Advanced Models for Project Management by Prof. L. Valadares Tavares (auth.)

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By Prof. L. Valadares Tavares (auth.)

More than 40 years have handed because the early makes an attempt to version tasks. a wide area of theoretical advancements has grown generating a excessive variety of analytical and numerical effects, however it turns out that the most version remains to be an identical: the concept that of undertaking community. this idea has come to symbolize the 2 significant good points underlying the thought of a venture: the sequential and the aggressive nature of its parts, the project's actions. really, the sequential estate defines the constitution of the undertaking and the aggressive nature stems from using universal assets (facilities, items, gear, administration, etc.) to hold out the various actions. even though, major advances were accomplished in undertaking modelling, permitting the construction of even more robust effects: A. the concept that of priority and the outline of actions has been generalized to supply a variety of sensible illustration of initiatives. B. the stochastic research of the positive factors of initiatives equivalent to the length and value in their actions is performed via numerous analytical and numerical types, permitting experimental and forecasting analyses. C. the allocation of assets will be now studied for extra advanced events and regulations. D. the monetary description of tasks is extra effectively studied and its optimization is punctiliously pursued. E. the overview and the review of tasks now may be studied in the framework of multicriteria selection concept contemplating a number of views and assisting the undertaking supervisor to choose the main applicable compromises among possibility, time and anticipated gains.

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Unfortunately, this more realistic formulation requires analytic methods much more complex than the standard algorithms. However, a very simple and well known method allows the minimization of the total cost of a project, C = LCj (OJ), obtaining a total duration not higher than a maximal bound, LT, the Crash Duration Method. This method is based on the following iterative procedure: 1 - Schedule the project with Dei) = M j • If the total duration, T, is lower than L T , this is the optimal schedule.

Obviously, this relation also should be considered as a dummy activity without any cost or resources consumption. Basic models for project management 31 3. Resources In job-shop scheduling, the concept of activity concerns a well defined job which has to be performed using a set of specific resources. The available choices concern the scheduling and the selection of a technology which determines the required resources and the job duration. The problems of Project Management have a different nature as each activity corresponds usually to a sub-project or, at least, to a large set of actions.

Kelly, 1961 and Clark, 1962). The simplest case assumes that D is detenninistically known and then T can be computed by the Critical Path Method: a) The earliest start time of any activity, Ai, is given by assuming that ti = 0 for activities with Ji = 0 . b) The minimal T can be detennined by: T* = max{t. } . I I I c) The latest start time of any activity, Ai, compatible with T* is given by: t~ = min {t~ keKi - D(k)} making t; = T- D(i) for any activity Ai with K(i) = 0. Basic models for project management 43 This method also allows the identification of the critical activities.

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