A Model of Contiguity for Spatial Unit Allocation

Abstract

We consider a problem of allocating spatial units (SUs) to particular uses to form ''regions'' according to specified criteria, which is here called ''spatial unit allocation.'' Contiguity-the quality of a single region being connected-is one of the most frequently required criteria for this problem. This is also one that is difficult to model in algebraic terms for algorithmic solution. The purpose of this article is to propose a new exact formulation of contiguity that can be incorporated into any mixed integer programming model for SU allocation. The resulting model guarantees to enforce contiguity regardless of other included criteria such as compactness. Computational results suggest that problems involving a single region and fewer than about 200 SUs are optimally solved in fairly reasonable time, but that larger problems must rely on heuristics for approximate solutions. It is also found that a problem of any size can be formulated in a more tractable form when a fixed number of SUs are to be selected or when a certain SU is selected in advance.

Zone design of specific sizes using adaptive additively weighted Voronoi diagrams

“…A number of spatial and thematic conditions are established for defining zones, and these may vary considerably from one field of application to the next. The main spatial constraints are integrity, compactness and contiguity, the latter being the priority criterion in zoning problems (Shirabe 2005).…”

“…The following models have been developed within this line of research: integer linear programming (IP or ILP), which has been largely unsuccessful due to the difficulty of explicitly formalizing the contiguity constraint in algebraic terms; and mixed linear programming (MIP), which, from a computational point of view, is only efficient in problems involving sizes that are reduced, both in the number of basic units and in the number of zones to be generated. The most important MIP models are those created by Zoltners and Sinha (1983), applied to sales zone design; Cova and Church (2000) and Williams (2002), applied to land-use allocation or terrain acquisition; Shirabe (2005), used for generic zoning problems; and, finally, Solis et al (2009) and Rios-Mercado and Fernandez (2009), which is applied in designing commercial zones.…”

Determination of Optimum Environmental Conservation: Using Multi-Criteria Decision-Making Techniques

“…In such cases, multi-objective decision analysis (MODA) is used as the second basic technique of MCDM that generally generates optimal allocation alternatives using optimization techniques. MCDM is widely used for optimum land-use allocation in land-use planning (Bammi & Bammi, 1979;Gilbert et al, 1985;Chuvieco, 1993;Dokmeci et al, 1993;Grabaum & Meyer, 1998;Gabriel et al, 2006;Ligmann-Zielinska et al, 2008), in the determination of facility locations (Malczewski, 1991;Minor & Jacobs, 1994;Eastman et al, 1995;Maniezzo et al, 1998;Cheng et al, 2003), in land-allocation problem with a shape constraint such as compactness (Aerts & Heuvelink, 2002;Aerts et al, 2003), convexity and contiguity (Minor & Jacob, 1994;Williams, 2003;Shirabe, 2005) and environmental conflict analysis (Malczewski et al, 1997). Besides, Ogryczak (1995, 1996) discussed multiple criteria location problem with MCDA methods.…”

Exploring Regionalization in the Network Urban Space

“…The connectivity of a network region is less developed in regionalization research but appears more often in research in transportation modeling (Li et al 2014a). Shape factors are considered extensively in the literature and are often related to a specific application setting (Shirabe 2005;Williams et al 2004). Li et al (2013) introduced the compactness measure of a shape based on the moment of inertia and presented the mathematical formalization.…”