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Project Management Concepts
Sudip R Chandra
Computer Science & Engg.
24th September 2013
1
PROJECT MANAGEMENT CONCEPTS
Project, Defined
A project is an endeavor to accomplish a specific objective through a unique set of interrelated tasks and the effective utilization of resources.
It has a well-defined objective stated in terms of scope, schedule, and costs.
Project s are “born” when a need is identified by the customer – the people or organization willing to provide funds to have the need satisfied.
It is the people (project manager and project team), not the procedures and techniques, that are critical to accomplishing the project objective.
Procedures and techniques are merely tools to help the people do their jobs.
Examples of Projects
Planning a wedding
Designing and implementing a computer system
Hosting a holiday party
Designing and producing a brochure
Executing an environmental clean-up of a contaminated site
Holding a high school reunion
Performing a series of surgeries on an accident victim
Phases of the Project Life Cycle 1 The first phase involves the identification of a
need, problem, or opportunity.
The need and requirements are usually written by the customer into a document called a request for proposal (RFP).
Phases of the Project Life Cycle 2 The second phase is the development of a
proposed solution to the need or problem.
This phase results in the submission of a proposal.
The customer and the winning contractor negotiate and sign a contract (agreement).
Phases of the Project Life Cycle 3 The third phase is performing the project.
Different types of resources are utilized
Results in the accomplishment of the project objective
Phases of the Project Life Cycle 4
The final phase is terminating the project.
Perform close-out activities
Evaluate performance
Invite customer feedback
The Project Management Process
The project management process means planning the work and then working the plan. 7 steps of planning
1. Clearly define the project objective. 2. Divide and subdivide the project scope into major “pieces”3. Define the specific activities for each piece (work package)4. Graphically portray the activities that need to be performed fro each work
package in order to accomplish the project objective – in the form of network diagram.
5. Make a time estimate for how long it will take to complete each activity – resources needed.
6. Make a cost estimate for each activity.7. Calculate a project schedule and budget to determine whether the project can
be completed within the required time, with the allotted founds, and with the available resources.
Project Control Process
Work Breakdown Structure (WBS) The second step is to determine what activities
need to be performed. A list of all the activities must be developed. The WBS is a hierarchical tree of end items to
be accomplished. A work item is one small piece of the project. A work package is the lowest-level item.
Microsoft Project WBS
1. Start new project Turn on the Project Guide
On the Tools menu, click Options, and then click the Interface tab.
In the Project Guide settings section, select the Display Project Guide check box.
Manually set up a new project
Project – Project Information…or View – Turn on project guide…
http://office.microsoft.com/en-us/project/HA102639631033.aspx
Tools - Options
2. Tasks There are four major types of tasks:
1. Summary tasks - contain subtasks and their related properties
2. Subtasks - are smaller tasks that are a part of a summary task
3. Recurring tasks - are tasks that occur at regular intervals
4. Milestones - are tasks that are set to zero duration and are like interim goals in the project
Add tasks
Insert new task
Outlining tasks
Tools – Options… - check “Show project summary task”
Predecessor
Tasks can be linked in four ways
Finish-Start FS Predecessor finishes and the other starts
Start-Finish S-F Task begins at the same time as its predecessor
Finish-Finish F-F Both tasks finish at the same time Start-Start S-S Start of the predecessor determines
when the other starts
Constraints Certain tasks need to be completed
within a certain date. Intermediate deadlines may need to be
specified. By assigning constraints to a task you
can account for scheduling problems. There are about 8 types of constraints
and they come under the flexible or inflexible category.
3. Managing task
Defining a Timeline
Find an optimistic value, D(o), a pessimistic value, D(p) and a realistic value, D(r) .
Then: Duration = ( D(o) + D(p) + 4 x D(r) ) / 6
The importance of tracking progress
Techniques to manage projects effectively: Critical Path Management (CPM) and Program Evaluation and Review Techniques (PERT). They are similar and you will now often find the technique referred to as:
CPM/PERT. The technique involves using network models to trace the links between tasks
and to identify the tasks which are critical to meeting the deadlines. Once you've identified the critical path, any delay on any part of the critical path will cause a delay in the whole project. It is where managers must concentrate their efforts.
In MS Project, you use the Tracking Gantt diagram to show the critical path in red and you can see the PERT diagram by looking at the Network view.
Gantt Chart View – critical path
A Gantt chart is a type of bar chart that illustrates a project schedule.
