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Spatio-temporal Allocation

Takeshi Shirabe

Technical University of Vienna

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• Spatial Allocation

• Mathematical Programming

• Spatio-temporal Allocation

Outline

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Spatial Allocation

Allocation of discrete spatial units (SUs)to larger groups or regionsaccording to criteria concerning such properties as size, shape,

and spatial relation.

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Spatial Allocation

Carve out regions!

Spatial Relation

Size & Shape

Size & Shape

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Spatial Allocation

Partition an area!

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Mathematical Programming

A methodology to formulate and solvedecision (programming or planning) problems

in algebraic terms.

Tool

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LP

If a problem is expressed as a set of linear equations,

we have a linear programming model.

For example…

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Problem: How to make a cup of the best cappuccino

by mixing coffee, milk, and foam?

LP

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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

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0

x

bAx

cx

Solution:

LP

Feasible Region

polyhedron

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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…

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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

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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.

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• 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

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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????

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• 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