A Geographical Solution to Scale and Aggregation Problems in Region-Building, Partitioning and Spatial Modelling

Extending the automated zoning procedure to reconcile incompatible zoning systems

“…In certain situations, such as those in which both zonal geographies must be matched perfectly, the problem is one that may be solved analytically, but where it is necessary to approximate one geography by precise aggregation of another then the problem is more appropriately tackled with an iterative zoning procedure. Openshaw's (1977) AZP has been extended into an automated zone matching (AZM) algorithm by employing an intermediate boundary processing layer and a program written for its implementation.…”

“…There is a long history of the modification of electoral geographies in order to achieve approximately equal political representation, and the automated partitioning of geographical space in this context is discussed by Horn (1995) and Mehrotra et al (1998). Openshaw's (1977) Automated Zoning Procedure (AZP) provides a means to automate the process of designing a zonal system in order to maximise the value of some objective function. The procedure is based on the iterative recombination of building block zones into output regions from an initial random aggregation (IRA) by examining the effect of swapping individual building blocks between output regions.…”

“…This is a difficult problem, in which the 'best' solution may actually represent a complex trade-off between competing constraints. This paper presents an automated zone matching (AZM) algorithm for the design of tracts, that is developed from Openshaw's (1977) automated zoning procedure (AZP). AZP is a computationally intensive procedure which seeks to optimize objectives such as minimum or target population sizes, zonal compactness or social homogeneity, iteratively recombining a large set of building block polygons into a smaller set of output areas.…”

Dots to dots: a general methodology to build local indicators using spatial micro-data

“…The modifiable areal unit problem (MAUP) (Openshaw, 1977;1984) states that changing the geographical limits or spatial boundaries can influence the results obtained. If one wish to adopt a different definition of the geographical limits, then it is possible that this aggregation will result in different values of a given indicator and, consequently, in different conclusions.…”

Spatial Aspects of Census Districting

“…In other words, a contiguous area cannot have any holes ( Figure 2). Several methods have been proposed to apply contiguity constraint in the partitioning problem, including contiguity matrix (Openshaw, 1977) and mixed integer programming (MIP) models (Cova and Church, 2000;Ricca et al, 2011;Shirabe, 2009;Zoltners and Sinha, 1983).…”