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)
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
0 *2 2 2 1 0
1 1 2 2 2 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
0 1 2 2 1 0
0 1 1 1 1 0
0 0 0 0 0 0
(a) Raw image
(b) Spectral pattern- recognition (w=0)
(c) Spectral and spatial pattern-recognition (0.5< w < 1.0)
Legend
* Representative pixel
Contextual image-classification using p-medoid method
ResultClassification using p-medoid (3 classes)
W=0.5
i´
i j
z
Legenddemandsfacility
i, i´
j
Y
X
3-dimensional Space-filling Curve
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
2 3
1
1 4 5
0.80.60.40.20
Medical-evacuation Problem
5
ORIGINAL MODEL
0
1
2
3
Available resource: 400Two vehicles stationed.
Initial Inventory Level: 100Minimum Inventory Level: 0Maximum Inventory Level: 500 Cost Function: q(z1) = 2600 - 8z1
3
3.5
2
4
3.8
5
Legendzi = delivery to depot i
zij = lateral re-supply from node i to j
SOLUTIONS: A COMPARISON
14
Feasible solutions
zij Operating cost
Inventory cost
Total cost
1 z03 = 4 z21 = 6
14.5 126.25 140.75
2 z01 = 6z02 = 4
17 118.25 135.25
3 z01 = 6z32 = 4
15.3 118.25 133.55
4 z01 = 6z12 = 4 z13 = 3
15.3 112.25 127.55
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)
W1
p1
r1
Wn’pn’
rn’W2
p2r2
Wi piri
• • •
A probable configuration of zonal activities
Legend
Wi Facility in zone i
pi Price of goods and services at zone i
ri Land rent in zone i
Responses to a New Shopping Center in zone 2
Facilitystock atzone 1
Facilitystock atzone 2
Facilitystock at
zone 3 & 4
< 14
= 70
W1(t)
time t0|
2.5|
5.0|
7.5
0.4–
0.3–
0.2 –
W2(t)
time t0|
2.5|
5.0|
7.5
0.2–
0.26–
0.29 –
= 14
= 70
= 0.35
W3(t) W4(t)
time t0|
2.5|
5.0|
7.5
0.22–
0.17–
0.12 –
= 70
= 14 = 0.35
Dallas
San Antonio
Houston
1 2 3 4 . . .
. . . 398 399 400
ST
UD
Y A
RE
A
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/allocationAll 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 isotropyA 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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