## Old city preservation example

In this example* we show how geometric modelling can be used in trading-off preservation of an old city against other, more general, objectives. Consider the plan shown in Figure 8.1. The plan shows that the old city is near petrochemical industries. The regional planning department has formulated different general objectives for the allocation of new urban functions:

*This case, concerning the Daya Bay region in China, was prepared by the authors for their workshop at Tsinghua University, Beijing, in February 2005.

• There should be enough urban area for new industrial development (ID);

• The new residential area should be in balance with the new industrial area (RA);

• There has to be enough space for leisure for the new residents like sporting, outdoor meetings and cultural events (LE);

• Nature protection is necessary as a compensation for the new urban developments (NA).

These objectives are quantified as follows:

• Industrial Development: ID > 20 square kilometres;

Rearranging these equations to fit into the standard LP structure yields:

The plan is then divided into zones as shown in Figure 8.2. This results in the capacity per zone. Because of the spatial arrangement of the zones and their capacities not all zones are suited for all functions. This is why the planners decided that:

• Zone 2 and 8 are not suitable as a residential area;

• Zone 2,3, 7 and 8 are not suitable as an industrial area;

• Zone 1 is not suitable as a leisure area;

• Zone 1,3, 4 and 7 are not suitable as a a nature area.

### Table 8.2 shows how this is fed into the model.

The model is then run to maximise the total industrial area. Table 8.3 shows the results of this run. It shows how much of a certain function is allocated to a certain zone. As can be seen from the results, both the general and geometrical objectives are met. One can easily explore different allocations by simply

Table 8.2 Allowed allocations

Zones

Residential 10 111110 Industries 10 0 1110 0 Leisure 0 1111111 Nature 0 10 0 110 1

Table 8.3 Model output (initial allocations)

Zones

Table 8.4 Allowed allocations (after negotiations)

Zones

Residential 10 111110

Industries 10 0 1110 0

Table 8.5 Model output (altered allocations)

Zones

Table 8.5 Model output (altered allocations)

Zones

 1 2 3 4 5 6 7 8 Residential 5 0 6 0 0 5 7 0 Industries 1 0 0 10.5 14 0 0 0 Leisure 0 0 0 0 0 0 0 2.3 Nature 0 10 0 0 0 0 0 0

altering the allowed spatial allocations. For instance, suppose a second optimisation is conducted after negotiation has taken place about allowed allocations of the different functions. This is represented in Table 8.4 (input) and Table 8.5 (output).

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