Critical path: View – More views… - Detail Gant
PERT diagram - Network view
Views Views allow you to examine your project from different
angles based on what information you want displayed at any given time.
You can use a combination of views in the same window at the same time.
Project Views are categorized into two types:
• Task Views (5 types)
• Resource Views (3 types)
Saving a baseline Baseline plan: The original project plans used to track
progress on a project. The baseline plan is a snapshot of your schedule at the
time that you save the baseline and includes information about tasks, resources, and assignments.
You can set a baseline for your project, enabling you to compare your progress with the original plan and any additional baselines you set at milestones throughout your project.
Saving a Baseline
Tools – Tracking – Save Baseline…
http://office.microsoft.com/home/video.aspx?assetid=ES102776241033&width=1024&height=768&startindex=0&CTT=11&Origin=HA102751251033&app=WINPROJ&ver=12
RESOURCES
Manage the project resources:
Resources are of three types: work resources, material resources and cost resources.
Work resources complete tasks by expending time on them. They are usually people and equipment that have been assigned to work on the project (you track their participation by the amount of time they spend).
Material resources are supplies and stocks that are needed to complete a project. You assign material resources by the quantity that you need: two tons of gravel or 300 gallons of diesel fuel, for instance. Because materials aren't measured by time, quantities usually affect only the cost of your project. Materials affect dates or duration only when you have to wait for those materials to become available.
Cost. Cost resources are the new kid on the Project 2007 block, and they're strictly cost; no time, no quantities—just dollars. Expenses, such as travel or fees, increase the project price tag, but they aren't associated with work or material resources.
You must start by identifying the resources available along with their costs.
Resource costs will be multiplied by duration to calculate project costs. You have to open the Resource sheet to specify the project resources
and costs.
• people • equipme
nt • supplies
Fields in the Resource Sheet may be blank or contain different types of information depending on the type of resource. For example, a work resource doesn't have a Material label, and costs are calculated initially as dollars per hour. Material resources have a cost per unit—per pound, gallon, or piece—and the Material label field defines the units. Cost resources receive a value only when you assign them to tasks.
Use the Detail Gantt view to find slack (float)
On the View menu, click More Views. In the Views list, click Detail Gantt, and then
click Apply. On the View menu, point to Table, and then
click Schedule. In the chart portion of the view, slack appears as thin bars to the right of tasks, with slack values adjoining the regular Gantt bars.
To shorten a project schedule
Reduce duration of activities on critical pathMore resourcesChange their scope
Technically Constrained Activity Sequence
Resource-Constrained Planning
Painting Project Showing Needed Resources
Create a budget for your project
Step 1: Create budget resources for your project
Step 2: Assign the budget resources to the project summary task
Step 3: Enter values for the budget resources Step 4: Categorize resource costs according t
o their budget type Step 5: Group resources to view how they co
mpare against the budget
Step 1: Create budget resources for your project
Create Budget-Travel and Budget-Labor on your resource sheet
View – Resource Sheet
Check the check box for Budget
Step 2: Assign the budget resources to the project summary task
Gent chart view – Tools – Options – View Tab – Show project summary task (check box)
Task is added to the top of the project list. Select this task.
Click on Button “Assign Resources” Select the two budget resources you
created earlier and click “Assign”
Step 3: Enter values for the budget resources
View – Resource Usage view Add Budget Cost and Budget Work fields
(columns): Insert – Column – Budget Cost and Budget
WorkAdd values for travel and Labor cost
Add: 15,000 for Budget-Travel and 30,000 for Budget-Labor (Budget Work column)
Step 4: Categorize resource costs according to their budget type
Create custom filed (column) Open Resource Sheet view Tools – Customize – Fields Choose Resource text filed and rename:
Budget Type
Select Option Button: Roll down unless manually entered
Add field to the resource sheet view: Insert – column – choose Budget Type column ( you can now identify your resources as labor or travel
Step 5: Group resources to view how they compare against the budget
Resource Usage view Project – Group by: No Group –
Customize Group By… - Select the Budget Type field
Viewing Project Cost Information
Right click the Select All button and click Cost
Or View – Table: Entry – Cost
Reports
Cost Report: Reports - Reports – Costs – Cash Flow:Edit – Column list
Project Summary report: Reports – Overview – Project Summary
Resource Usage Report
Current Activity Reports
Scheduling
One of the most
important things you
can do is schedule. Also one of the first things you should do! Tools help
Microsoft ProjectOpenProj.org OpenWorkbench.org
Coming up: Planning
Planning The bad news: time flies The good news: you’re the pilot!
