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A supply chain design problem with facility location and bi-objective transportation choices


  • Elias Olivares-Benitez


  • José González-Velarde


  • Roger Ríos-Mercado



A supply chain design problem based on a two-echelon single-product system is addressed. The product is distributed from plants to distribution centers and then to customers. There are several transportation channels available for each pair of facilities between echelons. These transportation channels introduce a cost–time tradeoff in the problem that allows us to formulate it as a bi-objective mixed-integer program. The decisions to be taken are the location of the distribution centers, the selection of the transportation channels, and the flow between facilities. Three variations of the classic ε-constraint method for generating optimal Pareto fronts are studied in this paper. The procedures are tested over six different classes of instance sets. The three sets of smallest size were solved completely obtaining their efficient solution set. It was observed that one of the three proposed algorithms consistently outperformed the other two in terms of their execution time. Additionally, four schemes for obtaining lower bound sets are studied. These schemes are based on linear programming relaxations of the model. The contribution of this work is the introduction of a new bi-objective optimization problem, and a computational study of the ε-constraint methods for obtaining optimal efficient fronts and the lower bounding schemes. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • Elias Olivares-Benitez & José González-Velarde & Roger Ríos-Mercado, 2012. "A supply chain design problem with facility location and bi-objective transportation choices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 729-753, October.
  • Handle: RePEc:spr:topjnl:v:20:y:2012:i:3:p:729-753
    DOI: 10.1007/s11750-010-0162-8

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    References listed on IDEAS

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    8. Current, John & Min, Hokey & Schilling, David, 1990. "Multiobjective analysis of facility location decisions," European Journal of Operational Research, Elsevier, vol. 49(3), pages 295-307, December.
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    Cited by:

    1. Cortinhal, M. J. & Lopes, M. J. & Melo, M. T., 2014. "Redesigning a three-echelon logistics network over multiple time periods with transportation mode selection and outsourcing opportunities," Technical Reports on Logistics of the Saarland Business School 7, Saarland University of Applied Sciences (htw saar), Saarland Business School.
    2. Soylu, Banu, 2015. "Heuristic approaches for biobjective mixed 0–1 integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 245(3), pages 690-703.
    3. Olivares-Benitez, Elias & Ríos-Mercado, Roger Z. & González-Velarde, José Luis, 2013. "A metaheuristic algorithm to solve the selection of transportation channels in supply chain design," International Journal of Production Economics, Elsevier, vol. 145(1), pages 161-172.
    4. Farahani, Reza Zanjirani & Rezapour, Shabnam & Drezner, Tammy & Fallah, Samira, 2014. "Competitive supply chain network design: An overview of classifications, models, solution techniques and applications," Omega, Elsevier, vol. 45(C), pages 92-118.


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