Constrained location of competitive facilities in the plane.

*(English)*Zbl 1061.90074Summary: This paper examines a competitive facility location problem occurring in the plane. A new gravity-based utility model is developed, in which the capacity of a facility serves as its measure of attractiveness. A new problem formulation is given, having elastic gravity-based demand, along with capacity, forbidden region, and budget constraints. Two solution algorithms are presented, one based on the big square small square method, and the second based on a penalty function formulation using fixed-point iteration. Computational testing is presented, comparing these two algorithms along with a general-purpose nonlinear solver.

##### Keywords:

Competitive facility location; Elastic demand; Penalty functions; Forbidden regions; Nonconvex optimization
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\textit{R. G. McGarvey} and \textit{T. M. Cavalier}, Comput. Oper. Res. 32, No. 2, 359--378 (2005; Zbl 1061.90074)

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