Fit of activities into spaces

In the representation of the space allocation described above, it is assumed that the total demanded space for activities equals the total supplied space for the activities. In the beginning of a design process this is often not the case. In architectural design and urban planning, demand and supply are independent of each other. They are not fixed at the start of a design process. Designers propose spatial arrangements of spaces based on their ideas, style, and concepts. Of course, these proposals are not that far from the required spaces, but they are not equal. So, a design can give ideas for activities one was not thinking of. Similarly, a designer can discover that he does not yet have space for an activity which certainly should be in the building. The designers have to find the best fit. With two extensions to the above model, it is possible to cope with this design question.

Minimise Z = ^^ cijXij for i = 1,2,..., m, j = 1,2,..., n (8.4)

subject to:

Figure 8.1 Urban area

Di > d_mini for i = 1,2,..., m Sj < d_maxj for j = 1,2,..., n Sj > d_minj for j = 1,2,..., n and xij > 0 for i = 1,2,..., m, j = 1,2,..., n Di > 0 for i = 1,2,..., m Sj > 0 for j = 1,2,..., n aij = {0,1} for i = 1,2,..., m, j = 1,2,..., n

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