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The ABCs of the Critical Path Method
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The ABCs of the Critical Path Method
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- Repetitive Project Scheduling: Theory and Methods - 1st Edition.
See the seller's listing for full details. See all condition definitions - opens in a new window or tab Read more about the condition. Repetitive Project Scheduling: Theory and Methods is the first book to comprehensively, and systematically, review new methods for scheduling repetitive projects that have been developed in response to the weaknesses of the most popular method for project scheduling, the Critical Path Method CPM.
As projects with significant levels of repetitive scheduling are common in construction and engineering, especially construction of buildings with multiple stories, highways, tunnels, pipelines, power distribution networks, and so on, the book fills a much needed gap, introducing the main repetitive project scheduling methods, both comprehensively and systematically. Users will find valuable information on core methodologies, including how to identify the controlling path and controlling segment, how to convert RSM to a network model, and examples based on practical scheduling problems.
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The carrying out of such construction projects, during which more than one building is to be built creates many difficulties. These are primarily organisational, technological and cost-related problems [ 1 , 2 ].
Repetitive Project Scheduling: Theory and Methods
This article addresses the issue of scheduling repetitive construction projects in a flexible way, taking into account technological constraints. Many methods have been developed to support planners in preparing schedules repetitive construction projects. Methods such as: Line of Balance [ 3 ], Time-Location Matrix Model [ 4 ], Horizontal and Vertical Logic Scheduling for Multistory Projects [ 5 ], Time-coupled method [ 6 ] as well as other ones [ 7 , 8 , 9 , 10 , 11 , 12 , 13 ] are still developed.
Scheduling construction works during which many structures are to be built is complicated, which is why many methods have also been developed to support decision making [ 14 ]. The article [ 15 ] presents the concepts of priority scheduling. Priority scheduling assumes that the planner can determine the validity of restrictions in a flexible way by ranking them.
The constraints that are higher in the ranking are considered as priorities and their adherence must be met, further constraints are less important and are to be met under the condition that the constraints that are higher in the ranking allow that.
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This article extends the priority scheduling model [ 15 ] taking into account technological constraints. The aim of the article is to develop a mathematical model that will allow technological constraints to be adhered to in a flexible way while planning the carrying out of repetitive construction projects. The aim of the article is not to eliminate technological breaks, but to set the dates of initiation and completion of works in order to meet as much as possible the assumed technological breaks.
We are given a repetitive construction projects carried out using a flow-shop system. There aremtasks to be completed by m specialised brigades on n structures. The duration of each task is deterministic and is assumed to be known.
Once started, tasks cannot be interrupted. The following sets of index pairs have been determined below:. The developed model requires knowledge of the duration of tasks being performed on all structures by all brigades t i , j. The goal function 1 is a sum of several components. The first element determines the value of the failure to ensure lower and upper flexible time coupling between structures. The second element allows us to determine the value of the failure to ensure lower and upper flexible time coupling between the tasks of successive brigades. The third element is the deadline for all work Z n , m signifies the time of completion of the last work.
The objective function will be minimized. This will allow us to set such deadlines for the work of brigades on the structure that best meet the technological constraint with the shortest project completion time. The model has the following constraints. Formula 2 makes it possible to link the initation and completion dates of all tasks performed during the carrying out of the project.
Formulas retain the dependencies of the CPM network, taking into account lower and upper flexible time couplings for both structures and brigades, and allow us to determine whether flexible couplings have not been ensured ck variables. All variables take on non-negative values 7. Both the constraints and the goal function are linear, which makes this a linear programming model.
The model developed by the authors has been implemented in the Python programming language. The Simplex algorithm was used to analyse the model. Figure 1 shows the concept of flexible time couplings. In a case in which the aforementioned difference is smaller than the value of the lower flexible coupling by t c i , j o d by c k i , j o d time units, the goal function will be increased by the quotient of of the value of the failure of ensuring to maintaining this coupling c k i , j o d and the determined c w i , j o d weight Figure 1b.
Flexible couplings between tasks carried out on one site by successive brigades can be interpreted in a similar manner. By adopting appropriate values of cw parameters, constraints can be flexibly complied with according to the priorities set by the planner. The developed model will be used to schedule repetitive construction projects with technological constrains. The set T will contain work indices after which the technological pause is to take place.
With these assumptions, an appropriate set of weights was prepared:. Weights 9 and 12 will ensure that there are no upper limits between the date of initiating a successive work and the compeltion date of a previous work - this applies to tasks performed on subsequent structures condition 9 as well as to tasks performed by subsequent brigades condition The weights described in condition 11 will cause the pause between the work of successive brigades on a structure will be equal to at least s j.
Such a developed set of weights will be called set A. A set of weights which will cause the technological pause to be exactly as long as parameter s l was developed as well:. Conditions are analogous to The condition 17 has been modified while condition 18 has been added to impose an upper limit on the length of the technological pause - now it will last exactly s j. This set of weights will be called set B. Each brigade must perform the following works on every structure: B 1 - excavation, B 2 - building a strip foundations, B 3 - erection of foundation walls, B 4 - erecting a floor slab above the basement.
The completion times of individual tasks by the brigades on each structure have been shown in Table 1. A technological pause of at least 7 days must be maintained between the task of Brigade B 2 strip foundations and B 3 erection of foundation walls. Meanwhile, a technological pause of at least 14 days must be maintained between the task of B 3 and B 4 constructing a floor slab over the basemenet. For a problem formulated in this manner, a solution shown on Figure 3 has been obtained using the model developed by the authors in conjunction with weight sets A weight shown on Figure 2.
The solution obtained using weight set A. OiBj — work performed on structure i by brigade j , S — tasks initiation time, F — tasks completion deadline, t — task completion time. Calculations were also performed for an analogous example, assuming that pauses are to last exactly 7 days between tasks performed by brigades B 2 and B 3 and exactly 14 days between the tasks performed by brigades B 3 and B 4.
In order to solve this problem the authors used the model that has been developed in conjunction with weight set B weight shown on Figure 4. The solution obtained has been shown in Figure 5. The solution obtained using weight set B.
Markings as in Figure 3. Using weight set A, the project will be completed within 80 days. The imposed minimum technological pauses will be maintained, and in some cases will last longer. For example, on structure 2, between tasks performed by brigades B 3 and B 4, the pause will be 16 days instead of All constraints resulting from network dependencies were also maintained. There will be no situation in which two different task are being performed simultaneously on one structure. In the case of using weight set. B, the project will be completed within 84 days.
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