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A dual RAMP algorithm for single source capacitated facility location problems

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Abstract

In this paper, we address the Single Source Capacitated Facility Location Problem (SSCFLP) which considers a set of possible locations for opening facilities and a set of clients whose demand must be satisfied. The objective is to minimize the cost of assigning the clients to the facilities, ensuring that all clients are served by only one facility without exceeding the capacity of the facilities. We propose a Relaxation Adaptive Memory Programming (RAMP) heuristic for solving the SSCFLP to efficiently explore the relation between the primal and the dual sides of this combinatorial optimisation problem. Computational experiments demonstrated that the proposed heuristic is very effective in terms of solution quality with reasonable computing times.

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References

  1. Farahani, R., Hekmatfar, M.: Facility location: concepts, models, algorithms and case studies. Physica-Verlag. (2009). https://doi.org/10.1007/978-3-7908-2151-2

  2. Rego, C.: RAMP: a new metaheuristic framework for combinatorial optimization. In: Rego, C., Alidaee, B. (eds.) Metaheuristic Optimization Via Memory and Evolution, pp. 441–460. Kluwer Academic Publishers (2005). https://doi.org/10.1007/0-387-23667-8_20

  3. Riley, C., Rego, C., Li, H.: A simple dual-RAMP algorithm for resource constraint project scheduling. In: Proceedings of the 48th Annual Southeast Regional Conference on - ACM SE ‘10. p. 1. ACM Press, New York, New York, USA (2010). https://doi.org/10.1145/1900008.1900097

  4. Gamboa, D.: Adaptive Memory Algorithms for the Solution of Large Scale Combinatorial Optimization Problems, PhD Thesis (in Portuguese), Instituto Superior Técnico, Universidade Técnica de Lisboa, (2008)

  5. Rego, C., Mathew, F., Glover, F.: RAMP for the capacitated minimum spanning tree problem. Ann. Oper. Res. 181, 661–681 (2010). https://doi.org/10.1007/s10479-010-0800-4

    Article  MathSciNet  MATH  Google Scholar 

  6. Matos, T., Gamboa, D.: Dual-RAMP for the Capacitated Single Allocation Hub Location Problem. In: Gervasi, O., Murgante, B., Misra, S., Borruso, G., Torre, C.M., Rocha, A.M.A.C., Taniar, D., Apduhan, B.O., Stankova, E., and Cuzzocrea, A. (eds.) Computational Science and Its Applications -- ICCSA 2017: 17th International Conference, Trieste, Italy, July 3–6, 2017, Proceedings, Part II. pp. 696–708. Springer International Publishing (2017). https://doi.org/10.1007/978-3-319-62395-5_48

  7. Matos, T., Maia, F., Gamboa, D.: Improving Traditional Dual Ascent Algorithm for the Uncapacitated Multiple Allocation Hub Location Problem: A RAMP Approach. In: The Fourth International Conference on Machine Learning, Optimization, and Data Science – September 13–16, 2018 – Volterra, Tuscany, Italy. pp. 243–253. Springer, Italy (2019). https://doi.org/10.1007/978-3-030-13709-0_20

  8. Glover, F.: Tabu Search—Part I. ORSA J. Comput. 1, 190–206 (1989). https://doi.org/10.1287/ijoc.1.3.190

    Article  MATH  Google Scholar 

  9. Glover, F.: Tabu Search—Part II. Tabu Search—Part II. ORSA J. Comput. 2, 4–32 (1990). https://doi.org/10.1287/ijoc.2.1.4

    Article  MATH  Google Scholar 

  10. Oliveira, Ó., Matos, T., Gamboa, D.: A RAMP Algorithm for Large-Scale Single Source Capacitated Facility Location Problems. In: Matsatsinis, N.F., Marinakis, Y., and Pardalos, P. (eds.) Learning and Intelligent Optimization. LION 2019. pp. 171–183 (2020). https://doi.org/10.1007/978-3-030-38629-0_14

