Why, so often, do we build what no one wants? Whenever a new residential area is completed, the happiness of the people involved about the creation of something new is tempered by feelings of dissatisfaction, because the end result of the building process was not what they had hoped for.

In a multidisciplinary study (Rijksplanologische Dienst, 1983) on the development of the Randstad, i.e. the area of Amsterdam, Utrecht, Rotterdam, and The Hague, some typical Dutch values related to urban planning surfaced: tolerance, diversity, variety, freedom, autonomy, individual touch, etc.

These characteristics are well represented in Amsterdam, a city that has developed over several centuries towards its present status. New urban areas, by contrast, which were built in only a few years, do not reflect these characteristics. They look as if they all originate from the same drawing board. Actually, they do! Urban planners, project developers, architects, construction firms, etc., all tend to stick to proven concepts and methods. As a result, new residential areas look alike, quite contrary to what their new inhabitants would have preferred. Their preferences, however, were not taken into account at a stage when options were still open. They can only 'take it or leave it', not influence it. Hence their feelings of dissatisfaction.

We will show in this book that this disappointing state of affairs is not at all an unavoidable reality of life. Nowadays it is possible to incorporate the preferences of a multitude of players into the design of large and complex building projects or residential areas. Computer models and computer graphics have become so powerful and user friendly that the effect of an individual preference on the total design can be calculated and communicated numerically as well as graphically. The computer model we use for analysing the effect of constraints on desirable outcomes is the algorithm to solve a number of linear inequalities known as Linear Programming (LP). Basically the LP model is extremely simple, but to apply it meaningfully to real life situations requires specific skills.

Outcomes from the design process have to be communicated. The very nature of architectural design requires that communication is done to a large extent through images, two or three dimensional. The classical vehicle for this, the paper drawing, lacks the flexibility of the computer drawing, which can be altered almost instantly. Communicating outcomes per computer screen is basically simple, but requires specific skills to be effective in practice.

Computer modelling and computer graphics are important tools for the modern architect, but are not sufficient on their own to accomplish the incorporation of all the relevant preferences of stakeholders into the design. The most essential condition is that the architect must feel a genuine desire to do so. He or she must respect and value these preferences and leave the design process really open-ended, as opposed to using that process as a means to achieve what he or she had in mind all along. Such open-minded, non-manipulative behaviour, called Model II by Argyris and Sch5n (1996), as opposed to Model I which is focused on achieving one's own objectives, does not come about by itself. For most people, it has to be learned and pursued in practice with a lot determination and perseverance.

To summarise, the success of the modern architect depends increasingly on his ability to use the contributions of others. To this end he needs skills in computer modelling - both numerical and geometrical - , computer graphics and communication. His behaviour should encourage possible contributors to provide their input to him.

This book is intended to assist in developing the three essential skills required of urban planners and architects of large, complex construction projects:

• Skills in numerical computer modelling;

• Skills in geometrical modelling;

• Skills in managing open-ended processes.

We feel that a wider proliferation of these skills is essential to close the gap between the wishes and preferences of stakeholders and what is ultimately built.

We use the word stakeholder here, where in the literature we often see the word actor. A stakeholder is an actor who has a right to act because he has a stake in the issue. In our concept, an actor who does not have a stake cannot directly exercise power. He can only influence the design indirectly via a stakeholder who does have an interest in the outcome of the design process.

The meaning of the word architect has evolved over time. At first, the architect was the designer of the whole building, its shape as well as its technical details. When these technical details became too complex to be dealt with by a single individual, the architect's role was gradually reduced to designing the shape of the building - the use of space and light - leaving the details to specialists. Esthetical aspects are still very important, but not more than many other aspects like functionality and cost. The architect can only regain his central position in the design process, if he attaches the same weight to all relevant aspects. His function becomes similar to the role of the conductor of an orchestra, whose responsibility it is to ensure that the musicians of the orchestra produce a coherent piece of music collectively. An architect, in our view, is someone who creates a design that constitutes the best synthesis, as perceived by the stakeholders involved, of all possible design solutions. According to this definition there is no difference between an architect and a manager of the design process that results in a set of specifications of what has to be made. The architect is the manager of that process.

The application of mathematical modelling to urban planning and architecture has been pursued in the past by many scientists and practitioners (see for instance Ackoff and Sasieni (1968), Radford and Gero (1988)) but has never really taken off. We feel that a breakthrough in this respect has become possible due to two important developments in the nineties (Fig. 1):

1. The incorporation of the actor's viewpoint - actor's 'irrationality' - in the mathematical modelling (Van Loon, 1998);

2. The vastly increased capabilities and user friendliness of computers.

The latter constitutes a decisive change compared to the preceding decades.

This book is intended primarily for our students in architecture. Actually, we feel that every graduate in architecture ought to have knowledge and skills in the three areas mentioned before: computer modelling - both numerical and geometrical - , computer graphics and managing open-ended processes. Secondly, we address ourselves to architects who wish to update their knowledge in these areas. Finally, we hope that the book will be useful to other parties involved in the realisation of large construction projects: urban planners, contractors, suppliers, and so forth.

The concepts we present may appear rather straightforward and simple. The essence, however, is not only to obtain knowledge about them, but also to acquire the skills needed to apply them in practice. Like when learning to play a musical instrument, lots of practice is far more important than knowing how to play. But, like reading about music can contribute to becoming a good musician, we hope this book will help our readers to become good architects in the sense that their creations are perceived as being the best synthesis of all possible solutions to the issue concerned.

mathematical modelling architecture

(operations research) (and urban planning)

mathematical modelling architecture

(operations research) (and urban planning)

computer capabilities (storage, speed, user friendliness)

mathematical modelling architecture

computer capabilities

mathematical modelling architecture

computer capabilities

Figure 1 The potential of mathematical modelling for architecture and urban planning has increased dramatically in the nineties computer capabilities

Figure 1 The potential of mathematical modelling for architecture and urban planning has increased dramatically in the nineties

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