A mixed integer programming formulation for the 1-maximin problem

A mixed integer programming formulation for the 1-maximin problem

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Article ID: iaor20011174
Country: United Kingdom
Volume: 51
Issue: 3
Start Page Number: 371
End Page Number: 375
Publication Date: Mar 2000
Journal: Journal of the Operational Research Society
Authors:
Keywords: programming: integer
Abstract:

In this paper, I present a mixed integer programming (MIP) formulation for the 1-maximin problem with rectilinear distance. The problem mainly appears in facility location while trying to locate an undesirable facility. The rectilinear distance is quite commonly used in the location literature. Our numerical experiments show that one can solve reasonably large location problems using a standard MIP solver. We also provide a linear programming formulation that helps find an upper bound on the objective function value of the 1-maximin problem with any norm when extreme points of the feasible region are known. We discuss various extension alternatives for the MIP formulation.

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