An empirical comparison of spatial demand representations in maximal coverage modeling

Spatial demand representation is critical for applying location models to planning processes and the efficiency of modeling solutions. Current research has focused primarily on assessing and mitigating demand representation error but ignored the computational complexity of implementing demand representations and solving the associated models. We first use set theory to formulize Cromley et al's (Institutional Journal of Geographical Information Science 26 495-512) demand representation with the least common demand coverage unit (LCDCU). Then, in the application of using the maximal covering location problem (MCLP) to site base stations optimally for a cellular network, we compare the LCDCU-based representation with widely used point-lattice-based and polygon-lattice-based demand representations in terms of both computational complexity and representation error. The LCDCU-based representation creates demand objects by partitioning a demand space into potential service areas, and has several advantages including offering solutions that provide real 100% demand coverage and eliminating some errors associated with other demand representations. However, the computational complexity of implementing the LCDCU-based representation could easily become extremely high as the number of potential facility sites increases, which could be a challenge to current geographic information systems. In addition, unlike point-based and polygon-based demand representations, the LCDCU-based representations cannot be applied to the planar covering location problems where a facility can be sited anywhere. The results of our study suggest that point-lattice-based demand representations with fine granularity are a good alternative to the LCDCU-based representations due to their effective modeling solutions without extensive computation. Polygon-lattice-based demand representations are not recommended owing to both high computational complexity and relatively large representation error. This study provides some indicators on how to choose an appropriate spatial demand representation in practical applications.