A Bayesian spatial interaction framework for optimal facility location in urban environments

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Abstract

The actions of many interacting entities within socio-economic systems proclaim the configurations such as the spatial structure in urban environments. Hence understanding these underlying interactions are important in making the location decisions for growth in urban systems. In this thesis, a Bayesian spatial interaction model, henceforth BSIM, is developed to provide probabilistic predictions about revenues generated by a particular business location, based on its features and the potential customers’ characteristics in a given region. BSIM explicitly accounts for the competition among the facilities through a probability determined by evaluating a store-specific Gaussian distribution at a particular customer location. I propose a scalable variational inference framework that exhibits comparable performance in terms of parameter identification and uncertainty quantification while being significantly faster than competing Markov Chain Monte Carlo inference schemes.

The advantages of the introduced BSIM are explored in addressing the competitive facility location problem that typically arises when businesses plan to enter a new market or expand their presence in an environment with existing competitors. A mathematical modelling framework is formulated to simultaneously identify the location and design of new stores in order to maximise the revenue predicted from BSIM in a geographical region. Solving the underlying optimisation problem requires the provision of an exhaustive set of potential sites, which is difficult in practice. Instead, a search algorithm is proposed based on the quadtree method to overcome this challenge by hierarchically exploring geographic regions of varying spatial resolution.

This thesis introduces multiple large-scale real-world datasets compiled with open and proprietary data. Finally, demonstrate the proposed framework by producing optimal facility locations and corresponding designs for two case studies in the supermarket and pub sectors in Greater London, providing valuable insights for planning and decision-making under uncertainty.

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