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Capture, Capacities, and Thresholds

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Location Covering Models

Part of the book series: Advances in Spatial Science ((ADVSPATIAL))

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Abstract

There can be a number of different problem settings under which covering models can be defined and applied. Many of the models that are discussed in this chapter were originally inspired by issues associated with retail and competition. Although one at first blush may think of retail siting and coverage models as having little in common, except for something obvious like a pizza chain attempting to locate facilities so that it can deliver pizzas everywhere in a city within 30 min, there are surprisingly many retail elements that can be defined and addressed using coverage constructs.

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Notes

  1. 1.

    Hotelling (1929) suggested that if the two vendors could change location, they would eventually reach a price equilibrium while locating close together at the center of the linear market. Here they would attract an equal share of the customers. However, d’Aspremont et al. (1979) has since shown that a price equilibrium does not hold when the vendors are sufficiently close together.

  2. 2.

    As in ReVelle (1986), we assume here that customers see no difference in price or offerings between competitors, so they patronize their closest facility. This may not be the case when making multi-purpose trips, like a person stopping off at a facility on their way to work, or on their way home.

  3. 3.

    This nuance is formulated differently than in ReVelle’s original maximum capture paper, as the constraints proposed by ReVelle (1986) actually force demand nodes where there could be multiple shares of capture to have at least one new facility located at that distance, clearly an unintended feature.

  4. 4.

    Note that this equivalent form of the p-median problem cannot handle the case when more than one new facility is placed at the same distance of a competitors involving a given customer.

  5. 5.

    To be complete, Christaller (1933) suggests a hierarchy of centers and types of goods. For instance a village may have a grocery store, a hardware store, and a gas station, whereas a town will offer all of those goods as well as many other facilities, like clothing stores, automobile dealerships, and a hospital. Cities have an even larger set of services, including all of those offered in villages and towns, but in addition even “higher-ordered” goods and services. These include such businesses as medical specialists and high-end jewelry stores. It is important to note that Church and Bell (1990) have demonstrated that co-location of competitors can exist in stable market central place configurations, so that, depending on the nature of the business, competing firms will locate in the same area.

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Authors and Affiliations

  1. Department of Geography, University of California, Santa Barbara, California, USA

    Richard L. Church & Alan Murray

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  1. Richard L. Church
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  2. Alan Murray
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Church, R.L., Murray, A. (2018). Capture, Capacities, and Thresholds. In: Location Covering Models. Advances in Spatial Science. Springer, Cham. https://doi.org/10.1007/978-3-319-99846-6_7

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