Skip to main content
SpringerLink
Log in

On efficient matheuristic algorithms for multi-period stochastic facility location-assignment problems

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

In this work we present two matheuristic procedures to build good feasible solutions (frequently, the optimal one) by considering the solutions of relaxed problems of large-sized instances of the multi-period stochastic pure 0–1 location-assignment problem. The first procedure is an iterative one for Lagrange multipliers updating based on a scenario cluster Lagrangean decomposition for obtaining strong (lower, in case of minimization) bounds of the solution value. The second procedure is a sequential one that works with the relaxation of the integrality of subsets of variables for different levels of the problem, so that a chain of (lower, in case of minimization) bounds is generated from the LP relaxation up to the integer solution value. Additionally, and for both procedures, a lazy heuristic scheme, based on scenario clustering and on the solutions of the relaxed problems, is considered for obtaining a (hopefully good) feasible solution as an upper bound of the solution value of the full problem. Then, the same framework provides for the two procedures lower and upper bounds on the solution value. The performance is compared over a set of instances of the stochastic facility location-assignment problem. It is well known that the general static deterministic location problem is NP-hard and, so, it is the multi-period stochastic version. A broad computational experience is reported for 14 instances, up to 15 facilities, 75 customers, 6 periods, over 260 scenarios and over 420 nodes in the scenario tree, to assess the validity of proposals made in this work versus the full use of a state-of the-art IP optimizer.

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. Aghezaaf, E.: Capacity planning and warehouse location in supply chains with uncertain demands. J. Oper. Res. Soc. 56, 453–462 (2005)

    Article  Google Scholar 

  2. Albareda-Sambola, M., Alonso-Ayuso, A., Escudero, L.F., Fernández, E., Hinojosa, Y., Pizarro, C.: A computational comparison of several formulations for the multi-period location-assignment problem. TOP 18, 62–80 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Albareda-Sambola, M., Fernández, E., Hinojosa, Y., Puerto, J.: The multi-period incremental service facility location problem. Comput. Oper. Res. 36, 1356–1375 (2009)

    Article  MATH  Google Scholar 

  4. Albareda-Sambola, M., Alonso-Ayuso, A., Escudero, L.F., Fernández, E., Pizarro, C.: Fix-and-relax-coordination for a multi-period location-allocation problem under uncertainty. Comput. Oper. Res. 40, 2878–2892 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Alonso-Ayuso, A., Escudero, L.F., Garín, A., Ortuño, M.T., Pérez, G.: An approach for strategic supply chain planning based on stochastic 0–1 programming. J. Glob. Optim. 26, 97–124 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Alonso-Ayuso, A., Escudero, L.F., Ortuño, M.T.: On modeling planning under uncertainty in manufacturing. Stat. Oper. Res. Trans. 31, 109–150 (2007)

    MATH  Google Scholar 

  7. Albareda-Sambola, M., Fernández, E., Saldanha-da-Gama, F.: The facility location problem with Bernoulli demands. Omega 39, 335–345 (2011)

    Article  Google Scholar 

  8. Barahona, F., Anbil, R.: The volume algorithm: producing primal solutions with a subgradient method. Math. Program. Ser. A 87, 385–399 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Birge, J.R., Louveaux, F.V.: Introduction to Stochastic Programming, 2nd edn. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

  10. Castro, J., Nasini, S., Saldanha-da-Gama, F.: A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method. Math. Program. Ser. A 163, 414–444 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  11. Cavalier, T.M., Sherali, H.D.: Sequential location–allocation problems on chains and trees with probabilistic demands. Math. Program. 32, 249–277 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen, G., Daskin, M.S., Max-Shen, Z.J., Uryasev, S.: The a-reliable mean-excess regret model for stochastic facility location modeling. Nav. Res. Logist. 53, 617–626 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Correia, I., Saldanha da Gama, F.: Facility location under uncertainty. In: Laporte, G., Nickel, S., Saldanha da Gama, F. (eds.) Location Science, pp. 177–203. Springer, Berlin (2015)

