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 analogous: the idea that of undertaking community. this idea has come to symbolize the 2 significant beneficial properties underlying the inspiration of a venture: the sequential and the aggressive nature of its elements, 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 different actions. in spite of the fact that, major advances were accomplished in venture 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 quite a lot of real looking illustration of tasks. B. the stochastic research of the positive factors of tasks comparable to the period and price in their actions is conducted by means of numerous analytical and numerical versions, permitting experimental and forecasting analyses. C. the allocation of assets will be now studied for extra complicated events and regulations. D. the monetary description of initiatives is extra safely studied and its optimization is punctiliously pursued. E. the evaluate and the assessment of tasks now should be studied in the framework of multicriteria choice thought contemplating a number of views and aiding the venture supervisor to choose the main acceptable compromises among threat, time and anticipated gains.

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If the total cost, C, is lower than Lc this is the optimal schedule. If not, go to the next step. 2 - IdentifY the activity k which belongs to the critical path and with the lowest fk = /}C(k)l. e is achieved or @- k leaves the critical path or @- fk is no longer the minimum. Whenever b or c happens one should go back to 2 until ® occurs. An equivalent problem can be fonnulated if it is assumed that for each activity a set of alternatives discrete modes [Multi-mode assumlltion] is available instead of a continuous function C(i) = f (D(i»: [C(i),D(i)]k with k=l, ...

Will be defined in terms of the corresponding interest rate adopted for this type of project. For instance, assuming a. 09 ). This means that long tenD effects are poorly represented by financial analysis tending to ignore impacts above 20 or 25 years. This myopic nature is particularly serious if a. is high. ) . Thus, the assessment or evaluation of projects should be carried out within a more comprehensive and consistent framework, the financial perspective being just one dimension of such analysis.

In any case. the activities are the result of the decomposition of the project. Therefore. • N} being mutually exclusive and giving an exhaustive description of the project (N is the number of activities); b) a set of precedence conditions. L. • N} where Ji is the set of activities immediately preceding Ai. Ji can be defined by: Ji = {k & Ji') ( l (k & J'm) = 0 for any m & Ji'} where Ji' or J'm is the whole set of activities which have to be completed before starting Ai or before starting Am. • BQ (i)} with Q ~ 1 defined for each activity and describing its properties relevant for project management such as duration.

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