PROJECT MANAGEMENT
Learning Objectives: At the end of this module you should be able to:
- Break a project down into activities and relationships and determine the project completion time
- Evaluate a project with uncertain activity times
- Analyze a project where activity times can be changed by spending more money
Topics: | TOOLS | | NETWORK MODELS | | STOCHASTIC TIMES | | CRASHING PROJECTS | | LINKS |
Project: a series of related tasks directed towards a major output
Characteristics
|
product volume |
single unit |
|
product variety |
very high |
|
market type |
unique |
|
flow of product |
none |
|
cost per item |
high |
|
flexibility required |
high |
Projects tend to be one-time ventures. There are several aspects to successfully completing projects.
1. Setting project objectives - clear and measurable
2. Selecting project teams - defining skills needed to complete the project and the areas and people affected by the project. Include representatives from areas impacted.
3. Planning the project -define the activities involved in the project, their relationships and the expected time required.
4. Estimating completion time - completion time depends on the activities, their relationships and time and also on the resources available to complete the different activities. All need to be considered to determine how long a project will likely take and how will be needed when. Planning the activity sequence and timing can be accomplished using project analysis methods like CPM/PERT. To accomplish activity planning and resource requirements planning you can use project planning software like Microsoft Project.
Project Components
Activity: the smallest unit of work that consumes time and resources which the project manager can schedule and control
Precedence relationship: a constraint between related activities whereby one activity cannot start until a preceding activity has been completed
Schedule: an allocation of resources to activities, including the setting of activity priorities and activity start and finish times
Project Management Tools
1. Graphical methods
- use bar charts, time lines, or other pictorial methods to illustrate activity durations, activity start and finish times, precedence relationships, milestone events, etc.
examples: bar charts, time lines, Gantt charts
2. Network methods
Network representation of projects: treat the project as a set of related activities that can be displayed visually in a network diagram consisting of nodes (circles) and arcs (arrows) that depict the relationships between activities
examples:
PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method). These have been combined into one method CPM/PERT.
Project Management Using Network Models
Step 1: describe the project in terms of activities, activity times and precedence relationships between activities.
Step 2: diagram the network using nodes (circles) and arcs (arrows)
activity-on-node (AON) network (eg., CPM) puts activities on nodes, with arcs showing precedence relationships This is the method which we will use!
activity-on-arc (AOA) network (eg., PERT) puts activities on arcs, and events (when an activity starts or finishes) on nodes
Step 3: estimate the activity duration times (the length of time required to complete each activity)
Step 4: determine the critical path, the sequence of activities from the project's start to its finish that requires the longest total time to complete (and hence determines the completion date of the project)
Step 5: monitor the progress of the project
Critical Activities - The most important activities are the ones on the critical path because they determine when the project will be completed. However, we also must monitor activities not on the critical path because if one of these activities becomes delayed too much, the critical path will change.
Example 1. Completing Assignment 1
|
Activity |
Activity Name |
Activity Time(hours) |
Immediate Predecessors |
|
Analyze information |
A |
1 |
- |
|
Design Financial Model |
B |
3 |
A |
|
Breakeven Analysis |
C |
1 |
A |
|
Capacity Planning Analysis |
D |
1 |
B |
|
Create Decision Tree |
E |
2 |
B |
|
Sensitivity Analysis |
F |
1 |
E |
|
Write up Memo and results |
G |
3 |
C, D, F |
Calculating Activity Slack
Activity slack: the maximum time that an activity can be delayed without delaying the entire project each activity that is part of ("on") the critical path will have zero slack, because any delay in any activity on the critical path will affect the project completion date.
There are two ways to calculate slack for an activity i, Si
Si = LSi - ESi or Si = LFi - EFi
Earliest start time (ES): the earliest time an activity can start
Earliest finish time (EF): the earliest time an activity can finish (equals the activity's earliest start time plus the activity's duration time)
Calculate ES and EF times by working forward
through the network from beginning to end. 
Latest start time (LS): the latest time an activity can be started without delaying the entire project (equals the activity's latest finish time minus the activity's duration time)
Latest finish time (LF): the latest time an activity can be finished without delaying the entire project (equals the minimum of the latest start times of all activities that start immediately after the activity being considered)
Calculate LS and LF times by working backward
through the network from end to beginning. 
