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Global Management Studies
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GMS 450
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Stan Katz
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Chapter 5

School

Ryerson University
Department

Global Management Studies

Course Code

GMS 450

Professor

Stan Katz

Description

CGMS450- Chapter 5- Scheduling the Project
Project schedule is simply the project plan in an altered format
Convenient form for monitoring and controlling project activities
Take on several forms
o Gantt charts
o PERT/ CPM networks
o Convert a project plan or WBS into these formats
5.1 PERT And CPM Networks
PERT developed by US Navy, Booz-Allen Hamilton and Lockheed Aircraft
CPM developed by Dupont De Nemours Inc.
When developed there were significant differences
o PERT used probabilistic estimates of activity durations
o CPM used deterministic estimates but included both time and cost estimates to
allow time/cost trade offs to be used
o Both employed networks to schedule and display task sequences
Identified a critical path of tasks that could not be delayed without delaying
the project
Identified activities with slack that could be somewhat delayed without
extending the time required to complete project
Anything one can do with PERT, they could do with CPM
Traditional PERT is used less often than CPM
CPM can be used with 3 time estimates
We can do things with PERT that were restricted to CPM in “olden times”
The Language Of PERT/ CPM
Terms used in discussing PERT/ CPM
o Activity—task or set of tasks required by the project
Use resources and time
o Event—an identifiable state resulting from the completion of one or more activities
Consume no resources or time
Before event is achieved—all predecessor activities must be complete
o Milestones—identifiable and noteworthy events marking significant progress on the
project
o Network—A diagram of nodes connected by directional arcs that defines the project
and illustrates the technological relationships of all activities
Drawn with a start node on the left an a finish mode on the right
o Path—series of connected activities between any 2 events in a network
o Critical path—set of activities on a oath from the projects start event to its finish
event that, of delayed, will delay the competition date of the project
o Critical time—time required to complete all activities on the critical path
Building The Network
2 ways displaying the project network
o Depicts the activities as arrows and events in nodes
Activity-on-arrow (AOA) network—usually associated with
PERT
o Create an activity-on-nodes (AON) network by showing each task as a
node and linking the nodes to arrows that show their technological relationship
Usually associated with CPM
Easy to draw—more then 15-20 are more
difficult to draw by hand
Often do not show events but it is simple
enough to add them by showing the event
exactly as if it were an activity but with zero
time duration and no resources
o Avoids lines crossing each other
o Dummy activity—used in situations where 2 activities have the same starting and
finishing nodes or where a single activity connects 2 or more nodes
Require no time or resources
Problem: difficult to distinguish the tasks form one another
1 CGMS450- Chapter 5- Scheduling the Project
Solution: add an extra ending node for one of the tasks and then draw a
dummy task from the new node to the previously shared node—ensures
that the tasks have unique identifies while at the same time maintaining the
correct technological precedence relationship
Finding The Critical Path And Critical Time
We can add information to the nodes in the networks
o Above each node—earliest start time (ES) and
earliest finish time (EF)
o Below each node—latest start time (LS) and
latest finish time (LF)
All activities and thus all paths must be completed to
finish the project
Shortest time for completion of the network is equal to
the longest path through the network
Forward pass ES ad EF is found for each activity by
beginning at the start node and moving from left to right through the network calculating as
we go from node to node
Backward pass to calculate LS and LF—we begin by assuming that we would like to
complete the project within the critical time identified in the forward pass
Calculating Activity Slack
Within limits—if activities on the critical path cannot be delayed without causing the entire
project to be delayed, it follows that activities not on the critical path can be delayed without
delaying the project
Slack or float- the amount of time a noncritical task can be delayed without delaying the
project
o Slack= LS-ES=LF-EF
Any task on the critical path—LS must be the same is EF therefore 0 slack
