Chapter Overview
1) Overview – This chapter continues the discussion of project implementation by
covering various scheduling techniques.
2) Background – Per the text, “A schedule is the conversion of a project action plan into
an operating timetable.” Because projects are unique, a schedule is especially
important because there is often no on-going process that simply has to be repeated
on a daily basis. The basic process is to identify all the tasks and the sequential
relationships among them, that is, which tasks must precede or succeed others. There
are a number of benefits to the creation and use of these networks including:
a) It is a consistent framework for planning, scheduling and controlling the project.
b) It can be used to determine a beginning and ending date for every project task.
c) It identifies the activities that if delayed will delay the project.
3) Network Techniques: PERT (ADM) and CPM (PDM) – PERT and CPM are the most
commonly used approaches to project scheduling. Both were introduced in the
1950’s. PERT has been primarily associated with R&D projects, while CPM with
construction projects. Today PERT is not used much since project management
software generates CPM style networks. The primary difference between them is that
PERT uses probabilistic techniques to determine task durations, while CPM relies on
a single duration estimate for each task. Both techniques identify the critical path
(tasks that cannot be delayed without delaying the project) and associated float or
slack in the schedule. In 2005 the Project Management Institute (PMI) deemed it
necessary to change the names of these techniques. According to PMI, PERT is
called ADM/PERT (Arrow Diagram Method) and CPM is PDM/CPM (Precedence
Diagramming Method).
a) Terminology – The following are the key terms associated with the development
and use of networks:
i) Activity – A specific task or set of tasks that have a beginning and end and
consume resources.
ii) Event – The result of completing one or more activities. Events don’t use
resources.
iii) Network – The arrangement of all activities and events in their logical
sequence represented by arcs and nodes.
iv) Path – The series of activities between any two events.
v) Critical – Activities, events or paths which, if delayed, will delay the project.
To construct the network the predecessors and successors of each activity must be
identified. Activities that start the network will have no predecessor. Activities
that end the network have no successor. Regardless of the technique used, it is
good practice to link the activities with no other predecessor to a START
milestone. Those without any successor should be linked to an END milestone.
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PDM/CPM networks identify the activities as nodes in the network: the so-called
Activity on Node (AON) network. The arrows in between the nodes depict the
predecessor/successor relationships among the activities. The ADM/PERT
method, on the other hand, uses Activity on Arrow (AOA) networks. Here the
nodes represent events and the arrows represent the actual activities.
b) Constructing the Network, AON Version – The text illustrates the development of
a simple AON network. All the major project management software packages
will generate this type of network.
c) Constructing the Network, AOA Version – The AOA network has some
development rules that make it somewhat more difficult to construct than the
AON network. The primary rule is that any given activity must have its source in
one and only one node. As a result, some network relationships can only be
depicted with the use of a “dummy” activity. This is an activity that has no
duration and consumes no resources. Its sole purpose is to indicate a precedence
relationship. The text uses various figures to illustrate the use of dummy
activities.
d) Gantt (Bars) Charts and Microsoft® Project (MSP) – The most familiar tool for
depicting project schedules is the Gantt chart, invented by Henry L. Gantt in
1917. The activities are depicted as horizontal bars with their length proportional
to their duration. This method results in an easy to read graphical depiction of the
project schedule. Gantt charts can be difficult to maintain if there are large
changes in the project schedule. Tools like Microsoft® Project (MSP) will
automatically draw the Gantt chart as a by-product of the network entered by the
user. The disadvantage of the Gantt chart is that it typically does not depict the
network relationships.
e) Solving the Network – The text illustrates the development of another AON
network based on the project detailed in Table 8-1.
f) Calculating Activity Times – The sample project in the text has three duration
estimates for each activity: optimistic (a), most likely (m) and pessimistic (b).
Optimistic and pessimistic are defined as the durations that represent 99 percent
certainty. In other words the actual duration of an activity will be less than the
optimistic or greater than the pessimistic only one percent of the time. Then the
expected time (TE) is found with the formula:
TE = (a + 4m + b)/6
where:
a = optimistic time estimate
b = pessimistic time estimate
m = most likely time estimate, the mode
This formula is based on the beta statistical distribution. In spite of a flurry of
discussion in the 1980’s the assumptions used to derive this formula have stood
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the test of time. Along with TE, the variance of the durations can be calculated
as:

2

ba / 6
2
and the standard deviation as:
 2
g) Critical Path and Time – Using the example network, the text describes the
concept of the critical path. For simple projects, the critical path can be found by
determining the longest path through the network.
h) Slack (aka, Float) – In the previous section, the earliest possible dates for each
activity were determined. By starting the analysis at the end of the network and
working through it backwards, the latest possible dates for each activity can be
determined. The difference between the early dates and the late dates is float or
slack. Activities on the critical path have zero float.
i) Precedence Diagramming – The Precedence Diagram Method allows for
additional relationships to be established between activities. They are:
i) Finish to Start – The successor activity cannot begin until the predecessor
finishes. This is the most common relationship depicted in networks.
ii) Start to Start – The successor activity cannot begin until the predecessor
begins.
iii) Finish to Finish – The successor activity cannot finish until the predecessor
activity finishes.
iv) Start to Finish – The successor activity cannot finish until the predecessor
activity starts. This relationship is rarely used.
In addition to these relationships, PDM allows for leads and lags which is the
introduction of a specific time period between the linked activities. For example,
in a Start to Start relationship with five days of lag, the successor activity cannot
begin until five days after the predecessor starts. The critical path and slack
calculation resulting from these relationships can be complicated and counter
intuitive.
j) Once again, Microsoft® Project – The text illustrates the use of MSP for
calculating the most likely project duration using the PERT method.
k) Exhibits Available from Software, a Bit More MSP – The text illustrates the types
of outputs available from MSP.
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