  14. Current, J., Ratick, S., ReVelle, C.: Dynamic facility location when the total number of facilities is uncertain: a decision analysis approach. Eur. J. Oper. Res. 110, 597–609 (1998)

    Article  MATH  Google Scholar 

  15. Diabatr, A., Richard, J-Ph: An integrated supply chain problem: a nested Lagrangian relaxation approach. Ann. Oper. Res. 229, 303–323 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. Dias, J., Captivo, M.E., Climaco, J.: Dynamic location problems with discrete expansion and reduction sizes of available capacities. Investig. Oper. 27, 107–130 (2007)

    Google Scholar 

  17. Escudero, L.F., Garín, A., Merino, M., Pérez, G.: An algorithmic framework for solving large scale stochastic mixed 0–1 problems with nonsymmetric scenario trees. Comput. Oper. Res. 39, 1133–1144 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Escudero, L.F., Garín, A., Merino, M., Pérez, G.: On time stochastic dominance induced by mixed integer-linear recourse in multi-period stochastic programs. Eur. J. Oper. Res. 249, 164–176 (2016)

    Article  MATH  Google Scholar 

  19. Escudero, L.F., Garín, A., Pérez, G., Unzueta, A.: Scenario cluster decomposition of the Lagrangian dual in two-stage stochastic mixed 0–1 optimization. Comput. Oper. Res. 40, 362–377 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Escudero, L.F., Garín, A., Unzueta, A.: Cluster Lagrangean decomposition in multistage stochastic optimization. Comput. Oper. Res. 67, 48–62 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  21. Escudero, L.F., Garín, A., Unzueta, A.: Scenario cluster Lagrangean decomposition for risk-averse in multistage stochastic optimization. Comput. Oper. Res. 85, 154–171 (2017)

    Article  MathSciNet  Google Scholar 

  22. Galvão, R.D., Santibañez-González, E.R.: A Lagrangean heuristic for the \(p_k\)-median dynamic location problem. Eur. J. Oper. Res. 58, 250–262 (1992)

    Article  Google Scholar 

  23. Geoffrion, A.M.: Lagrangean relaxation for integer programming. Math. Programm. Stud. 2, 82–114 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  24. Guignard, M., Kim, S.: Lagrangean decomposition. A model yielding stronger Lagrangean bounds. Math. Program. 39, 215–228 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  25. Held, M., Karp, R.M.: The traveling salesman problem and minimum spanning trees: part II. Math. Program. 1, 6–25 (1971)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  27. Hernández, P., Alonso-Ayuso, A., Bravo, F., Escudero, L.F., Guignard, M., Marianov, V., Weintraub, A.: A branch-and-cluster coordination scheme for selecting prison facility sites under uncertainty. Comput. Oper. Res. 39, 2232–2241 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Hinojosa, Y., Puerto, J., Fernández, F.R.: A multi-period two-echelon multicommodity capacitated plant location problem. Eur. J. Oper. Res. 123, 45–65 (2000)

    Article  MATH  Google Scholar 

  29. Homem-de-Mello, T., Pagnoncelli, B.K.: Risk aversion in multistage stochastic programming: a modeling and algorithmic perspective. Eur. J. Oper. Res. 249, 188–199 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  30. IBM ILOG. CPLEX v12.6.1 http://www.ilog.com/products/cplex (2017)

  31. Jena, S.D., Cordeau, J.F., Gendron, B.: Dynamic facility location with generalized modular capacity. Transp. Sci. 49, 484–499 (2015). https://doi.org/10.1287/trsc.2014.0575

    Article  Google Scholar 

  32. Jiménez-Redondo, N., Conejo, A.J.: Short-term hydro-thermal coordination by Lagrangean relaxation: solution of the dual problem. IEEE Trans. Power Syst. 14, 89–95 (1997)

