A Normalization Procedure in Building Methodology

In the design of large electrical, mechanical, structural, etc., systems, the architect frequently faces a normalization problem: given a system made by a large number of components, a procedure, generally a numerical procedure, is available for the determination of the minimum size required by each one of the components. The adoption of the sizes obtained in this fashion would then represent the optimum design solution in the sense of minimum cost if it were not for the well-known fact that repetition of components in a system yields a reduction in fabrication and assemblage costs. If the fractional reduction in cost due to repetition is assumed to be known for each type of component, the problem consists in determining the combination of sizes for which the greatest reduction is achieved. This is a combinatorial problem of vast arithmetic proportions unless a methodological approach is employed. In the present research a method based in the theory of Dynamic Programming has been developed using elements of Graph Theory and Optimization. The model and its solution is presented using as an example of application the problem of normalizing the structural sections of a housing project. Application to other areas of building methodologies are also discussed. A computer program and numerical illustrative results complete the presentation of the model. At present, a stochastic version of the model is being developed.