Using location-allocation models for regional planning in GIS environment




Applying the models
Some of the models in each of the private sector and public sector are selected to apply for the study area.
  1. Private sector model


    2. Minimizing travel distance model: Using this model we want to determine a suitable location for a number of specific utilities, so that the total traveling distance is minimized.

    The constraints in this model are as following:

    • The utilities are limited


    • Each demand node will be traveled to the nearest unity center


  2. Specifications of the model:


    3. In this model the utility center is located in the weighting center of the area, which is in the middle location of demands node. As the model minimizes traveling distance and traveling costs, it is suitable for private sector. It should be noticed that minimizing total traveling distance might be concluded a point, which is not the nearest one to the center.

  3. Running the model:


    4. A district called Pevejen from Mashhad country has been chosen to use it data for running the model. The case study is to determine the best location for building two schools.

  4. The results of running minimizing rural distance model for the district is shown in map 1 in figure 3.
Public sector model
  1. Maximizing of service covering model (MSCM):


    2. This model is used to find a location for service centers, so that maximum demands can be respond.

  2. The constraints of this model are as following:


    • There are only limited service center


    • Each demands should go to the nearest service center


    • The covering of service area is reduced as travel distance increased.

  3. The specifications of the model:


    4. In this model the service centers are located where the demand density is high. MSCM model is planned to maximize demands and should be located somewhere in the area, so that probability of using the services is reduced as traveling distance increased. Therefore the more closer demand to the service center, the highest utilizing from the services .we need to determine a limitation for traveling distance which services will not be available outside.

    The limitations of the friction of distance is defined as ß and its value is derived from the equation (1)

    ß = 1 / d -------------------(1)

    Where d is a distance beyond which there is no responsibility for giving services.




    Figure 1. The diagrams representing different ß value

    Figures 1 shows the diagrams representing ß, likelihood of traveling to the service center and distance between facility and demand.

  4. Running the model:


    5. The result of this model is shown in map 2 in figure 3. As it can be seen in the map most of the villages (demands points) are covered by the north center, where the density of the demand points are high.

  5. Maximum Attendance Model:


    6. This model is used to allocate services center for maximizing attendance.

  6. The constraints of the model are as following:


    • There are limited service centers available


    • Each demand goes to the nearest service center.


    • Attendance of demand facility change linearly with distance

  7. The specifications of the model:


    8. unlike the previous model maximizing attendance, load services to the demand points, which are further from the service center.

  8. Running the model:


    9. Map 3 shows the result of running the model.

  9. Minidistance power function:


    10. In this model when distance from the center increases the exponent function exaggerate the effect of distance. Therefore by applying larger power function the distance that individual demand points should travel to their nearest facility will be equalized.

    In the study area, most demand points are located in distance between 1 and 8 Km. If we consider one more demand point, x, which is 20 Km away. In this case the total distance traveled to this facility is 64 Km as optimized arrangement. When this point is determined as optimized by the model, it means that if this facility were moved in any direction, the total distance traveled would increase using power function in the model we exaggerate the distance. Let's consider the exponent of 2 in this example.

    Points range in distance between 1 and 64 Km and demand point x is 400 Km away. It should be noticed that 400 km is exaggerated by exponent, of 2.

    Comparing the demand points distance, 1-64 Km, with 400 Km, shows that the current location is not optimized any more, and should be moved toward x point .if the facility center moves 5 Km toward x point, the effective distance will be 225 Km.. In this case though many demand points will have to travel slightly further, but the amount is relatively small compared to the savings produced by locating the facility closer to demand location x.

  10. Running the model:


    11. The previous area, called Pevejen was chosen to run this model and the results are shown in Figure 3. As map 4 in this figure shows, the utility centers are located in Soltan-Abod-Nomak and Avareshk, villages, based on the model.

    Comparing this map and map 1 shows that utility centers are displaced. The displacement can be explained based on ß coefficient. In this analysis ß is calculated for a distance equal to 8 Km, which is 0/000125




    Figure 2. Comparing linear function and power function in allocation model

    Comparing the diagrams in figure 2 shows that if we displace the center slightly, the power function will be changed considerably. Therefore if we change the location site to new optimal configuration, say, 15 Km from demand point x, the effective distance will be 225 Km. this displacement will cost only a slight change in traveling distance for other demand points. Map 3 in figure 3 shows the utility center allocation in the area. Displacement in the utility centers and the related demand points can be seen in comparing with map 4. Using this model, Eslam-Ghale and Gol-Baghra which are close together will be served by Bazeh-Hour center.

    It can be seen when we use the power function model, the utility centers location is changed and the village covered by the centers are also differ from the previous modes. Eslam Ghale and Gol Baghra have moved to the north center which means the power function model increased the covered area for this center an the result all exponent all 2 for the distance

    Minimizing distance (with constraints) model: The objective of this model is the same as minimizing distance model, in which the location of a given number of facilities are specified. The specified number is as many that the total distance traveled is minimized.

  11. Running the model:


    12. This model is similar to the minimizing distance model and the only difference is distance threshold, which considered by this model. In this study the threshold is considered to be 8 Km and the results are shown in map 5 in figure 3. As the map in shows, a considerable displacement has been occurred in the location of utility centers. Both of the centers are determined in the north of area. This is because the number of demand points is higher in north of the area than in the south.
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