A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational or logit type model. Both the location and the quality (design) of the new facility are to be found so as to maximize the profit obtained for the chain. Several types of constraints and costs are considered. Applying an interval analysis based global optimization method on several spatial patterns in a quasi-real-world environment, the behaviour of optimal solutions is investigated when changes are made in the basic model parameters. The study yields valuable insight for modelers into the impact of spatial pattern and various model parameters of the model on the resulting location and design decision. Spatial patterns differ in distribution of demand, of own and/or competing facilities, and of facility qualities. Studied model parameters include distance decay, income function, and push force effects, as well as investment restrictions and aggregation of demand.
A shortened version of this working paper, without part of the sensitivity analyses, several figures and without the appendix is to appear in OR Spectrum 2009 as Boglárka Tóth, Frank Plastria, José Fernández and Blas Pelegrín: On the impact of spatial pattern, aggregation, and model parameters in planar Huff-type competitive location and design problems.