Example 2
|
Activity |
Time (days) |
Immediate Predecessors |
|
A |
2 |
- |
|
B |
4 |
- |
|
C |
8 |
A |
|
D |
3 |
B |
|
E |
5 |
B |
|
F |
2 |
D, E |
|
G |
3 |
C, F |
|
H |
4 |
C |
COST AND RESOURCE CONSIDERATIONS IN PROJECT PLANNING
In many instances you can actually change activity completion times by allocating more resources to it. How can you decide which activities are the best to give more resources to and how much you should give?
"crashing an activity" ("crashing the network"): reducing the time required to complete an activity (in hopes that this will reduce the completion time of the entire project) by assigning additional resources to that activity but reducing the duration time of the activities on the critical path may change the critical path
- normal time (NT): the expected time to complete an activity
- normal cost (NC): the cost to complete the activity in its normal time
- crash time (CT): the shortest possible time in which the activity can be completed
- crash cost (CC): the cost to complete the activity in the shortest possible time (ie., the cost to complete the activity in its crash time)
- crash cost per time period = (CC - NC) / (NT - CT)
APPROACHES TO CRASHING A PROJECT NETWORK
I. "minimum-time schedule" method:
- use the normal times for each activity to determine the critical path
- crash every activity from its normal time to its crash time (minimum duration time) - this gives the minimum-time schedule
If you must make the minimum time but you want to reduce the cost you can uncrash activities that aren't critical, beginning with those that are most expensive.
II. "minimum cost schedule" method:
- use the normal times for each activity to determine the critical path
- crash the activity on the critical path that has the lowest cost to crash per unit time, until: the activity duration time cannot be reduced any further; or another path becomes critical; or the additional costs of crashing outweigh savings from crashing
- repeat step 2 until the cost of continuing to crash the project is greater than the savings from crashing
- when there is more than one critical path, it may be necessary to simultaneously crash an activity on each path if so, select the activities that give the lowest total cost per unit time
Example 3
|
Activity |
Predecessors |
Normal Time |
Crash Time |
Normal Cost |
Crash Cost |
Crash Cost/Week |
|
A |
- |
4 |
3 |
11,000 |
11,700 |
700 |
|
B |
A |
3 |
1 |
7,000 |
9,000 |
1000 |
|
C |
A |
2 |
1 |
5,000 |
5,600 |
600 |
|
D |
B |
4 |
3 |
14,000 |
16,000 |
2,000 |
|
E |
B, C |
1 |
1 |
2,000 |
2,000 |
- |
|
F |
C |
3 |
2 |
8,700 |
10,000 |
1,300 |
|
G |
E, F |
4 |
2 |
23,000 |
28,000 |
2,500 |
|
H |
D |
3 |
2 |
10,000 |
11,200 |
1,200 |
|
Total |
|
|
|
80,700 |
93,500 |
|
Project
Planning with Uncertain Activity Times
Generally the distribution of the activity times is unknown and must be estimated. A typical method of dealing with the situation is to estimate three activity duration times for each activity, optimistic, most likely and pessimistic. Use these estimates to estimate a normally distributed activity time:
most optimistic time (a): the probability of completing the activity in less than a is about 1%
most likely time (m): the estimated average time required to complete the activity
most pessimistic time (b): the probability of taking longer than b is about 1%
The activity time is assumed to be normally distributed with mean, te, and variance as follows:
Expected time: te = ( a + 4m + b ) / 6
Variance: var[te] = [ ( b - a) / 6 ]2
Assumptions:
1. Duration of activities along the critical path determine project completion time
2. Duration time of one activity is independent of duration times of all other activities. Using the Central Limit Theorem, the project completion time is assumed to be normally distributed with the mean equal to the sum of the activity times on the critical path the variance is equal to the sum of the variances of the activities on the critical path.
Once the mean and standard deviation of the critical path are known it is possible to calculate the probability of completing the project in a certain time.
If a project has two critical paths, the critical path with the largest variance should be used to calculate the probability that the project will be completed within a certain time.
Note - Only considering the critical path makes a very strong assumption. In real situations you should be aware of the other paths which may become critical. If an activity that is not on the critical path has a large variance of duration time, it is possible for that activity to become a critical path activity simply through random occurrences.
Project Management Using Excel - and lots of project planning info. at Syd Sytsma's Project Management Course site.