【正文】 ect）The most widely used scheduling technique is the critical path method (CPM) for scheduling, often referred to as critical path scheduling.（選擇）The critical path itself represents the set or sequence of predecessor/successor activities which will take the longest time to plete. The duration of the critical path is the sum of the activities’ durations along the path. Thus, the critical path can be defined as the longest possible path through the” network” or project activities, as described before. The duration of the critical path represents the minimum time required to plete a project. There may be more than one critical path among all the project activities, so pletion of the entire project could be delayed by delaying activities along any one of the critical paths.（全選，A到E）This artificial precedence constraint insures that the two activities requiring the same resource will not be scheduled at the same time.（B卷）With an activityonbranch network, dummy activities may be introduced for the purposes of providing unique activity designations and maintaining the correct sequence of activities. A dummy activity is assumed to have no time duration and can be graphically represented by a dashed line in a network. Several cases in which dummy activities are useful are illustrated in Figure 91.（全選）Many puter scheduling systems support only one network representation, either activityonbranch or activityonnode.（填空）A good project manager is familiar with either representation.The concept of float is to use part or all of this allowable range to schedule an activity without delaying the pletion f the project.Float is a very valuable concept since it represents the scheduling flexibility or “maneuvering room” available to plete particular tasks. Activities on the critical path do not provide any flexibility for scheduling nor leeway in case of problems.For activities with some float, the actual starting time might be chosen to balance work loads over time, to correspond with material deliveries, or to improve the project’s cash flow.Three separate categories of float are defined in critical path scheduling: Free float。 Independent float。 Total float.The activity diagrams shown in the previous section were topological networks in that only the relationship between nodes and branches were of interest.In timescaled network diagrams, activities on the network are plotted on a horizontal axis measuring the time since project mencement.Another useful graphical representation tool is a bar or Gantt chart illustrating the scheduled time for each activity.The bar chart lists activities and shows their scheduled start, finish and duration.The small “v” marks on each activity represent the current state of each activity.For planning purposes, bar charts are not as useful since they do not indicate the precedence relationships among activities.Other graphical representations are also useful in project monitoring. Time and activity graphs are extremely useful in portraying the current status of a project as well as the existence of activity float. For example, Figure 94 shows two possible schedules for the nine activity project described and shown in the previous figures. The first schedule would occur if each activity was scheduled at its earliest start time, ES( i, j) consistent with pletion of the project in the minimum possible time.（全選）The horizontal time difference between the two feasible schedules gives an indication of the extent of possible float.Two simple approaches to dealing with the uncertainty: First, the uncertainty in activity durations may simply be ignored and scheduling done using the expected or most likely time duration for each activity. A second simple approach to incorporation uncertainty also deserves mention. Many managers recognize that the use of expected durations may result in overly optimistic schedules, so they include a contingency allowance in their estimate of activity durations.（注意是simple）While this simple approach might be defended, it has two drawbacks. First, the use of expected activity durations typically results in overly optimistic schedules for pletion。 a numerical example of this optimism appears below. Second, the use of single activity durations often produces a rigid, in flexible mindset on the part of schedulers.The most mon formal approach to incorporate uncertainty in the scheduling process is to apply the critical path scheduling process and then analyze the results from a probabilistic perspective. This process is usually referred to as the PERT scheduling or evaluation method.（選擇）While the PERT method has been made widely available, it suffers from three major problems. First, the procedure focuses upon a single critical path, when many paths might bee critical due to random fluctuations.As a second problem with the PERT procedure, it is incorrect to assume that most construction activity durations are independent random variables. In practice, durations are correlated with one another.（選擇）Finally, the PERT method requires three duration estimates for each activity rather than the single estimate developed for critical path scheduling. Thus, the difficulty and labor of estimating activity characteristics is multiplied threefold.