You must begin planning immediatelyGiven limited informationPlan anyway and then
revise
Coming up: Creating a plan: Things to know
Creating a plan: Things to know
Scope Context. How does the software to be built fit into a larger system,
product, or business context and what constraints are imposed as a result of the context?
Information objectives. What customer-visible data objects (Chapter 8) are produced as output from the software? What data objects are required for input?
Function and performance. What function does the software perform to transform input data into output? Are any special performance characteristics to be addressed?
Software project scope must be unambiguous and understandable at the management and technical levels.
Coming up: Creating a plan: Things to do
Creating a plan: Things to do
Problem Decomposition: Sometimes called partitioning or problem elaboration
Once scope is defined … It is decomposed into constituent functions It is decomposed into user-visible data objectsor It is decomposed into a set of problem classes
Decomposition process continues until all functions or problem classes have been defined (this won’t be far at the beginning of your project)
Coming up: Create a schedule
Schedule
List of tasksWith datesWith assigned resources (people)With durations With predecessors and successors
How do you get buy-in from the team for a schedule?History Increments
Coming up: Schedule Terms
Schedule Terms
Critical path Sequence of tasks that form the longest path to completion of the
project. Any delay on any of these will make the overall completion date move.
Slack Amount of time a task can be delayed without affecting the overall
completion date. Start slack - amount before task needs to start Finish slack - amount before task needs to finish
Milestone - An import date in the schedule Dependencies - relationship between tasks
Coming up: Schedule Dependencies
Schedule Dependencies FS - Finish to start (most common)
A FS B. B doesn’t start until A is finished Build wall FS Paint wall
FF - Finish to finish A FF B. B doesn’t finish before A is finished Write final chapter FF Complete Index
SS - Start to start A SS B. B doesn’t start until A has started Project funded SS project management activities begin
SF - Start to finish A SF B. B doesn’t finish before A has started Once A starts, B is allowed to finish B=Baby sit a child, A=parent comes home Coming up: Resource
Leveling
Resource Leveling
A process to examine a project for an unbalanced use of people and to resolve over-allocations or conflicts
Happens when multiple tasks are scheduled at the same time for the same person
Solution: Make tasks sequential by introducing “fake” dependencies Split resource usage among tasks (50% on task 1, 50%
on task 2)
Coming up: Auto Resource Leveling
Auto Resource Leveling
Some tools (not Open Project) provide auto resource leveling
Tool automatically ensures no person works over 100% of the time (automatically makes tasks sequential)
Advantageous because this does not introduce “fake” dependencies
Coming up: Gantt Chart
Gantt Chart
Coming up: Finding Critical Path
Finding Critical Path Draw a network diagram of the activities Determine the Early Start (ES) of each
node. Work from beginning node (ES=0) to final node
ES - earliest time the activity can start ES = Max(ESprevNode + DurationPrevNode)
Coming up: Finding Critical Path
A
C
B
ES: 4
ES: 2 10
7 ES: ??
Finding Critical Path Determine the Late Start (LS) of each
node. Work from the final node to the beginning node. The latest time the activity can start without
changing the end date of the projectLS = MIN(LSnext - DurationNode)For the last node LS = ES
Coming up: Example
A
C
B
LS: ?
LS: ? 10
7 LS: 12A
C
B
LS: ?
