New computer methods for global optimization
New computer methods for global optimization
Competitive location in the plane
Annals of Operations Research - Special issue on locational decisions
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
Using Interval Analysis for Solving Planar Single-Facility Location Problems: New Discarding Tests
Journal of Global Optimization
Computers and Operations Research - Location analysis
Constrained location of competitive facilities in the plane
Computers and Operations Research
New interval methods for constrained global optimization
Mathematical Programming: Series A and B
Empirical convergence speed of inclusion functions for facility location problems
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Obtaining an outer approximation of the efficient set of nonlinear biobjective problems
Journal of Global Optimization
Parallel algorithms for continuous competitive location problems
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
Solving the multiple competitive facilities location and design problem on the plane
Evolutionary Computation
The big cube small cube solution method for multidimensional facility location problems
Computers and Operations Research
The theoretical and empirical rate of convergence for geometric branch-and-bound methods
Journal of Global Optimization
Parallel algorithms for continuous multifacility competitive location problems
Journal of Global Optimization
Theoretical rate of convergence for interval inclusion functions
Journal of Global Optimization
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
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Companies frequently decide on the location and design for new facilities in a sequential way. However, for a fixed number of new facilities, the company might be able to improve its profit by taking its decisions for all the facilities simultaneously. In this paper we compare three different strategies: simultaneous location and independent design of two facilities in the plane, the same with equal designs, and the sequential approach of determining each facility in turn. The basic model is profit maximization for the chain, taking market share, location costs and design costs into account. The market share captured by each facility depends on the distance to the customers (location) and its quality (design), through a probabilistic Huff-like model. Recent research on this type of models was aimed at finding global optima for a single new facility, holding quality fixed or variable, but no exact algorithm has been proposed to find optimal solutions for more than one facility. We develop such an exact interval branch-and-bound algorithm to solve both simultaneous location and design two-facility problems. Then, we present computational results and exhibit the differences in locations and qualities of the optimal solutions one may obtain by the sequential and simultaneous approaches.