Location, Transport and Land-use: Modelling Spatial-Temporal Information Yupo Chan, PhD PE Professor & Founding Chair Department of Systems Engineering.

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