By Prof. L. Valadares Tavares (auth.)
More than 40 years have handed because the early makes an attempt to version initiatives. 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 continues to be an identical: the concept that of undertaking community. this idea has come to symbolize the 2 significant gains underlying the inspiration of a venture: the sequential and the aggressive nature of its elements, the project's actions. truly, the sequential estate defines the constitution of the venture and the aggressive nature stems from using universal assets (facilities, items, gear, administration, etc.) to hold out the several actions. in spite of the fact that, major advances were completed in venture modelling, permitting the creation of even more strong effects: A. the idea that of priority and the outline of actions has been generalized to provide quite a lot of sensible illustration of initiatives. B. the stochastic examine of the good points of initiatives resembling the period and value in their actions is conducted via a number of analytical and numerical versions, permitting experimental and forecasting analyses. C. the allocation of assets may be now studied for extra complicated occasions and regulations. D. the monetary description of tasks is extra appropriately studied and its optimization is punctiliously pursued. E. the overview and the review of initiatives now may be studied in the framework of multicriteria determination concept contemplating a number of views and aiding the undertaking supervisor to pick the main acceptable compromises among chance, time and anticipated gains.
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Extra info for Advanced Models for Project Management
The difference Sk = (t\ - tk) is called the node flout (or slack) and four other definitions of float can be given for a generic activity Ai connecting two generic nodes, k, m (Fig. 18 EXAMPLE OF FLOATS S(k,m)M = t'm-tk - OJ S(k,m)L = t'm-t'k-Oj S(k,mh = tm -tk - OJ S(k,mh= max[t m -t'k-Oj;O] designated by Total Float (actually, the correct name should be Maximal Float), Safety Float, Free Float and Interfered Float. S (k, m)M corresponds to a maximal float as it assumes that k occurs as early as possible and m as late as possible.
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. If not, go to the next step. 2 - IdentifY the activity k which belongs to the critical path and with the lowest fk = 1/}C(k)l.
The optimal solution is then given by: Q* =~2Kr h Basic modelsfor project management 35 Often, r(t) is not constant along the development of a project and so this optimization can be adapted either sub-dividing the duration into sub-periods with an approximate constant consumption rate or developing a dynamic solution in terms of time. The latter is usually studied by simulation. The uncertainty concerning r(t) can be significant and then a random or stochastic model should be adopted. Usually, a safety stock is then adopted to reduce the probability of shortage.
Advanced Models for Project Management by Prof. L. Valadares Tavares (auth.)