LS: 13
10
7 LS: 12
Example
Here's the example: Activity Description Predecessor DurationA Product design (None) 5 monthsB Market research (None) 1C Production analysis A 2D Product model A 3E Sales brochure A 2F Cost analysis C 3G Product testing D 4H Sales training B, E 2I Pricing H 1J Project report F, G, I 1Coming up: Example Node
Network
Example Node Network
A
E
D
C
I
G
F
J
B
H Here's the example: Activity Description Predecessor DurationA Product design (None) 5 monthsB Market research(None) 1C Production A 2D Product model A 3E Sales brochure A 2F Cost analysis C 3G Product testing D 4H Sales training B, E 2I Pricing H 1J Project report F, G, I 1
ES:0LS:
ES:5LS:
ES:0LS:
ES:5LS:
ES:5LS:
ES:7LS:
ES:9LS:
ES:8LS:
ES:7LS:
ES:12LS:
Coming up: Example Node Network
ES(H) ES(E)+dur(E) = 5 + 2 = 7 ES(B)+dur(B) = 0 + 1 = 1Maximum = 7 = ES(H)
ES(J) ES(F)+dur(F) = ? ES(G)+dur(G) = ? ES(I) + dur(I) = ?Maximum = ? = ES(J)
Example Node Network
A
E
D
C
I
G
F
J
B
H Here's the example: Activity Description Predecessor DurationA Product design (None) 5 monthsB Market research(None) 1C Production A 2D Product model A 3E Sales brochure A 2F Cost analysis C 3G Product testing D 4H Sales training B, E 2I Pricing H 1J Project report F, G, I 1
ES:0LS:0
ES:5LS:5
ES:0LS:8
ES:5LS:7
ES:5LS:7
ES:7LS:9
ES:9LS:11
ES:8LS:8
ES:7LS:9
ES:12LS:12
Coming up: Example Node Network
LS(F) LS(J)-dur(F) = 12 – 3 = 9
LS(A) = LS(C) – dur(A) = 7 – 5 = 2 LS(D) – dur(A) = 5 – 5 = 0 LS(E) – dur (A) = 7 – 5 = 2Minimum = 0 = LS(A)
Example Node Network
A
E
D
C
I
G
F
J
B
H Here's the example: Activity Description Predecessor DurationA Product design (None) 5 monthsB Market research(None) 1C Production A 2D Product model A 3E Sales brochure A 2F Cost analysis C 3G Product testing D 4H Sales training B, E 2I Pricing H 1J Project report F, G, I 1
ES:0LS:0
ES:5LS:5
ES:0LS:8
ES:5LS:7
ES:5LS:7
ES:7LS:9
ES:9LS:11
ES:8LS:8
ES:7LS:9
ES:12LS:12
Coming up: Game Development In-Class Exercise
Game Development In-Class Exercise
TASK DURATION (days) PREDECESSORs
A Graphics Engine 14
B Sound Engine 5 I
C Music Engine 5 J
D Input Engine 10 A
E Gameplay/general programming
31 B, C, D
F Physics 7 E
G 2D Artwork 14
H 3D Artwork 21 G
I Sound Effects 14
J Music 9
K Level Design 21 F, H
Find the critical path
Coming up: Review Questions
Schedule Example Lets try to schedule this work among our
three developers “John, Mary, Carl”
Coming up: Scheduling Steps
TASK DURATION (days) PREDECESSORs
A Graphics Engine 14
B Sound Engine 5 I
C Music Engine 5 J
D Input Engine 10 A
E Gameplay/general programming
31 B, C, D
F Physics 7 E
G 2D Artwork 14
H 3D Artwork 21 G
I Sound Effects 14
J Music 9
K Level Design 21 F, H
Scheduling Steps
Add in all the tasks (preferably in a hierarchy) Add in all the dependencies Break down large tasks into smaller tasks.
Optimally (in Dan Fleck’s opinion) you want to schedule so the duration of each smallest task is at most 3-5 days
Assign people (resources) to tasks Level your resources
Coming up: Classic Mistakes
Classic Mistakes
Overly optimistic schedule Failing to monitor schedule Failing to update schedule Adding people to a late project Failure to manage expectations of others Leaving out a task
Coming up: Scope Creep
Earned Value Management
How much work you planned to have accomplished by now (in dollars or hours) called the Planned Value
How much you have actually spent by now (in dollars or hours), called Actual Cost
The value, in terms of your baseline budget, of the work accomplished by now (in dollars or hours), called the Earned Value!
Coming up: Earned Value Management
Idea is to link schedule and cost together to monitor both in the same “units” of value
Earned Value Management
Planned value (PV) - the value of all resources needed to meet the project’s objectives Each objective of a project has an associated
planned value Budgeted (cost) at completion (BAC) - The sum
of all the PVs Earned value (EV) - the amount of value
completed at any point during the project Actual Cost (AC) - actual amount of money you
have spent so far. In a perfect project AC and EV are the same.
Coming up: Earned Value Management Example
Earned Value Management Example We’ve budgeted $200 to buy, setup, network
and test a new system Our planned values (PVs) of each task are:
Buy - $50, Setup - $75, network - $50, test - $25 Our BAC is therefore $200
We’ve now completed phase one, and thus our earned value (EV) is now $50.
