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 a similar: the idea that of venture community. this idea has come to symbolize the 2 significant positive aspects underlying the proposal of a undertaking: 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, apparatus, administration, etc.) to hold out the several actions. in spite of the fact that, major advances were completed in undertaking modelling, permitting the creation of even more strong effects: A. the concept that of priority and the outline of actions has been generalized to provide a variety of practical illustration of initiatives. B. the stochastic examine of the positive factors of tasks equivalent to the length and price in their actions is performed through a number of analytical and numerical types, permitting experimental and forecasting analyses. C. the allocation of assets could be now studied for extra complicated events and regulations. D. the monetary description of tasks is extra thoroughly studied and its optimization is punctiliously pursued. E. the overview and the overview of initiatives now could be studied in the framework of multicriteria determination conception contemplating a number of views and aiding the undertaking supervisor to choose the main applicable compromises among possibility, time and anticipated gains.
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The start and the end are now represented by the initial and dummy nodes (S, E) and redundant precedence links cannot exist. However, now representing the full set of activities with the appropriate precedence links may be more difficult and it may require the introduction of additional and dummy activities as is shown in the example (Fig. 3) using dotted lines. In any case, the project network will be represented by a finite and discrete set of nodes and by a set of direct links defining a set of connections between nodes.
14 CAPACITY CURVE 36 Advanced models for project management Therefore, the achievement of a uniform level of use of renewable resources is much more efficient than having a consumption curve with strong fluctuations. This objective is called "resource levelling". There are also resources doubly constrained which means that there are restrictions concerning their accumulated function, R (t), and also their capacity constraint, C(t). The most common example is human resources with R (t) restricted in terms of (man.
Even assuming the statistical independence between the duration of different activities, the study of the project's total duration, T, is a very difficult problem because the cumulative distribution function of T, FT (X) is given by: where Lk with k=I, ... , K describes all paths from the start until the end of the project, DLk (DIo ... ,DN) is the duration of Lk given the duration of the activities, D j, and f (OJ) is its probability density function, with i= 1, ... , N. The method PERT has simplified drastically this problem substituting ~[DLk (Dl, ...