springer, New York (2009)

    Google Scholar 

  12. Eksioglu, S.D., Romeijn, H.E., Pardalos, P.M.: Cross-facility management of production and trasportation planning problem. Comput. Oper. Res. 33(11), 3231–3251 (2006)

    Article  MATH  Google Scholar 

  13. Eppen, G.D., Martin, R.K.: Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper. Res. 35, 832–848 (1997)

    Article  MATH  Google Scholar 

  14. FICO Xpress Optimization Suite

    Google Scholar 

  15. Fumero, F., Vercellis, C.: Synchronized development of production, inventory, and distribution schedules. Transp. Sci. 33(3), 330–340 (1999)

    Article  MATH  Google Scholar 

  16. Geunes, J., Pardalos, P.M.: Network optimization in supply chain management and financial engineering: an annotated bibliography. Networks 42(2), 66–84 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. Held, M., Wolfe, P., Crowder, H.P.: Validation of subgradient optimization. Math. Program. 6, 62–88 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  18. Miller, C., Tucker, A., Zemlin, R.: Integer programming formulations and travelling salesman problems. J. Assoc. Comput. Mach. 7(4), 326–329 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  19. Pei, J., Pardalos, P.M., Liu, X., Fan, W., Yang, S., Wang, L.: Coordination of production and transportation in supply chain scheduling. J. Ind. Manage. Optim. 11(2), 399–419 (2015)

    MathSciNet  MATH  Google Scholar 

  20. Ruokokoski, M., Solyali, O., Cordeau, J.-F., Jans, R., Süral, H.: Efficient formulations and a branch-and-cut algorithm for a production-routing problem. GERAD Technical report G-2010-66. HEC Montréal, Canada (2010)

    Google Scholar 

  21. Shor, N.Z.: Minimization Methods for Non-Differentiable Functions. Springer, Heidelberg (1985)

    Book  MATH  Google Scholar 

  22. Solyali, O., Süral, H.: A branch-and-cut algorithm using a strong formulation and an a priori tour-based heuristic for an inventory-routing problem. Transp. Sci. 45(3), 335–345 (2011)

    Article  Google Scholar 

  23. Solyali, O., Süral, H.: A relaxation based solution approach for the inventory control and vehicle routing problem in vendor managed systems. In: Neogy, S.K., Das, A.K., Bapat, R.B. (eds.) Modeling, computation and Optimization, pp. 171–189. World Scientific, Singapore (2009)

    Google Scholar 

  24. Solyali, O., Süral, H.: The one-warehouse multi-retailer problem: reformulation, classification and computational results. Ann. Oper. Res. 196(1), 517–541 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The research of the first and third authors was supported through CIDMA and FCT, the Portuguese Foundation for Science and Technology, within project UID/MAT/ 04106/2013. The research of the second author was financed by the ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme within project “POCI-01-0145-FEDER-006961”, and by FCT within project UID/EEA/50014/2013.

Author information

Authors and Affiliations

  1. University of Aveiro and CIDMA, 3810-193, Aveiro, Portugal

    Agostinho Agra & Cristina Requejo

  2. University of Trás-os-Montes e Alto-Douro, 5001-801, Vila Real, Portugal

    Adelaide Cerveira

  3. INESC TEC, Porto, Portugal

    Adelaide Cerveira

Authors
  1. Agostinho Agra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adelaide Cerveira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cristina Requejo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Agostinho Agra .

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Semantic Technology Laboratory, National Research Council (CNR), Catania, Italy

    Piero Conca

  3. Dipartimento di Sociologia e Metodi della Ricerca Sociale, Università di Catania, Catania, Italy

    Giovanni Giuffrida

  4. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    Giuseppe Nicosia

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Agra, A., Cerveira, A., Requejo, C. (2016). Lagrangian Relaxation Bounds for a Production-Inventory-Routing Problem. In: Pardalos, P., Conca, P., Giuffrida, G., Nicosia, G. (eds) Machine Learning, Optimization, and Big Data. MOD 2016. Lecture Notes in Computer Science(), vol 10122. Springer, Cham. https://doi.org/10.1007/978-3-319-51469-7_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-51469-7_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51468-0

  • Online ISBN: 978-3-319-51469-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation