Download projectscheduling

9-1
Chapter 9
Project Scheduling
McGraw-Hill/Irwin
Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
9-2
The Elements of Project Scheduling

Project Definition. Statement of project, goals, and
resources required.

Activity Definitions. Content and requirements of
each activity.

Project Scheduling. Specification of starting and
ending times of all activities.

Project Monitoring. Keeping track of the progress
of the project.
9-3
Network Representation
Projects may be represented as networks with:

Arrows representing activities.

Nodes representing completion of a set of
activities (milestones).

Pseudo activities may be required to satisfy
precedence relationships.
(Figure 9-4 (next) shows a typical project network.)
Correct Network
Representation for Example 9.3
9-4
9-5
Critical Path Method
An analytical tool that provides a schedule that
completes the project in minimum time subject to
the precedence constraints. In addition, CPM
provides:

Starting ending times for each activity

Identification of the critical activities (i.e., the
ones whose delay necessarily delay the project).

Identification of the non-critical activities, and the
amount of slack time available when scheduling
these activities.
9-6
Time Costing Methods

Suppose that projects can be expedited by reducing
the time required for critical activities. Doing so
results in an increase in some costs and a decrease in
others. The goal is to determine the optimal number of
days to schedule the project to minimize total cost.

Assume that there is a linear time/cost relationship for
each activity. (See Figure 9-10).

Since direct costs decline with the project time and
indirect costs increase with the project time, the total
cost curve is a convex function whose minimum
corresponds to the optimal solution (See Figure 9-11).
The CPM Cost-Time
Linear Model
9-7
Optimal Project
Completion Time
9-8
PERT: Project Evaluation and Review
Technique
9-9
PERT is a generalization of CPM to allow for
uncertain activity times. For each activity the user
must specify:
a = minimum completion time
b = maximum completion time
m = most likely completion time
The method assumes each activity time follows a
beta distribution, which can be fit precisely with
specification of a, b, and m.
(See Figure 9-12 for an example with a= 5, b=20 and
m=17).
Probability Density
of Activity Time
9-10
9-11
PERT (continued)
The mean and standard deviation of activity times
are estimated from the following formulas (based
on the beta distribution)
a  4m  b
ba

and  
6
6
In PERT one assumes that the path the with longest
expected completion time is the true critical path
(this is only an approximation, since true critical
path is a random variable).
9-12
PERT (concluded)
One assumes that the expected value of the project
completion time is the sum of the expected values
of the critical activities and variance of the project
completion time is the sum of the variances of the
critical activities. (This is strictly true if the
activity times are independent random variables.)
Finally, one invokes the Central Limit Theorem to
conclude that the total project completion time is a
random variable whose distribution is
approximately normal.
9-13
Resource Considerations

When multiple projects compete for resources (such
as materials and worker time), projects schedules may
be impacted due to insufficient resources.

For example, consider two projects requiring
Resources A and B as pictured Figure 9-20.

One can generate a resource load profile such as the
one in Figure 9-21 to be certain that critical resources
are sufficient to meet project requirements.
Two Projects
Sharing Two Resources
9-14
9-15
Load Profiles for RAM and Permanent
Memory (Refer to Example 9.10)