  11. Garey, M.R., Johnson, D.S.: Computers and Intractability: a Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Francisco (1979). https://doi.org/10.2307/2273574, Michael R. ΠGarey and David S. Johnson. Computers and intractability. A guide to the theory of NP-completeness. W. H. Freeman and Company, San Francisco1979, x + 338 pp

  12. Neebe, A.W., Rao, M.R.: An algorithm for the fixed-charge assigning users to sources problem. J. Oper. Res. Soc. 34, 1107–1113 (1983). https://doi.org/10.1057/jors.1983.242

    Article  MATH  Google Scholar 

  13. Barceló, J., Casanovas, J.: A heuristic Lagrangean algorithm for the capacitated plant location problem. Eur. J. Oper. Res. 15, 212–226 (1984)

    Article  Google Scholar 

  14. Klincewicz, J.G., Luss, H.: A Lagrangian relaxation heuristic for capacitated facility location with single-source constraints. J. Oper. Res. Soc. 37, 495–500 (1986). https://doi.org/10.1057/jors.1986.84

    Article  MATH  Google Scholar 

  15. Erlenkotter, D.: A dual-based procedure for Uncapacitated facility location. Oper. Res. 26, 992–1009 (1978). https://doi.org/10.1287/opre.26.6.992

    Article  MathSciNet  MATH  Google Scholar 

  16. Sridharan, R.: A Lagrangian heuristic for the capacitated plant location problem with side constraints. J. Oper. Res. Soc. 66, 579–585 (1991). https://doi.org/10.1057/jors.1991.117

    Article  MATH  Google Scholar 

  17. Pirkul, H.: Efficient algorithms for the capacitated concentrator location problem. Comput. Oper. Res. 14, 197–208 (1987). https://doi.org/10.1016/0305-0548(87)90022-0

    Article  MATH  Google Scholar 

  18. Beasley, J.E.: Lagrangean heuristics for location problems. Eur. J. Oper. Res. 65, 383–399 (1993). https://doi.org/10.1016/0377-2217(93)90118-7

  19. Delmaire, H., Díaz, J.A., Fernández, E., Ortega, M.: Comparing new heuristics for the pure integer capacitated plant location problem. Investig. Oper. 8, 217–242 (1997)

    Google Scholar 

  20. Delmaire, H., Díaz, J.A., Fernández, E., Ortega, M.: Reactive Grasp and Tabu search based heuristics for the single source capacitated plant location problem. INFOR Inf. Syst. Oper. Res. 37, 194–225 (1999). https://doi.org/10.1080/03155986.1999.11732381

    Article  Google Scholar 

  21. Rönnqvist, M., Tragantalerngsak, S., Holt, J.: A repeated matching heuristic for the single-source capacitated facility location problem. Eur. J. Oper. Res. 116, 51–68 (1999). https://doi.org/10.1016/S0377-2217(98)00045-9

    Article  MATH  Google Scholar 

  22. Holmberg, K., Rönnqvist, M., Yuan, D.: An exact algorithm for the capacitated facility location problems with single sourcing. Eur. J. Oper. Res. 113, 544–559 (1999). https://doi.org/10.1016/S0377-2217(98)00008-3

    Article  MATH  Google Scholar 

  23. Hindi, K.S., Pieńkosz, K.: Efficient solution of large scale, single-source, capacitated plant location problems. J. Oper. Res. Soc. 50, 268–274 (1999). https://doi.org/10.1057/palgrave.jors.2600698

    Article  MATH  Google Scholar 

  24. Ahuja, R.K., Orlin, J.B., Pallottino, S., Scaparra, M.P., Scutellà, M.G.: A multi-exchange heuristic for the single-source capacitated facility location problem. Manag. Sci. 50, 749–760 (2004). https://doi.org/10.1287/mnsc.1030.0193

    Article  MATH  Google Scholar 

  25. Cortinhal, M.J., Captivo, M.E.: Upper and lower bounds for the single source capacitated location problem. Eur. J. Oper. Res. 151, 333–351 (2003). https://doi.org/10.1016/S0377-2217(02)00829-9