To do this we spent $60 (our actual cost (AC))
Coming up: Earned Value Management Example
Earned Value Management Example Schedule performance index (SPI)
EV / PV --> 50/50 = 1 (perfect). Our group is on schedule
Cost performance index (CPI) EV / AC --> 50/60 = 0.83 For every dollar spent, I get 83 cents worth of work.
Estimated cost at completion (EAC) BAC / CPI = 200 / 0.83 = $240.96
Schedule Variance (SV) : EV - PV Cost Variance (CV) : EV - AC
Coming up: EVM Example 2 from: http://www.hyperthot.com/pm_cscs.htm
Memorization Hint: Most equations begin with earned value
EVM Example 2 from: http://www.hyperthot.com/pm_cscs.htm
PLANNED VALUE (Budgeted cost of the work scheduled) = 18 + 10 + 16 + 6 = $50
EARNED VALUE (Budgeted cost of the work performed) = 18 + 8 + 14 + 0 = $40
ACTUAL COST (of the work performed) = $45 (Data from Acct. System)
Therefore: Schedule Variance = 40 - 50 = -$10 Schedule Performance Index = 40 / 50 = 0.8 Coming up: What is earned
value?
What is planned value at time X?
What is earned value at time X?
Line is at 16, blue bar ends at 14
Line is at 6
Earned – Planned. Perfect is?
What is earned value?
A. The amount of money you get upon completion of a task
B. The value of an activity C. The value of the work completed by
now in the schedule D. The value of all activities planned to be
completed by now in the schedule
Coming up: Why do you use earned value management?
Why do you use earned value management? A.It is required by my contract B. Measuring value give you more
information than measuring cost or time alone
C. I don’t use it D. It guarantees my project will be done on
time
Coming up: Scheduling Rules of Thumb
Scope Creep
The scope of your project is all the work you initially planned to do.
Scope creep is when your project gets new tasks throughout it’s lifetime without adding more resources to handle new tasks. The scope is “creeping” up…
Scope changes are OK, and really unavoidable… that’s fine. However you must update the resources (time, features or people accordingly)
Coming up: Why would scope changes occur?
Scope
BOO!
Why would scope changes occur? A. You get more money to do more things B. The customer asks you to do something
extra because “it is critical for success” C. A competing product has a feature that
you must have to be competitive D. All of these
Coming up: Which are causes of scope creep?
Scope Change versus Creep
Your company has a $1million dollar contract with a defined scope.
Scope change:
Customer: please add all these requirements, and I’ll increase the contract to $2million dollars
Manager: Certainly!
Scope creep:
Customer: please add all these requirements, and I’ll be really happy.
Manager: Certainly!
Change is good!
Which are causes of scope creep?
A. poor change control B. lack of proper initial identification of what
is required to satisfy project objectives C. a weak project manager D. all of these
Source: Wikipedia: Scope Creep
Coming up: Managing Scope
Managing Scope
How to deal with the inevitable “Scope creep”?
Joint Application Development and prototyping
Formal change approval Defer additional requirements as future
system enhancements
Scope
Coming up: Managing Risk
Managing Risk
Document your risks in a risk management plan1 Description of risk
2 Likelihood of occurrence (0-100%)
3 Impact - 1(low) 5 (high), or cost $20,000
4 Exposure = Impact * Likelihood
5 Mitigation strategy How to lessen the impact of the risk How to lessen the likelihood An action plan if risk occurs
Update and track your risks Communicate your risks to upper managementComing up: Projects get
into trouble when…
Coming up: Common-Sense Approach to Projects
Projects get into trouble when…
Software people don’t understand their customer’s needs. The product scope is poorly defined. Changes are managed poorly. The chosen technology changes. Business needs change [or are ill-defined]. Deadlines are unrealistic. Users are resistant. Sponsorship is lost [or was never properly obtained]. The project team lacks people with appropriate skills. Managers [and practitioners] avoid best practices and lessons
learned.
Coming up: References
Common-Sense Approach to Projects Start on the right foot. This is accomplished by working hard (very hard) to
understand the problem that is to be solved and then setting realistic objectives and expectations.
Maintain momentum. The project manager must provide incentives to keep turnover of personnel to an absolute minimum, the team should emphasize quality in every task it performs, and senior management should do everything possible to stay out of the team’s way.
Track progress. For a software project, progress is tracked as work products (e.g., models, source code, sets of test cases) are produced and approved (using formal technical reviews) as part of a quality assurance activity.
Make smart decisions. In essence, the decisions of the project manager and the software team should be to “keep it simple.”
