Facility Layout and Spatial Configuration Efficiency Assessment

With rapid regional development and urbanization, many public and private facilities and infrastructures (e.g., sirens, cellphone base stations, bike sharing stations, wind turbines, etc.) require regular renovation or supplementation. Evaluating existing facility efficiency and expanding to new facility locations are of broad interest among stakeholders, including businesses, urban planners, government agencies, and the public more generally. Such evaluation can be used to improve overall social accessibility, equity and efficiency by reconfiguring or adding new facilities in the best way possible. A regularly distributed lattice is often viewed as an optimal configuration given important observed properties and characteristics. In this paper, we formulate a spatial optimization model to evaluate spatial coverage efficiency. Specifically, given two sets of points, the model seeks the optimal location and orientation of an idealized lattice to align with an existing facility configuration. The distance between existing facilities and the ideally configured lattice under the optimal alignment represents efficiency. An iterative heuristic based on gradient descent and spatial indexing is developed to solve this problem. Extensive computational experience demonstrates the importance of this problem and the effectiveness of the derived solution approach, as well as highlights assistance provided to decision makers in identifying inefficiencies as well as improving existing infrastructure service systems.