Optimal continuous location in the geographic and perceptual space using attractiveness and market share.

• Introduction
• A generic, dual marketing problem
• Location analysis and OR
• The problem being solved and it’s original solution
• Suggested extensions
• Drezner’s model - A problem centric reformulation
• Presentation
• Problem centric vs. techno centric
• Computing constant elements
• The competitors’ share in each demand point
• The objective function
• Analogies with the minisum problem
• Alternative optimisation algorithms
• Weiszfeld’s procedure
• Similarities with the gradient method
• Performance comparison:  Weiszfeld vs. Gradient – The data
• Performance comparison:  Weiszfeld vs. Gradient
• Weiszfeld’s method systematic convergence towards local optima – An empirical test
• Finding the global optimum through spatial decompositions
• Using heuristics
• A biologically regulated triangles population
• Illustration
• 3D extension using a biologically regulated tetrahedron population
• Finding most local optima using hybrid solutions
• Stepwise triangulation and gradient
• Local convergence at decreasing rate
• Triangles elimination
• Stepwise nearest points merger
• Conclusions
• Conclusions
• References
• References