Przegląd Geograficzny (2017) vol. 89, iss. 2
Application of the Voronoi Diagram in analysing of spatial patterns to the distribution of discount stores and access to them
Przegląd Geograficzny (2017) vol. 89, iss. 2, pp. 187-212 | 
Full text
doi: https://doi.org/10.7163/PrzG.2017.2.1
Abstract
The aim of the work detailed here has been to achieve a methodological goal relating to methods, which focuses on the application of the Voronoi diagram in studying spatial aspects of the accessibility of retail stores. The Voronoi diagram is a partitioning of a plane into regions (cells) based on distances to points (seeds) in a specific subset of the plane. Each point located within a given cell of the diagram lies closer to the seed located in this cell than to any other seeds in the network. In the geographical literature, these are also often referred to as Thiessen polygons. The objective set was accomplished by analysing the distribution and accessibility of discount stores of the Biedronka retail chain in the Polish city of Poznań. As of 30 June 2015, there were 61 Biedronka discount stores there, making this chain the city’s largest. The Voronoi diagram was used as a spatial frame of reference facilitating analysis of the distribution of these discount stores across the city. However, in-depth statistical study was conducted using indexing methods that estimate the level of accessibility, as well as indicators of spatial autocorrelation. This allowed for the identification of spatial patterns to the distribution of attributes examined. Taking into account two basic dimensions to the accessibility of services, i.e. proximity (a relationship between the distributions of supply and demand) and availability (a relationship between the volume and type of services offered and the volume and type of consumer needs), variables established for each cell of the diagram were: (1) average weighted distance from the place of residence to the nearest discount store and (2) the quotient of population size and store size (weight). These indicators provided for the determination of a synthetic index of accessibility, as the average of the values of the variables under study, which had previously undergone a standardisation procedure. The synthetic indicator showing the level of accessibility of discount stores in particular cells of the diagram was used to measure spatial autocorrelation. Analysis allowed for the identification of spatial regimes which made it easier to evaluate the distribution of discount stores and indicate new potential locations on the basis thereof. The results obtained showed that, notwithstanding the presence of a considerable number of Biedronka discount stores, mainly in the most densely-populated parts of the city, the accessibility of these discount stores across Poznań was diverse. The most favourable pattern for the spatial distribution of Biedronka discount stores as set against population distribution was identified in the central area of Poznań. In turn, a spatial regime characterised by a low level of accessibility was found to extend over large areas in the eastern part of the city. The research showed that application of the Voronoi diagram facilitates analysis of the distribution and accessibility of retail stores. The transformation of a set of points into a diagram with cells of a polygon type permits the identification of spatial relations and regularities used in estimating accessibility. It would be impossible to achieve this were point-type methods to be applied. The research discussed in this paper represents one of the few studies in Polish geographical or economic literature in which the spatial variability of social and economic phenomena is analysed to generate a Voronoi diagram. This situation stands in marked contrast to the vast body of foreign literature on this topic. This paper therefore helps bridge a substantial research gap in its field.
Keywords: diagram Woronoja, dostępność przestrzenna, autokorelacja przestrzenna, reżimy przestrzenne, Poznań, dyskonty Biedronka
[wojciech.kisiala@ue.poznan.pl], Uniwersytet Ekonomiczny w Poznaniu, Instytut Informatyki i Ekonomii Ilościowej
Citation
APA: Kisiała, W., & Rudkiewicz, M. (2017). Zastosowanie diagramu Woronoja w badaniu przestrzennych wzorców rozmieszczenia i dostępności sklepów dyskontowych. Przegląd Geograficzny, 89(2), 187-212. https://doi.org/10.7163/PrzG.2017.2.1
MLA: Kisiała, Wojciech and Rudkiewicz, Magdalena. "Zastosowanie diagramu Woronoja w badaniu przestrzennych wzorców rozmieszczenia i dostępności sklepów dyskontowych". Przegląd Geograficzny, vol. 89, no. 2, 2017, pp. 187-212. https://doi.org/10.7163/PrzG.2017.2.1
Chicago: Kisiała, Wojciech and Rudkiewicz, Magdalena. "Zastosowanie diagramu Woronoja w badaniu przestrzennych wzorców rozmieszczenia i dostępności sklepów dyskontowych". Przegląd Geograficzny 89, no. 2 (2017): 187-212. https://doi.org/10.7163/PrzG.2017.2.1
Harvard: Kisiała, W., & Rudkiewicz, M. 2017. "Zastosowanie diagramu Woronoja w badaniu przestrzennych wzorców rozmieszczenia i dostępności sklepów dyskontowych". Przegląd Geograficzny, vol. 89, no. 2, pp. 187-212. https://doi.org/10.7163/PrzG.2017.2.1