    Article  Google Scholar 

  33. Kall, P., Mayer, J.: Stochastic Linear Programming, 2nd edn. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

  34. Laporte, G., Nickel, S., Saldanha da Gama, F. (eds.): Location Science. Springer, Berlin (2015)

  35. Li, D., Sun, X.: Nonlinear Integer Programming. Springer, Berlin (2006)

    MATH  Google Scholar 

  36. Løkketangen, A., Woodruff, D.L.: Progressive hedging and tabu search applied to mixed integer (0,1) multistage stochastic programming. J. Heuristics 2, 111–128 (1996)

    Article  MATH  Google Scholar 

  37. Lucas, C., MirHassani, S.A., Mitra, G., Poojari, C.A.: An application of Lagrangian relaxation to a capacity planning problem under uncertainty. J. Oper. Res. Soc. 52, 1256–1266 (2001)

    Article  MATH  Google Scholar 

  38. Melo, M.T., Nickel, S., Saldanha da Gama, F.: Dynamic multi-commodity capacitated facility location: a mathematical modeling framework for strategic supply chain planning. Comput. Oper. Res. 33, 181–208 (2006)

    Article  MATH  Google Scholar 

  39. Nickel, S., Saldanha-da-Gama, F., Ziegler, H.P.: A multi-stage stochastic supply network design problem with financial decisions and risk management. Omega 40, 511–524 (2012)

    Article  Google Scholar 

  40. Nickel, S., Saldanha da Gama, F.: Multi-period facility location. In: Laporte, G., Nickel, S., Saldanha da Gama, F. (eds.) Location Science, pp. 289–310. Springer, Berlin (2015)

    Google Scholar 

  41. Pagès-Bernaus, A., Ramalhinho, H., Juan, A., Calvet, L.: Designing e-commerce supply chains: a stochastic facility-location approach. Int. Trans. Oper. Res. (2017). https://doi.org/10.1111/itor.12433

    Google Scholar 

  42. Pflug, G.Ch., Pichler, A.: Multistage Stochastic Optimization. Springer, Berlin (2014)

  43. Pflug, G.Ch., Pichler, A.: Time consistent decisions and temporal decomposition of coherent risk functional. Math. Oper. Res. 41, 682–699 (2015)

  44. Rockafellar, R.T., Wets, R.J.-B.: Scenario and policy aggregation in optimisation under uncertainty. Math. Oper. Res. 16, 119–147 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  45. Shapiro, A.: Time consistency of dynamic risk measures. Oper. Res. Lett. 40, 436–439 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  46. Snyder, L.: Facility location under uncertainty: a review. IIE Trans. 38, 527–554 (2006)

    Google Scholar 

Download references

Acknowledgements

This research has been partially supported by the projects Grupo de Investigación EOPT (IT-928-16) from the Basque Government, projects on Estadística y Optimización (PPG17/32 and GIU17/011) from University of the Basque Country, UPV/EHU, and projects MTM2015-65317-P and MTM2015-63710-P from the Spanish Ministry of Economy and Competitiveness. We would like to express our gratitude to Prof. Dr. Fernando Tusell for making it easier to access the Laboratory of Quantitative Economics from the University of the Basque Country (UPV/EHU, Bilbao, Spain) to perform and check the computational experience reported in the paper.

Author information

Authors and Affiliations

  1. Area de Estadística e Investigación-Operativa, Universidad Rey Juan Carlos, Móstoles, Madrid, Spain

    Laureano F. Escudero & Celeste Pizarro

  2. Dpto. de Economía Aplicada III, Universidad del País Vasco, UPV/EHU, Bilbao, Bizkaia, Spain

    María Araceli Garín

  3. Dpto. Matemática Aplicada, Universidad del País Vasco, UPV/EHU, Bilbao, Bizkaia, Spain

    Aitziber Unzueta

Authors
  1. Laureano F. Escudero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. María Araceli Garín
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Celeste Pizarro
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Aitziber Unzueta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to María Araceli Garín.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Escudero, L.F., Garín, M.A., Pizarro, C. et al. On efficient matheuristic algorithms for multi-period stochastic facility location-assignment problems. Comput Optim Appl 70, 865–888 (2018). https://doi.org/10.1007/s10589-018-9995-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10589-018-9995-0

Keywords

Search

Navigation