1. 1 Spatio-temporal Allocation Takeshi Shirabe Technical University of Vienna

2. 2 Spatial Allocation Mathematical Programming Spatio-temporal Allocation Outline

3. 3 Spatial Allocation Allocation of discrete spatial units (SUs) to larger groups or regions according to criteria concerning such properties as size, shape, and spatial relation.

4. 4 Spatial Allocation Carve out regions!

5. 5 Spatial Allocation Partition an area!

6. 6 Mathematical Programming A methodology to formulate and solve decision (programming or planning) problems in algebraic terms. Tool

7. 7 LP If a problem is expressed as a set of linear equations, we have a linear programming model. For example…

8. 8 Problem: How to make a cup of the best cappuccino by mixing coffee, milk, and foam? LP

9. 9 Formulation : ConstraintsObjective function Minimize or Maximize LP

10. 10 Solution : LP Feasible Region polyhedron

11. 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…

12. 12 IP is a tool for spatial allocation since 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

13. 13 Spatio-temporal Allocation It is concerned with where to do something and when to do it while spatial variation changes over time. My interest. Research has been going on elsewhere.

14. 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

15. 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????

16. 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