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An exact algorithm for designing optimal districts in the collection of waste electric and electronic equipment through an improved reformulation

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  • Ríos-Mercado, Roger Z.
  • Bard, Jonathan F.

Abstract

In this paper, a maximum dispersion districting problem is considered that arises in the collection of waste electric and electronic equipment. For a given geographic region, the problem is to partition a set of collection or basic units such that each district in the region is assigned to a different company in a way that maximizes a dispersion function subject to a set of planning requirements. Starting with the traditional mixed-integer programming model, a covering-type model is proposed that is shown to be much more effective. In addition, a new upper bound for the maximum dispersion partitioning problem – a relaxation of the problem studied – is developed. Next, an exact algorithm based on the reformulated model is presented along with the newly derived upper bound. The algorithm intelligently exploits properties of the problem in a manner that allows for a large number of binary variables to be fixed and eliminated in a pre-processing step.

Suggested Citation

  • Ríos-Mercado, Roger Z. & Bard, Jonathan F., 2019. "An exact algorithm for designing optimal districts in the collection of waste electric and electronic equipment through an improved reformulation," European Journal of Operational Research, Elsevier, vol. 276(1), pages 259-271.
    • Handle: RePEc:eee:ejores:v:276:y:2019:i:1:p:259-271
    DOI: 10.1016/j.ejor.2018.12.030
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    1. Juan Carlos Duque & Raúl Ramos & Jordi Suriñach, 2007. "Supervised Regionalization Methods: A Survey," International Regional Science Review, , vol. 30(3), pages 195-220, July.
    2. Andris A. Zoltners & Prabhakant Sinha, 2005. "The 2004 ISMS Practice Prize Winner—Sales Territory Design: Thirty Years of Modeling and Implementation," Marketing Science, INFORMS, vol. 24(3), pages 313-331, September.
    3. Hammond, David & Beullens, Patrick, 2007. "Closed-loop supply chain network equilibrium under legislation," European Journal of Operational Research, Elsevier, vol. 183(2), pages 895-908, December.
    4. S C Lee & L H Shih, 2012. "A novel heuristic approach to determine compromise management for end-of-life electronic products," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(5), pages 606-619, May.
    5. Federica Ricca & Andrea Scozzari & Bruno Simeone, 2013. "Political Districting: from classical models to recent approaches," Annals of Operations Research, Springer, vol. 204(1), pages 271-299, April.
    6. Z P Fan & Y Chen & J Ma & S Zeng, 2011. "A hybrid genetic algorithmic approach to the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 92-99, January.
    7. J Mar-Ortiz & B Adenso-Diaz & J L González-Velarde, 2011. "Design of a recovery network for WEEE collection: the case of Galicia, Spain," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(8), pages 1471-1484, August.
    8. Martí, Rafael & Gallego, Micael & Duarte, Abraham, 2010. "A branch and bound algorithm for the maximum diversity problem," European Journal of Operational Research, Elsevier, vol. 200(1), pages 36-44, January.
    9. E Fernández & J Kalcsics & S Nickel & R Z Ríos-Mercado, 2010. "A novel maximum dispersion territory design model arising in the implementation of the WEEE-directive," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(3), pages 503-514, March.
    10. Erkut, Erhan, 1990. "The discrete p-dispersion problem," European Journal of Operational Research, Elsevier, vol. 46(1), pages 48-60, May.
    11. Fernández, Elena & Kalcsics, Jörg & Nickel, Stefan, 2013. "The maximum dispersion problem," Omega, Elsevier, vol. 41(4), pages 721-730.
    12. Sourour Elloumi & Martine Labbé & Yves Pochet, 2004. "A New Formulation and Resolution Method for the p-Center Problem," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 84-94, February.
    13. Z P Fan & Y Chen & J Ma & S Zeng, 2011. "Erratum: A hybrid genetic algorithmic approach to the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1423-1430, July.
    14. M Gallego & M Laguna & R Martí & A Duarte, 2013. "Tabu search with strategic oscillation for the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(5), pages 724-734, May.
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    Cited by:

    1. Diglio, Antonio & Peiró, Juanjo & Piccolo, Carmela & Saldanha-da-Gama, Francisco, 2023. "Approximation schemes for districting problems with probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 307(1), pages 233-248.
    2. Shi, Jianmai & Chen, Wenyi & Verter, Vedat, 2023. "The joint impact of environmental awareness and system infrastructure on e-waste collection," European Journal of Operational Research, Elsevier, vol. 310(2), pages 760-772.
    3. Sergey Kovalev & Isabelle Chalamon & Fabio J. Petani, 2023. "Maximizing single attribute diversity in group selection," Annals of Operations Research, Springer, vol. 320(1), pages 535-540, January.
    4. Bruno, Giuseppe & Diglio, Antonio & Passaro, Renato & Piccolo, Carmela & Quinto, Ivana, 2021. "Measuring spatial access to the recovery networks for WEEE: An in-depth analysis of the Italian case," International Journal of Production Economics, Elsevier, vol. 240(C).
    5. Sandoval, M. Gabriela & Álvarez-Miranda, Eduardo & Pereira, Jordi & Ríos-Mercado, Roger Z. & Díaz, Juan A., 2022. "A novel districting design approach for on-time last-mile delivery: An application on an express postal company," Omega, Elsevier, vol. 113(C).
    6. Gliesch, Alex & Ritt, Marcus, 2021. "A hybrid heuristic for the maximum dispersion problem," European Journal of Operational Research, Elsevier, vol. 288(3), pages 721-735.

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