**activity**
performance of an individual job or work effort that requires labor, resources, and time and is subject to management control.
**activity-on-arrow (AOA)**
a convention for constructing a CPM/PERT network in which the branches between nodes represent project activities.
**activity-on-node [AON)**
a convention for constructing a CPM/PERT network in which the nodes represent project activities.
**backward pass**
starting at the end of a CPM/PERT network, a procedure for determining latest activity times.
**beta distribution**
a probability distribution traditionally used in CPM/PERT for estimating the mean and variance of project activity times.
**crash cost**
the cost of reducing the normal activity time.
**crash time**
the amount of time an activity is reduced.
**crashing**
a method for shortening the project duration by reducing the time of one or more critical activities at a cost.
**critical path**
the longest path through a CPM/PERT network, indicating the minimum time in which a project can be completed.
**dummy**
an activity in a network that shows a precedence relationship but represents no passage of time.
**earliest finish time (EF)**
the earliest time an activity can be completed.
**earliest start time (ES)**
the earliest time an activity can begin subject to preceding activities.
**earned value analysis (EVA)**
a standard procedure for measuring a project's progress, forecasting its completion time and cost, and measuring schedule and budget variation.
**event**
the completion or beginning of an activity in a project.
**forward pass**
starting at the beginning of a CPM/PERT network, a procedure for determining earliest activity times.
**Gantt chart**
a graphical display using bars (or time lines) to show the duration of project activities and precedence relationships.
**latest finish time (LF)**
the latest time an activity can be completed and still maintain the project critical path time.
**latest start time (LS)**
the latest time an activity can begin and not delay subsequent activities.
**matrix organization**
an organizational structure of project teams that includes members from various functional areas in the company.
**most likely time (m)**
the subjective estimate of the time that would occur most frequently if the activity were repeated many times.
**optimistic time (a)**
the shortest possible time to complete the activity if everything went right.
**organizational breakdown structure (OBS)**
a chart that shows which organizational units are responsible for work items.
**pessimistic time (b)**
the longest possible time to complete the activity given that everything went wrong.
**precedence relationship**
the sequential relationship of project activities to each other.
**project**
a unique, one-time operation or effort.
**responsibility assignment matrix (RAM)**
shows who in the organization is responsible for doing the work in the project.
**scope statement**
a document that provides an understanding, justification and expected result for the project.
**slack**
the amount by which an activity can be delayed without delaying any of the activities that follow it or the project as a whole.
**statement of work**
a written description of the objectives of a project.
**work breakdown structure [WBS)**
a method for subdividing a project into different hierarchical levels of components.
SOLVED PROBLEMS
• Animated Demo Problem
CPM/PERT NETWORK ANALYSIS
Given the following network and activity time estimates, determine earliest and latest activity times, slack, the expected project completion time and variance, and the probability that the project will be completed in 28 days or less.
SOLUTION
*Step 1.* Compute the expected activity times and variances:
For example, the expected time and variance for activity 1 are
These values and the remaining expected times and variances for each activity are shown in the following table:
*Step 2.* Determine the earliest and latest activity times and activity slack:
*As an example, the earliest start and finish times for activity 1 are*
*ES = max (EF immediate predecessors)*
The latest start and finish times for activity 7 are
LF = min (LS following activities)
*Step 3.* Identify the critical path and compute expected project completion time and variance. Observing the preceding table and those activities with no slack (i.e., s = 0), we can identify the critical path as 1-3-5-7. The expected project completion time *(t*_{p}*)* is 24 days. The variance is computed by summing the variances for the activities in the critical path:
*Step 4.* Determine the probability that the project will be completed in 28 days or less. The following normal probability distribution describes the probability analysis.
Compute Z using the following formula:
The corresponding probability from the normal table in __Appendix A__ is 0.4633; thus,
• Internet Exercises Weblinks
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