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A Lagrangean Heuristic for a Modular Capacitated Location Problem

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  • Isabel Correia
  • M. Captivo

Abstract

This paper considers the Modular Capacitated Location Problem (MCLP) which consists of finding the location and capacity of the facilities, to serve a set of customers at a minimum total cost. Each customer has an associated demand and the capacity of each potential location must be chosen from a finite and discrete set of available capacities. Practical applications of this problem can be found in the location of warehouses, schools, health care services or other types of public services. For the MCLP different mixed integer linear programming models are proposed. The authors develop upper and lower bounds on the problem's optimal value and present computational results with randomly generated tests problems. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Isabel Correia & M. Captivo, 2003. "A Lagrangean Heuristic for a Modular Capacitated Location Problem," Annals of Operations Research, Springer, vol. 122(1), pages 141-161, September.
    • Handle: RePEc:spr:annopr:v:122:y:2003:i:1:p:141-161:10.1023/a:1026146507143
    DOI: 10.1023/A:1026146507143
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    Citations

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    Cited by:

    1. Chandra Ade Irawan & Dylan Jones, 2019. "Formulation and solution of a two-stage capacitated facility location problem with multilevel capacities," Annals of Operations Research, Springer, vol. 272(1), pages 41-67, January.
    2. Sanjay Jena & Jean-François Cordeau & Bernard Gendron, 2015. "Modeling and solving a logging camp location problem," Annals of Operations Research, Springer, vol. 232(1), pages 151-177, September.
    3. Becker, Tristan & Lier, Stefan & Werners, Brigitte, 2019. "Value of modular production concepts in future chemical industry production networks," European Journal of Operational Research, Elsevier, vol. 276(3), pages 957-970.
    4. Sondes Hammami & Aida Jebali, 2021. "Designing modular capacitated emergency medical service using information on ambulance trip," Operational Research, Springer, vol. 21(3), pages 1723-1742, September.
    5. Correia, Isabel & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2010. "Single-assignment hub location problems with multiple capacity levels," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1047-1066, September.
    6. Christensen, Tue Rauff Lind & Klose, Andreas, 2021. "A fast exact method for the capacitated facility location problem with differentiable convex production costs," European Journal of Operational Research, Elsevier, vol. 292(3), pages 855-868.
    7. Amin Akbari & Ronald Pelot & H. A. Eiselt, 2018. "A modular capacitated multi-objective model for locating maritime search and rescue vessels," Annals of Operations Research, Springer, vol. 267(1), pages 3-28, August.
    8. Broek, John v.d. & Schutz, Peter & Stougie, Leen & Tomasgard, Asgeir, 2006. "Location of slaughterhouses under economies of scale," European Journal of Operational Research, Elsevier, vol. 175(2), pages 740-750, December.
    9. Tue R. L. Christensen & Kim Allan Andersen & Andreas Klose, 2013. "Solving the Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem by Dynamic Programming," Transportation Science, INFORMS, vol. 47(3), pages 428-438, August.
    10. Silva, Allyson & Aloise, Daniel & Coelho, Leandro C. & Rocha, Caroline, 2021. "Heuristics for the dynamic facility location problem with modular capacities," European Journal of Operational Research, Elsevier, vol. 290(2), pages 435-452.
    11. Šárka Štádlerová & Sanjay Dominik Jena & Peter Schütz, 2023. "Using Lagrangian relaxation to locate hydrogen production facilities under uncertain demand: a case study from Norway," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.
    12. G．-Tóth, Boglárka & Anton-Sanchez, Laura & Fernández, José, 2024. "A Huff-like location model with quality adjustment and/or closing of existing facilities," European Journal of Operational Research, Elsevier, vol. 313(3), pages 937-953.
    13. Ge, Houtian & Goetz, Stephan & Canning, Patrick & Perez, Agnes, 2018. "Optimal locations of fresh produce aggregation facilities in the United States with scale economies," International Journal of Production Economics, Elsevier, vol. 197(C), pages 143-157.
    14. Young, Anisa & Tucker, Emily L. & Fernandez, Mariela & White, David & Brookover, Robert & Harris, Brandon, 2024. "An optimization approach to improve equitable access to local parks," Socio-Economic Planning Sciences, Elsevier, vol. 92(C).
    15. Shilian Han & Jerry Mendel, 2012. "A new method for managing the uncertainties in evaluating multi-person multi-criteria location choices, using a perceptual computer," Annals of Operations Research, Springer, vol. 195(1), pages 277-309, May.
    16. Chandra Ade Irawan & Martino Luis & Said Salhi & Arif Imran, 2019. "The incorporation of fixed cost and multilevel capacities into the discrete and continuous single source capacitated facility location problem," Annals of Operations Research, Springer, vol. 275(2), pages 367-392, April.
    17. Sanjay Dominik Jena & Jean-François Cordeau & Bernard Gendron, 2017. "Lagrangian Heuristics for Large-Scale Dynamic Facility Location with Generalized Modular Capacities," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 388-404, August.
    18. Sanjay Dominik Jena & Jean-François Cordeau & Bernard Gendron, 2015. "Dynamic Facility Location with Generalized Modular Capacities," Transportation Science, INFORMS, vol. 49(3), pages 484-499, August.
    19. Correia, Isabel & Gouveia, Luís & Saldanha-da-Gama, Francisco, 2010. "Discretized formulations for capacitated location problems with modular distribution costs," European Journal of Operational Research, Elsevier, vol. 204(2), pages 237-244, July.
    20. Dupont, Lionel, 2008. "Branch and bound algorithm for a facility location problem with concave site dependent costs," International Journal of Production Economics, Elsevier, vol. 112(1), pages 245-254, March.
    21. Puntipa Punyim & Ampol Karoonsoontawong & Avinash Unnikrishnan & Vatanavongs Ratanavaraha, 2022. "A Heuristic for the Two-Echelon Multi-Period Multi-Product Location–Inventory Problem with Partial Facility Closing and Reopening," Sustainability, MDPI, vol. 14(17), pages 1-32, August.

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