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					Location, Transport
  and Land-use:
Modelling Spatial-Temporal
         Information

       Yupo Chan, PhD PE
   Professor & Founding Chair
 Department of Systems Engineering
University of Arkansas at Little Rock
 Underlying Principles
         for
• Siting
  Facility location
  Competitive allocation of
  products & service
• Product/service delivery
  Location-routing
• Community development
  Land-use planning
  Spatial forecasting
 When asked about the three
 most important factors for
    fast-food success,

      McDonald's founder :
"Location, location, location.”
       E-Commerce:
Location, price, service
   Extremal Solution

• Network facility-location
  models
• Nodal-optimality property
• Extremal conditions also exist
  in planar location models
Solutions to 3-city configuration
Cost Functions of Distance
        cij = dij
  Image Processing Using
    p-medoid Method
Original Picture (from GOES satellite IR2
channel)
 (a) Raw image         0   0    0    0   0   1

                       0   2    2    2   1   0

                       1   1    4    4   2   0

                       0   2    5    3   2   0

                       0   2    1    2   1   1

                       0   0    0    1   0   0




                       0   0    0    0   0   1
 (b) Spectral
    pattern-           0   *2   2    2   1   0

    recognition        1   1    2    2   2   0
    (w=0)
                       0   2    2    2   2   0

                       0   2    1    2   1   1

                       0   0    0    1   0   0




                       0   0    0    0   0   0

                       0   1    *1   1   1   0

                       0   1    *2   2   1   0
 (c) Spectral and
                       0   1    2    2   1   0
    spatial pattern-                             Legend
    recognition        0   1    1    1   1   0
    (0.5< w < 1.0)                                 *      Representative
                       0   0    0    0   0   0
                                                            pixel

Contextual image-classification using p-medoid method
              Result
Classification using p-medoid (3 classes)
                 W=0.5
    3-dimensional Space-filling Curve

                     z



            i                        j



                i´



Y




                                            X
                     Legend
                         i, i´   demands
                         j       facility
    1                                               2 3 4 5

0             0.2      0.4          0.6           0.8           1


i       Hospital    Xi Latitude   Yi Longitude   Zi Patients        
1   Charlotte         35.21          80.44              0      0.03125
2   Ft Gordon         33.37          81.97           39         0.8125
3   Ft Bragg          35.17          79.02          234         0.8594
4   Ft Jackson        33.94          81.12           44         0.9063
5   Charleston SC     32.90          80.04           29         0.9531




          Medical-evacuation Problem
                                    ORIGINAL MODEL
     Legend                                        Initial Inventory Level: 100
     zi = delivery to depot i                      Minimum Inventory Level: 0
                                                   Maximum Inventory Level: 500
                                       1           Cost Function: q(z1) = 2600 - 8z1

                                3          5   4



                                3.5
                0                                     2

Available resource: 400
                                2              3.8
Two vehicles stationed.



                                       3


                                                                                       5




            zij = lateral re-supply from node i to j
        SOLUTIONS: A COMPARISON



Feasible    zij       Operating   Inventory   Total cost
solutions             cost        cost


1           z03 = 4   14.5        126.25      140.75
            z21 = 6


2           z01 = 6   17          118.25      135.25
            z02 = 4


3           z01 = 6   15.3        118.25      133.55
            z32 = 4


4           z01 = 6   15.3        112.25      127.55
            z12 = 4
            z13 = 3
Braess-paradox Game
   Spatial Location &
       Allocation
• Gaming
• Generalized transportation
  model
  – Includes regional input-outputs
• Equilibrium vs. Disequilibrium
  – Generalized multi-regional
  growth equilibria
• Entropy
  –freq. with which an event occurs
• Entropy maximization
  – to capture all possible patterns
  (information-minimization or spatial
  uncertainty principle)
          p1           ri    Wi    pi

    r1


           W1                             •••               pn’
                                                      Wn’
               r2             p2
                        W2                      rn’




         Legend

          Wi Facility in zone i
          pi        Price of goods and services at zone i
          ri        Land rent in zone i




A probable configuration of zonal activities
             W1(t)

               0.4–                < 14
  Facility
  stock at
   zone 1      0.3–
                                               = 70


              0.2 –    |     |           |
                  0   2.5   5.0         7.5      time t

             W2(t)


               0.2–                    = 70
  Facility
  stock at
   zone 2     0.26–
                                   = 0.35
                                               = 14

             0.29 –    |     |           |
                  0   2.5   5.0         7.5      time t

      W3(t) W4(t)


             0.22–                 = 70
  Facility
  stock at
 zone 3 & 4 0.17–
                                    = 14  = 0.35


             0.12 –    |     |           |
                  0   2.5   5.0         7.5      time t




Responses to a New Shopping Center in zone 2
              1    2   3   4   . . .   Dallas




                                                                             STUDY AREA
San Antonio




                                                Houston. . .   398 399 400


                  Pixel map of Texas Gulf Coast
Single Pixel NVI Forecast Series
Spatial-Temporal Canonical-Analysis
Random or Poisson Field
• Backshift operator, lag
  operator, image-processing
  mask, & spatial
  location/allocation
 All based on a weight matrix
• Homoscedasticity,
  stationarity, homogeneity
 If the correlation parameters are
 finite, the derived local averaging
 field become a continuous parameter
 Gaussian field.
• Ergodicity and isotropy
 A useful property & through proper
 local-averaging, such properties can
 often be obtained
 Emerging Techniques
         for
• Emergency-response to natural
  and manmade hazards
• Supply-chain management
• Intelligent transportation
  systems
• Real-estate development
• Urban land-use plans
• Satellite remote-sensing
• Environmental planning
• Infrastructure management

				
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