An Efficient Algorithm for the Solution of the Weber Problem with Mixed Norms

Abstract

An algorithm is developed for the solution of the Weber problem when the distances are measured as arbitrary linear combinations of $l_p $-norms. Euclidean and rectilinear norms are used to illustrate the development. The algorithm applies the Dantzig–Wolfe decomposition method to the geometric programming dual of the Weber problem. The algorithm can be extended to the solution of the multifacilities location problem with constraints.

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