Please use this identifier to cite or link to this item: https://doi.org/10.1103/PhysRevE.84.036112
Title: Scaling and entropy in p-median facility location along a line
Authors: Gastner, Michael T 
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics, Mathematical
Physics
POPULATION
COMPLEXITY
ALGORITHM
DENSITY
LAWS
Issue Date: 20-Sep-2011
Publisher: AMER PHYSICAL SOC
Citation: Gastner, Michael T (2011-09-20). Scaling and entropy in p-median facility location along a line. PHYSICAL REVIEW E 84 (3). ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevE.84.036112
Abstract: The p-median problem is a common model for optimal facility location. The task is to place p facilities (e.g., warehouses or schools) in a heterogeneously populated space such that the average distance from a person's home to the nearest facility is minimized. Here we study the special case where the population lives along a line (e.g., a road or a river). If facilities are optimally placed, the length of the line segment served by a facility is inversely proportional to the square root of the population density. This scaling law is derived analytically and confirmed for concrete numerical examples of three US interstate highways and the Mississippi River. If facility locations are permitted to deviate from the optimum, the number of possible solutions increases dramatically. Using Monte Carlo simulations, we compute how scaling is affected by an increase in the average distance to the nearest facility. We find that the scaling exponents change and are most sensitive near the optimum facility distribution. © 2011 American Physical Society.
Source Title: PHYSICAL REVIEW E
URI: https://scholarbank.nus.edu.sg/handle/10635/168992
ISSN: 15393755
15502376
DOI: 10.1103/PhysRevE.84.036112
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