The critical-path method has been developed as a tool of management useful in specialized situations. It is required by several federal and state agencies on some contracts. CPM is based on planning and job analysis going far beyond that necessary for bidding a job. In addition to the step by-step breakdown of the job into its component tasks and sub tasks, and the plotting of sequential relationships, the planner must know how long each task will take.
For instance, the construction and installation of a large air handler inside the mechanical room requires shop drawings to be developed by the HVAC subcontractor.
The HVAC contractor must calculate the time needed to prepare the shop drawings, have them reviewed by the engineer, allow time for any subsequent revisions after the review and then time for review and approval. All of these sub tasks would need to be completed prior to manufacturing of the air ducts. All of the lead time for any other additional equipment needed inside the ducts, such as smoke detectors or dampers, would also need to be known. Some projects such as clean rooms or drug manufacturing facilities require lengthy testing periods of the HVAC equipment prior to acceptance. Even on the simplest of construction projects each task can have many sub tasks. Most computer programs will allow a large number of sub tasks to be shown, but for ease of reading, the sub tasks can be hidden or represented by a task line.
After the project has been broken down into all its activities, the activities are listed or plotted in such a way that all sequential relationships are shown. Activities may be represented by arrows (Fig.a) or by circles, or nodes, connected by sequence lines (Fig. b). Analysis, by examination or computer, should guide establishment of a realistic time schedule and pinpointing of the operations whose completion times are responsible for establishing the overall project duration. Also, the analysis should facilitate settling change orders by determining the operations affected and the effect on project duration. In addition, it should help in establishing the proper sequence of work operations and determining the status of work in progress in relation to the number of days behind or ahead of schedule.
An arrow diagram (Fig.a) is drawn by setting the tail of an arrow representing an activity, such as placing concrete, at the tip of an arrow representing the immediately preceding activity, such as placing electrical conduit and junction boxes. The nodes (tips and tails) are assigned unique numbers to identify the activities (1–2, 2–3, etc.). Each node represents the completion of the preceding activities and the start of the following activities. Sometimes, a dummy arrow is needed to complete the network. A precedence (PERT) diagram (Fig.b) is drawn by setting the node for an activity to the right of the node representing an immediately preceding activity. Each node is assigned a number greater than that of any preceding activity.
The nodes are connected by lines to indicate the sequence of the work. Precedence diagrams are simpler to draw and analyze than arrow diagrams. In either type of diagram, the critical path is the sequence of operations requiring the most time to complete. The critical path determines the duration of the project. To shorten the project, it is necessary to decrease the time required for one or more activities on the critical path (critical activities). These activities have zero total ﬂoat. Total ﬂoat is the difference between time required and time available to execute an activity. It is equivalent to the difference between earliest and latest start (or ﬁnish) times for an activity.
Table 1 shows the calculation of ﬂoat for the simple network in Fig. 1. Float is determined in two steps: a forward and a backward pass over the network. The forward pass starts with the early start (or scheduled) date for the ﬁrst activity, Erect Forms. In this case, the date is 0. Addition of the duration of this activity, 2 days, to the early start time yields the early ﬁnish date, 2, which is also the early start date for the next activity, Place Reinforcing. The early ﬁnish date for this activity is obtained by adding its duration, 1 day, to the early start date. The forward pass continues with computation of early start and ﬁnish times for all subsequent activities. Where one activity follows several others, its early start date is the largest of the early ﬁnish dates of those activities.
The backward pass determines late start and ﬁnish dates. It begins with the late ﬁnish date of the ﬁnal activity, Place Concrete, which is set equal to the early ﬁnish date, 6, of that activity. Subtraction of the duration, 1 day from the late ﬁnish date yields the late start date, 5, which is also the late ﬁnish date of preceding activities,Place Mechanical and Place Electrical, and their late start dates are found by subtracting their duration’s from the late ﬁnish dates. Where one activity precedes several others, its late ﬁnish date is the smallest of the late start dates of those activities.
The backward pass continues until late start and ﬁnish dates are
computed for all activities. Then, the ﬂoat can be found for each activity as the difference between early and late start times. Critical activities (those with zero total ﬂoat) are connected by heavy arrows in Fig. a and by double lines in Fig.b to indicate the critical path.
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