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 continues to be an analogous: the idea that of venture community. this idea has come to symbolize the 2 significant positive factors underlying the idea of a venture: the sequential and the aggressive nature of its parts, the project's actions. truly, 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 several actions. even if, major advances were completed in undertaking modelling, permitting the creation of even more robust effects: A. the concept that of priority and the outline of actions has been generalized to supply quite a lot of practical illustration of initiatives. B. the stochastic examine of the positive aspects of tasks akin to the length and price in their actions is conducted through numerous analytical and numerical versions, 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 initiatives is extra correctly studied and its optimization is punctiliously pursued. E. the review and the overview of initiatives now might be studied in the framework of multicriteria choice concept contemplating a number of views and aiding the undertaking supervisor to pick the main acceptable compromises among hazard, time and anticipated gains.
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Extra resources for Advanced Models for Project Management
Basic models for project management 23 2. Sequentiality The precedence conditions already defined in b) should describe a feasible project which means that: for any Aj E J\ one should have Ai ~ J'j for any activity Ai E Q. This property is called acyclicity condition and implies that there are one or more activities, Ai • with an empty Ji("initial activities", as they can start as soon as the project starts) not belonging to h of any activity Ak E n ("final activities". as the project will be finished as soon as they will be ended).
0 27 27 6 '1 13 I 13 5 21 21 21 121 3 . 16 EARLIEST AND LATEST OCCURRENCE TIME OF THE NODES OF THE NETWORK PRESENTED IN FIG. 17 EARLIEST AND LATEST STARTING TIMES OF THE ACTIVITIES OF THE NETWORK PRESENTED IN FIG. 1 Activity Duration 1 10 2 3 3 7 4 5 5 8 6 2 7 11 8 4 9 6 10 7 11 6 12 9 13 7 Obviously, the definition of a critical activity also can be given in terms of the earliest and latest times of the nodes using AoA: Ai is critical if: a) tk = t'k and tm Ai ends. b) Di = (tm - tk) = t'm' k being the node where Ai starts and m the node where It should be noted that the condition a) is just a necessary condition.
Obviously, the duration of the activity depends directly on such decisions. Therefore, any project manager tends to consider the allocated resources as independent variables and the durations of the activities as the dependent variables. Unfortunately, the study of Project Management has been influenced too much by the models of job shop scheduling which may explain why this distinction has not been clarified in literature. Therefore, in this book, the study of the resources or cost allocated to each activity precedes the study of the durations of the activities and of the network.
Advanced Models for Project Management by Prof. L. Valadares Tavares (auth.)