Conduct a postmortem analysis. Establish a consistent mechanism for extracting lessons learned for each project.
References
www.projity.com Wikipedia: Project Management Pressman R., Software Engineering A Practical Approach, Ch 21 Pressman R., Software Engineering A Practical Approach, Slides for Ch 21 Kazman R., The CIO, People Issues, Project & Change Management,
kazman.shidler.hawaii.edu/619ch12.ppt Pratt M, Earned Value Management,
http://www.computerworld.com/action/article.do?command=viewArticleBasic&articleId=110065&intsrc=article_pots_bot
End of presentation
Next week
Review student essays (due in a week) Homework 6 due
Please submit sceenshots (in a word document or pdf) to blackboard
Testing
Analyzing Cost-Time Trade-Offs
There are always cost-time trade-offs in project management. You can completing a project early by hiring more
workers or running extra shifts. There are often penalties if projects extend
beyond some specific date, and a bonus may be provided for early completion.
Crashing a project means expediting some activities to reduce overall project completion time and total project costs.
Cost to Crash
To assess the benefit of crashing certain activities, either from a cost or a schedule perspective, the project manager needs to know the following times and costs.
Normal time (NT) is the time necessary to complete and activity under normal conditions.
Normal cost (NC) is the activity cost associated with the normal time.
Crash time (CT) is the shortest possible time to complete an activity.
Crash cost (CC) is the activity cost associated with the crash time.
Cost to Crash per Period
The Cost to Crash per Time Period =
CC − NC
NT − CT
Crash Cost − Normal Cost
Normal Time − Crash Time
Linear cost assumption
8000 —
7000 —
6000 —
5000 —
4000 —
3000 —
0 —
Dire
ct c
ost (
dolla
rs)
| | | | | |5 6 7 8 9 10 11
Time (weeks)
Crash cost (CC)
Normal cost (NC)
(Crash time) (Normal time)
Estimated costs for a 2-week reduction, from 10 weeks to 8 weeks
5200
Cost-Time Relationships in Cost Analysis
The objective of cost analysis is to determine the project schedule that minimizes total project costs.
A minimum-cost schedule is determined by starting with the normal time schedule and crashing activities along the critical path in such a way that the costs of crashing do not exceed the savings in indirect and penalty costs.
Minimizing CostsMinimizing Costs
Use these steps to determine the minimum cost schedule:
1. Determine the project’s critical path(s).2. Find the activity or activities on the critical path(s) with
the lowest cost of crashing per time unit.3. Reduce the time for this activity until…
a. It cannot be further reduced orb. Until another path becomes critical, orc. The increase in direct costs exceeds the savings that result
from shortening the project (which lowers indirect costs & penalties).
4. Repeat this procedure until the increase in direct costs is larger than the savings generated by shortening the project.
Minimum Cost ScheduleMinimum Cost Schedule
Regular & Crash Times & Cost to Crash
Activity Regular Time Crash TimeTotal Costto Crash
Cost Per Unit of Crash Time
$ A* 2 1 $1,000
$ B* 4 2 $ 500
$ C* 2 2 C
$ D* 1 1 C
$ E 3 1 $ 200
$ F* 2 2 C
$ G* 1 1 C
$ H* 12 8 $ 800
$ I* 8 5 $1,200
$ J 6 6 C
$ K 5 3 $ 600
$ L*TOTAL
* Activities on critical path
3 3 C$4,300
START A2
B4
C2
D1
F2
G1
H12
J6
I8
K5
L3
ENDE3
Network for a Software Purchasing Project using Normal Times
IF ALL ACTIVITIES ARE CRASHED
START
A1
B2
C2
D1
F2
G1
H8
J6
I5
K3
L3
ENDE1
(1,5,4)
(8,8,0)(6,6,0)(5,5,0)(0,0,0) (1,1,0) (3,3,0)
(26)
(23,23,0)
(17,18,1)
(17,17,0)
(9,20,11)
(9,9,0)
*What is the minimum amount of time to complete the project?*What is the additional cost involved in achieving this reduction in time?