If it finishes later than EF, the activity will be late, causing the project to delay in the project
o Equally true for its LS and ES
Assumptions
o When calculating slack for a set of activities on a noncritical path, the calculation for
any given activity assumes that no other activity on the same path uses any of the
slack
Once activity s underway, if a predecessor activity uses come if its slack, its
EF is adjusted accordingly and the ES of successor activities must be
corrected
o Critical time for the project is also the projects due date—it is not common for a
project to have “project slack”
Milestones may be added to the display quite easily: add desired milestone event as a node
with zero duration
o ES=EF, LF=LS
o Immediate successors of the activities that result in results
o Common to show actual dates for EF, ES, LS, LF
PM primary attention must be paid to activities on the critical path
Doing It The Easy Way—Microsoft Project (MSP)
See pages 158-160 for steps in creating
networks with MSP
Free slack—the activity can be delayed
without affecting the start time of any
successor activity
Total slack= LF-EF or LS-ES
2 CGMS450- Chapter 5- Scheduling the Project
5.2 Project Uncertainties And Risk Management
Calculating Probabilistic Activity Times
All possible durations for some tasks can be represented by a statistical distribution
Optimistic (a) estimates for a task duration, a, such that the actual duration of the task will
be a or lower less than 1% of the time
Pessimistic (b) estimation duration for the same task such that the actual finish time will
be b or greater less than 1% of the time
Most likely or “normal duration” (m)
Mean of distribution- expected time
o TE=(a+4m+b)/ 6
o Approximation of the mean of a beta distribution
Beta distribution far more flexible than the more common normal distribution
o More accurately reflects actual time and cost outcome
o Calculation—weighted average of 3 time estimate, a,m,b, using weights of 1-4-1
o Standard deviation σ=(b-a)/6
6 is not a weighted average but rather an assumption that the range of the
distribution covers 6 standard deviations (6σ)
o Variance of this distribution is estimated as
Var=σ =((b-a)/6) 2
Range of distribution, b-a, covers 6 standard deviations is important
Assumes that the estimate actually attempted to judge a and b so that 99.7$ of all cases were
greater than a and less than b
o Less then 1% lay outside of these estimates
Estimators are not so uncomfortable making estimates at the 90-95% levels
o a is estimated so that 5-10% of all cases are less than a and 5-10% are greater than
b
o These levels do not cover 6σ instead we use
95% level σ=(b-a)/3.3
90% level σ=(b-a)/2.6
The Probabilistic Network, An Example
Look at page 162-164 for further explanation of the probabilistic network
Once More The Easy Way
MSP can easily handle the probabilistic network—does not do some calculations that we
demonstrated
Calculations can be easily done by excel
The stochastic (synonym for probabilistic) network used for the preceding discussion is
shown as a product of MSP
The Probability Of Completing The Project On Time
E.g. what is the probability that a project will be completed 50 days or less
o Answered with the information available concerning the level of uncertainty for the
various project activities
There is an assumption that should be noted
o Individual variances of the activities in a series of activities may be summed to find
the variance of the set of activities on the path itself—if the various activities in the
set are statistically independent
o E.g. if a is a predecessor of b and if a is early or late, it will not effect the duration of
b
Times when assumption of statistical independence is not met
o Re-estimating the duration of tasks
o This should be done anytime the resources supplied to a project are different from
those presumed then he duration of a project activities was originally estimated
3 CGMS450- Chapter 5- Scheduling the Project
To complete a project by a specific time requires that all the paths in the projects network by
completed by a specified time
o Determining the probability tat a project is completed by a specific time requires
calculating the probability that all paths are finished by a specific time
o
o D= the desired project completion time
o μ= the sum of the E activities on the path being investigated
o σ μ the variance of the path being considered (the sum of the variances of the
activities on the path
Simplify the task calculating the probability that a project is completed by a specific time—
practical purposes it is reasonable to consider only those paths whose expected completion
time have a reasonable chance of being greater than the specified time
Calculate the probability that a project will take longer than any specified t

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