1 spatio-temporal allocation takeshi shirabe technical university of vienna
TRANSCRIPT
![Page 1: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/1.jpg)
1
Spatio-temporal Allocation
Takeshi Shirabe
Technical University of Vienna
![Page 2: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/2.jpg)
2
• Spatial Allocation
• Mathematical Programming
• Spatio-temporal Allocation
Outline
![Page 3: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/3.jpg)
3
Spatial Allocation
Allocation of discrete spatial units (SUs)to larger groups or regionsaccording to criteria concerning such properties as size, shape,
and spatial relation.
![Page 4: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/4.jpg)
4
Spatial Allocation
Carve out regions!
Spatial Relation
Size & Shape
Size & Shape
![Page 5: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/5.jpg)
5
Spatial Allocation
Partition an area!
![Page 6: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/6.jpg)
6
Mathematical Programming
A methodology to formulate and solvedecision (programming or planning) problems
in algebraic terms.
Tool
![Page 7: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/7.jpg)
7
LP
If a problem is expressed as a set of linear equations,
we have a linear programming model.
For example…
![Page 8: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/8.jpg)
8
Problem: How to make a cup of the best cappuccino
by mixing coffee, milk, and foam?
LP
![Page 9: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/9.jpg)
9
Formulation:
252
0 , ,
50
3
21
321
321
x
xx
xxx
xxx 332211 xcxcxc
Constraints Objective function
Minimize or Maximize
ly.respective foam, andmilk cofee, of ][ amounts thebe and ,Let 321 mlxxx
LP
![Page 10: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/10.jpg)
10
0
x
bAx
cx
Solution:
LP
Feasible Region
polyhedron
![Page 11: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/11.jpg)
11
If a LP model requires one or more variables to be integer,
it is a (mixed) integer programming model.
IP
If you are lucky… In almost all cases…
![Page 12: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/12.jpg)
12
IP is a tool for spatial allocationsince SUs are finest or indivisible.
A decision is binary (0-1):whether or not each SU is allocated to a region.
Some work has been done by myself. Now…
IP for Spatial Allocation
![Page 13: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/13.jpg)
13
Spatio-temporal Allocation
It is concerned withwhere to do something andwhen to do itwhile spatial variation changes over time.
My interest.
Research has been going on elsewhere.
![Page 14: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/14.jpg)
14
• Static data and static decisions
(spatial allocation)• Dynamic data and static decisions
(e.g. facility siting)• Static data and dynamic decisions
(e.g. mining)• Dynamic data and dynamic decisions
(e.g. harvesting, routing)
Spatio-temporal Allocation
![Page 15: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/15.jpg)
15
Spatio-temporal Allocation
seems to be generalized to…
Allocation of discrete spatio-temporal units (?)to larger groups or regions (?)according to criteria concerning such properties as what????
![Page 16: 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna](https://reader030.vdocuments.us/reader030/viewer/2022032606/56649ea95503460f94bada99/html5/thumbnails/16.jpg)
16
• Is ST allocation special or is it just a trivial extension of spatial allocation (e.g. ST allocation = 3D spatial allocation)?
• What kinds of properties are additionally involved?(e.g. contiguity in a (spatio-) temporal sense)
• Can they be decomposed into a set of primitive properties?
• Can such primitives be modeled in terms amenable to algorithmic solution (like IP)?
• Can they be recomposed into complex ST properties?
• Can GIS or DSS (decision support systems) benefit from this scheme?
Research Questions