START
A2
B4
C2
D1
F2
G1
H12
J6
I8
K5
L3
END
E3
What is the minimum cost to achieve minimum time schedule for project
Activity Regular Time Crash TimeTotal Costto Crash
Cost Per Unit of Crash
Time
$ A 2 1 $1,000 $1,000
$ B 4 2 $ 500 $ 250
$ C 2 2 C C
$ D 1 1 C C
$ E 3 1 $ 200 $ 100
$ F 2 2 C C
$ G 1 1 C C
$ H 12 8 $ 800 $ 200
$ I 8 5 $1,200 $ 400
$ J 6 6 C C
$ K 5 3 $ 600 $ 300
$ L 3 3 C$4,300
C
START
A2
B4
C2
D1
F2
G1
H12
J6
I8
K5
L3
ENDE3
What is the minimum cost to achieve minimum time schedule for project
Activity Regular Time Crash TimeTotal Costto Crash
Cost Per Unit of Crash
Time
$ A 2 1 $1,000 $1,000
$ B 4 2 $ 500 $ 250
$ C 2 2 C C
1 1 C C
$ E 3 1 $ 200 $ 100
$ F 2 2 C C
$ G 1 1 C C
$ H 12 8 $ 800 $ 200
$ I 8 5 $1,200 $ 400
$ J 6 6 C C
$ K 5 3 $ 600 $ 300
$ L 3 3 C$4,300
C
START
A2
B4
C2
D1
F2
G1
H12
J6
I8
K5
L3
ENDE3
What is the minimum cost to reduce project time to 30 months
Activity Regular Time Crash TimeTotal Costto Crash
Cost Per Unit of Crash
Time
$ A 2 1 $1,000 $1,000
$ B 4 2 $ 500 $ 250
$ C 2 2 C C
1 1 C C
$ E 3 1 $ 200 $ 100
$ F 2 2 C C
$ G 1 1 C C
$ H 12 8 $ 800 $ 200
$ I 8 5 $1,200 $ 400
$ J 6 6 C C
$ K 5 3 $ 600 $ 300
$ L 3 3 C$4,300
C
START
A2
B4
C2
D1
F2
G1
H12
J6
I8
K5
L3
ENDE3
What is the optimal schedule if I incur a penalty of $280 for each month above the absolute minimum project time of 26 months?
Activity Regular Time Crash TimeTotal Costto Crash
Cost Per Unit of Crash
Time
$ A 2 1 $1,000 $1,000
$ B 4 2 $ 500 $ 250
$ C 2 2 C C
1 1 C C
$ E 3 1 $ 200 $ 100
$ F 2 2 C C
$ G 1 1 C C
$ H 12 8 $ 800 $ 200
$ I 8 5 $1,200 $ 400
$ J 6 6 C C
$ K 5 3 $ 600 $ 300
$ L 3 3 C$4,300
C
© 2007 Pearson Education
Calculating total CostCalculating total Cost Adding Adding Direct, Penalty & Overhead CostsDirect, Penalty & Overhead Costs
The overhead (indirect) costs are $200 per dayThere is a penalty of $100/day for completing project in more than 12 days
Network Diagram
© 2007 Pearson Education
Total Cost ProblemTotal Cost Problem
Assessing Risks
Risk is a measure of the probability and consequence of not reaching a defined project goal.
A major responsibility of the project manager at the start of a project is to develop a risk-management plan.
A Risk-Management Plan identifies the key risks to a project’s success and prescribes ways to circumvent them.
