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**A supply chain design problem with facility location and bi-objective transportation choices.**
*(English)*
Zbl 1262.90005

Summary: 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 \(\varepsilon\)-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 \(\varepsilon\)-constraint methods for obtaining optimal efficient fronts and the lower bounding schemes.

### MSC:

90-08 | Computational methods for problems pertaining to operations research and mathematical programming |

90B06 | Transportation, logistics and supply chain management |

90B10 | Deterministic network models in operations research |

90B80 | Discrete location and assignment |

90C11 | Mixed integer programming |

90C29 | Multi-objective and goal programming |

### Keywords:

integer programming; bi-objective programming; location; supply chain; branch and bound; \(\varepsilon\)-constraint method### Software:

CPLEX
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\textit{E. Olivares-Benitez} et al., Top 20, No. 3, 729--753 (2012; Zbl 1262.90005)

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