    Article  MathSciNet  MATH  Google Scholar 

  26. Contreras, I.A., Díaz, J.A.: Scatter search for the single source capacitated facility location problem. Ann. Oper. Res. 157, 73–89 (2007). https://doi.org/10.1007/s10479-007-0193-1

    Article  MathSciNet  MATH  Google Scholar 

  27. Laguna, M., Martí, R., Marti, R.: Scatter search. Oper. Res. Comput. Sci. Interfaces Ser. 24, 1–283 (2003). https://doi.org/10.1007/978-1-4615-0337-8

    Article  MathSciNet  MATH  Google Scholar 

  28. Kumweang, K., Kawtummachai, R.: Solving a SSCFLP in a supply chain with ACO. Suranaree J. Sci. 12, 28–38 (2005)

    Google Scholar 

  29. Chen, C.-H., Ting, C.-J.: Combining Lagrangian heuristic and ant Colony system to solve the single source capacitated facility location problem. Transp. Res. Part E Logist. Transp. Rev. 44, 1099–1122 (2008). https://doi.org/10.1007/11839088_55

    Article  Google Scholar 

  30. Lina, Y., Xu, S., Tianhe, C.: A Hybrid Ant Colony Optimization Algorithm with Local Search Strategies to Solve Single Source Capacitated Facility Location Problem. In: 2012 International Conference on Industrial Control and Electronics Engineering. pp. 83–85. IEEE (2012). https://doi.org/10.1109/ICICEE.2012.30

  31. Yang, Z., Chu, F., Chen, H.: A cut-and-solve based algorithm for the single-source capacitated facility location problem. Eur. J. Oper. Res. 221, 521–532 (2012). https://doi.org/10.1016/j.ejor.2012.03.047

    Article  MathSciNet  MATH  Google Scholar 

  32. Climer, S., Zhang, W.: Cut-and-solve: an iterative search strategy for combinatorial optimization problems. Artif. Intell. 170, 714–738 (2006). https://doi.org/10.1016/j.artint.2006.02.005

    Article  MathSciNet  MATH  Google Scholar 

  33. Ho, S.C.: An iterated tabu search heuristic for the single source capacitated facility location problem. Appl. Soft Comput. 27, 169–178 (2015). https://doi.org/10.1016/j.asoc.2014.11.004

    Article  Google Scholar 

  34. Guastaroba, G., Speranza, M.G.: A heuristic for BILP problems: the single source capacitated facility location problem. Eur. J. Oper. Res. 238, 438–450 (2014). https://doi.org/10.1016/j.ejor.2014.04.007

    Article  MathSciNet  MATH  Google Scholar 

  35. Tran, T.H., Scaparra, M.P., O’Hanley, J.R.: A hypergraph multi-exchange heuristic for the single-source capacitated facility location problem. Eur. J. Oper. Res. 263, 173–187 (2017). https://doi.org/10.1016/j.ejor.2017.04.032

    Article  MathSciNet  MATH  Google Scholar 

  36. Martello, S., Pisinger, D., Toth, P.: Dynamic programming and strong bounds for the 0-1 knapsack problem. Manag. Sci. 45, 414–425 (1999). https://doi.org/10.1287/mnsc.45.3.414

    Article  MATH  Google Scholar 

  37. Avella, P., Boccia, M.: A cutting plane algorithm for the capacitated facility location problem. Comput. Optim. Appl. 43, 39–65 (2009). https://doi.org/10.1007/s10589-007-9125-x

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work has been supported by national funds through FCT – Fundação para a Ciência e Tecnologia through project UIDB/04728/2020.

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Correspondence to Óscar Oliveira.

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Oliveira, Ó., Matos, T. & Gamboa, D. A dual RAMP algorithm for single source capacitated facility location problems. Ann Math Artif Intell 89, 815–834 (2021). https://doi.org/10.1007/s10472-021-09756-0

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