A spatial optimization approach for solving a multi-facility location problem with continuously distributed demand

Location-related decisions are important considerations in most aspects of human activity. Facility location models are usually employed to assist decision processes concerning the siting of one or more facilities in order to best serve underlying demand that is discretely or continuously distributed across space. Of interest in this chapter, it is the perspective that demand is continuously distributed. Though surfaces defined by mathematical functions or fitted through spatial interpolation can be employed to approximate a continuous demand representation, the results of both of these methods are subject to significant errors and uncertainties. For this reason, we introduce a generic location planning model and the continuous multi-Weber problem, in which facilities may be sited anywhere in space in order to best serve continuously distributed demand. Due to the complexity of the problem, a spatial optimization approach for dealing with continuous demand is proposed through the integration of optimization techniques with geographic information system (GIS) functionality. Results from empirical applications demonstrate the effectiveness of the developed approach and highlight the importance of incorporating GIS functionality into the solution process.