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**A method for solving to optimality uncapacitated location problems.**
*(English)*
Zbl 0707.90060

Summary: We develop a method for solving to optimality a general 0-1 formulation for uncapacitated location problems. This is a 3-stage method that solves large problems in reasonable computing times.

The 3-stage method is composed of a primal-dual algorithm, a subgradient optimization to solve a Lagrangean dual and a branch-and-bound algorithm. It has a hierarchical structure, with a given stage being activated only if the optimal solution could not be identified in the preceding stage.

The proposed method was used in the solution of three well-known uncapacitated location problems; the simple plant location problem, the p-median problem and the fixed-charge p-median problem. Computational results are given for problems of up to the size 200 customers\(\times 200\) potential facility sites.

The 3-stage method is composed of a primal-dual algorithm, a subgradient optimization to solve a Lagrangean dual and a branch-and-bound algorithm. It has a hierarchical structure, with a given stage being activated only if the optimal solution could not be identified in the preceding stage.

The proposed method was used in the solution of three well-known uncapacitated location problems; the simple plant location problem, the p-median problem and the fixed-charge p-median problem. Computational results are given for problems of up to the size 200 customers\(\times 200\) potential facility sites.

### MSC:

90B80 | Discrete location and assignment |

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

90C06 | Large-scale problems in mathematical programming |

90C09 | Boolean programming |

### Keywords:

uncapacitated location; 3-stage method; primal-dual algorithm; subgradient optimization; branch-and-bound; hierarchical structure; p- median
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\textit{R. D. Galvão} and \textit{L. A. Raggi}, Ann. Oper. Res. 18, No. 1--4, 225--244 (1989; Zbl 0707.90060)

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