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What would be the best way create a mathematical model of the construction of a large complex structure such as a high-rise building? It is preferable to model the 'people' rather than the actual activities.

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What do you want your model to capture, predict or describe? The rate of progress, the progressive costs of construction, the progressive expenditure in terms of cost of labour ... as it stands I'm having trouble knowing where to start with this question. –  Yemon Choi Mar 11 '10 at 3:57
    
Agreed; there is no way to evaluate models without knowing what the model is supposed to accomplish. This doesn't strike me as a particularly mathematical question, so I'm voting to close for now. –  Qiaochu Yuan Mar 11 '10 at 4:19
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I am trying to model the actual process. Let me explain. Almost all large Complex projects suffer from major delays. Planning for these projects is usually via Gant charts which however fails to capture the complexity of these systems. If you observe the actual operations they sometimes resemble traffic, with traffic jams, waves etc. I am thinking that a better way to simulate such processes is through automata (ie simulating the humans involved) rather than the activities involved. Any thoughts? –  yannis Mar 11 '10 at 4:51
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@yannis: maybe you can edit your question to include the extra details that you give in your comment? I think there might be some interesting responses if we could find a more focused version of the question. –  Yemon Choi Mar 11 '10 at 5:14
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Indeed, if your question is about the scheduling problems which arise, then you should say more about that, because the discrete-geometry tag suggests something else. –  Douglas Zare Mar 11 '10 at 7:22
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1 Answer

As You say:

Let me explain. Almost all large Complex projects suffer from major delays. Planning for these projects is usually via Gant charts which however fails to capture the complexity of these systems. If you observe the actual operations they sometimes resemble traffic, with traffic jams, waves etc. I am thinking that a better way to simulate such processes is through automata (ie simulating the humans involved) rather than the activities involved. Any thoughts?

I presume You should look at "intelligent agent interactions" modelling framework. This is rather well known approach to model systems involving interactions between entities within system, which was used in traffic predictions, network routing optimisation, evacuation modelling etc. But As You see deeper You may discover that in any of this situation, interactions between agents are well defined, and usually descried by a few parameters. As during project managements there is much more complicated information flow, and it will be very difficult to model this elations, there will be rather no progress in practical modelling. In practical project management, process approach ( called by You activity) is a kind of paradigm arising from the fact that business organizations tend to manage activities to be independent of people involved in it. In practical case, in order to model such people behaviour, You will have to describe certain people behaviour. You have to have enough parameters to set up very complex characteristic properties.

For example someone may have many creative ideas, but during typical coding work may perform many mistakes. He is useful worker during beginning of the process, when project constitutes, but rather not useful during finally implementation. When You model process by activities, manager perform decision to attach such person to tasks based on this knowledge. But Your system should made such decision by itself, taking into account this psychological property of such person. How many resources for every single agent You have to assign in order to describe such complex behaviour?

But it seems to be interesting to perform such approach to general statistical analysis of project management process. Maybe if You make certain assumptions You will be able to describe certain and general properties of this activity? For example maybe Your (simple ) model may show prolongation of projects when number of people involved rise? This may be kind of benchmark for any model: if You model do not show such effect probably You do not catch the point.

Direct answer to Your question: multiagen modelling may be used in simple interactions situation, which is obviously not the case of project management. From the other side, modelling interactions within group of people is possible, and if You create correct model, You may find proper description for some aspects of interactions. I do not expect to be possible to create "practical tools" with this approach in the meaning as Gantt diagrams has. But it may be interesting from "social interaction" modelling in statistical meaning.

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Thank you. >For example maybe Your (simple ) model may show prolongation of projects when number of people involved rise? This may be kind of benchmark for any model: if You model do not show such effect probably You do not catch the point. Yes this is the type of effect I need to capture (I have personally observed this on numerous Projects). You suggestion of using an intelligent agent framework is a good one and I will have a good look at it. Sorry I can't upvote you I am still new here. –  yannis Mar 11 '10 at 10:01
    
@yannis: upvotes are not very important to me;-) I suggests that using intelligent agents will not be very useful. Regards;-) –  kakaz Mar 11 '10 at 10:43
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