Advertisement

A Branch-and-Cut Algorithm for a Multi-item Inventory Distribution Problem

  • Agostinho Agra
  • Adelaide CerveiraEmail author
  • Cristina Requejo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10122)

Abstract

This paper considers a multi-item inventory distribution problem motivated by a practical case occurring in the logistic operations of an hospital. There, a single warehouse supplies several nursing wards. The goal is to define a weekly distribution plan of medical products that minimizes the visits to wards, while respecting inventory capacities and safety stock levels. A mathematical formulation is introduced and several improvements such as tightening constraints, valid inequalities and an extended reformulation are discussed. In order to deal with real size instances, an hybrid heuristic based on mathematical models is introduced and the improvements are discussed. A branch-and-cut algorithm using all the discussed improvements is proposed.

Finally, a computational experimentation is reported to show the relevance of the model improvements and the quality of the heuristic scheme.

Keywords

Multi-item inventory Hospital logistics Branch-and-cut Supply chain management 

Notes

Acknowledgements

The research of the first and third authors was partially supported through CIDMA and FCT, the Portuguese Foundation for Science and Technology, within project UID/MAT/ 04106/2013. The research of the second author is 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 National Funds through the FCT as part of project UID/EEA/50014/2013.

References

  1. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Agra, A., Andersson, H., Christiansen, M., Wolsey, L.: A maritime inventory routing problem: discrete time formulations and valid inequalities. Networks 62, 297–314 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Agra, A., Christiansen, M., Delgado, A.: Mixed integer formulations for a short sea fuel oil distribution problem. Transp. Sci. 47, 108–124 (2013)CrossRefGoogle Scholar
  4. 4.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Atamtürk, A., Küçükyavuz, S.: Lot sizing with inventory bounds and fixed costs: polyhedral study and computation. Oper. Res. 53(4), 711–730 (2005)CrossRefzbMATHGoogle Scholar
  7. 7.
    Bijvank, M., Vis, I.F.A.: Inventory control for point-of-use locations in hospitals. J. Oper. Res. Soc. 63, 497–510 (2012)CrossRefGoogle Scholar
  8. 8.
    Brown, G., Keegan, J., Vigus, B., Wood, K.: The Kellogg company optimizes production, inventory, and distribution. Interfaces 31, 1–15 (2001)CrossRefGoogle Scholar
  9. 9.
    Dacosta-Claro, I.: The performance of material management in health care organizations. Int. J. Health Plann. Manag. 17(1), 69–85 (2002)CrossRefGoogle Scholar
  10. 10.
    de Vries, J.: The shaping of inventory systems in health services: a stakeholder analysis. Int. J. Prod. Econ. 133, 60–69 (2011)CrossRefGoogle Scholar
  11. 11.
    Eppen, G.D., Martin, R.K.: Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper. Res. 35, 832–848 (1997)CrossRefzbMATHGoogle Scholar
  12. 12.
  13. 13.
    Fischetti, M., Lodi, A.: Local branching. Math. Program. Ser. B 98, 23–47 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Kelle, P., Woosley, J., Schneider, H.: Pharmaceutical supply chain specifics and inventory solutions for a hospital case. Oper. Res. Health Care 1(2–3), 54–63 (2012)CrossRefGoogle Scholar
  15. 15.
    Nemhauser, G., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, Hoboken (1988)CrossRefzbMATHGoogle Scholar
  16. 16.
    Pan, Z.X., Pokhareal, S.: Logistics in hospitals: a case study of some Singapore hospitals. Leadersh. Health Serv. 20(3), 195–207 (2007)CrossRefGoogle Scholar
  17. 17.
    Pochet, Y., Wolsey, L.A.: Production Planning by Mixed Integer Programming. Springer, Berlin (2006)zbMATHGoogle Scholar
  18. 18.
    Rosales, C.R., Magazine, M., Rao, U.: Point-of-use hybrid inventory policy for hospitals. Decis. Sci. 45(5), 913–937 (2014)CrossRefGoogle Scholar
  19. 19.
    Rais, A., Viana, A.: Operations research in healthcare: a survey. Int. Trans. Oper. Res. 18, 1–31 (2011)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Solyal, O., Sural, 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)CrossRefGoogle Scholar
  21. 21.
    Solyal, O., Sural, H.: The one-warehouse multi-retailer problem: reformulation, classification and computational results. Ann. Oper. Res. 196(1), 517–541 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Uthayakumar, R., Priyan, S.: Pharmaceutical supply chain and inventory management strategies: optimization for a pharmaceutical company and a hospital. Oper. Res. Health Care 2, 52–64 (2013)CrossRefGoogle Scholar
  23. 23.
    Volland, J., Fügener, A., Schoenfelder, J., Brunner, J.O.: Material logistics in hospitals: a literature review, Omega (2016, in press)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Agostinho Agra
    • 1
  • Adelaide Cerveira
    • 2
    • 3
    Email author
  • Cristina Requejo
    • 1
  1. 1.University of Aveiro and CIDMAAveiroPortugal
  2. 2.University of Trás-os-Montes e Alto-DouroVila RealPortugal
  3. 3.INESC TECPortoPortugal

Personalised recommendations