Probabilistic Probabilistic Time EstimatesTime Estimates
MeanMeanmmaa bb TimeTime
Pro
babi
lity
Pro
babi
lity
Beta Distribution
PessimisticOptimistic
TimeTime
Pro
babi
lity
Pro
babi
lity
Normal Normal DistributionDistribution
MeanMeanaa bbmm
33 33
Area under Area under curve curve between a between a and b is and b is 99.74%99.74%
Probabilistic Probabilistic Time EstimatesTime Estimates
te = a + 4m + b
6
Mean
22 = = ( )
bb – – aa
66
22
VarianceVariance
Probabilistic Time EstimatesProbabilistic Time Estimates
Calculating Means and Variances for a Beta Distribution
Where:
a is the Optimistic estimate
b is the pessimistic estimate
m is the most likely estimate
Optimistic Likely PessimisticActivity (a) (m) (b)
Time Estimates (wk)
A 11 12 13
B 7 8 15
C 5 10 15
D 8 9 16
E 14 25 30
F 6 9 18
G 25 36 41
H 35 40 45
I 10 13 28
J 1 2 15
K 5 6 7
St. John’s HospitalSt. John’s HospitalProbabilistic Time EstimatesProbabilistic Time Estimates
A F
I
C G Finish
D
E
HB J
K
Start
Activity BMost
Optimistic Likely Pessimistic(a) (m) (b)7 8 15
A F
I
C G Finish
D
E
HB J
K
Start
St. John’s HospitalSt. John’s HospitalProbabilistic Time EstimatesProbabilistic Time Estimates
te = = 9 weeks7 + 4(8) + 15
62 = = 1.78( )15 - 7
6
2
Calculating Means and Variances
Optimistic Likely Pessimistic Expected VarianceActivity (a) (m) (b) Time (te ) (2 )
Time Estimates (wk) Activity Statistics
A 11 12 13 12 0.11B 7 8 15 9 1.78C 5 10 15 10 2.78D 8 9 16 10 1.78E 14 25 30 24 7.11F 6 9 18 10 4.00G 25 36 41 35 7.11H 35 40 45 40 2.78I 10 13 28 15 9.00J 1 2 15 4 5.44K 5 6 7 6 0.11
St. John’s HospitalSt. John’s HospitalProbabilistic Time EstimatesProbabilistic Time Estimates
© 2007 Pearson Education
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
FinishStart
A
12
F
10
0 9
9 33
9 19 19 59
22 5712 22
59 63
12 27
12 22 63 690 12
48 63
53 63
59 63
24 59
19 59
35 59
14 24
9 19
2 14
0 9
63 69
Earliest start time Earliest finish time
Latest start time Latest finish time
2 = (variances of activities) z = T – TE
2
2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89
z =72 – 69
11.89
What is the Probability of finishing the project in 72 weeks?Given that: Critical Path = B - D - H - J - K
T = 72 Weeks TE = 69 Weeks
St. John’s HospitalSt. John’s HospitalAnalyzing ProbabilitiesAnalyzing Probabilities
From Normal Distribution appendix Pz = .8078 .81
= .87
.00 .01 .02 .03 .04 .05 .06 .07 .08 .09
.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359
.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .5753
.2 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6141
.3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517
.4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879
.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224
.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549
.7 .7580 .7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852
.8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133
.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389
1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621
1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830
1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015
1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177
1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319
1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441
1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545
1.7 .9554 .9564 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633
1.8 .9641 .9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .9706
1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767
2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817
2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857
2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890
2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 .9916
2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936
2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952
2.6 .9953 .9955 .9956 .9957 .9959 .9960 .9961 .9962 .9963 .9964
2.7 .9965 .9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974
2.8 .9974 .9975 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .9981
2.9 .9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986
3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990
3.1 .9990 .9991 .9991 .9991 .9992 .9992 .9992 .9992 .9993 .9993
3.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9995 .9995 .9995
3.3 .9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .9997
3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998
NORMAL DISTRIBUTION TABLE
z0 Ğ
Project duration (weeks)Project duration (weeks)6969 7272
Normal Normal distribution: distribution: Mean = 69 Mean = 69 weeks; weeks; = 3.45 weeks = 3.45 weeks Probability Probability
of of exceeding exceeding 72 weeks is 72 weeks is 0.1922 0.1922
St. John’s HospitalSt. John’s HospitalProbability of Completing Project On TimeProbability of Completing Project On Time
Probability Probability of meeting of meeting the the schedule schedule is 0.8078is 0.8078
Length of Length of critical critical pathpath
Optimistic Likely Pessimistic Expected VarianceActivity (a) (m) (b) Time (te ) (2 )
Time Estimates (Months) Activity Statistics
A 1 2 3B 3 4 6C 2 2 2D 1 1 1E 1 3 5F 1 2 3G 1 1 1H 8 12 14I 7 8 10J 5 6 7K 4 5 6L 2 3 6
Software Purchasing ProjectSoftware Purchasing ProjectProbabilistic Time EstimatesProbabilistic Time Estimates
START A2
B 4.17
C2
D1
F2
G1
H11.67
J6
I8.17
K5
L3.33
ENDE3
Network for a Software Purchasing Project using the Mean Times
Critical Path: A—B—C—D—F—G—H—I—LExpected Time to complete the project:
2+4.17+2+1+2+1+11.67+8.17+3.33 = 35.33
What is the probability in finishing in less than 37 months?
What is the probability in finishing in less than 31 months?
Copyright 2009 John Wiley & Sons, Inc. 9-133
Lecture Outline
Project Planning Project Scheduling Project Control CPM/PERT Probabilistic Activity Times Project Crashing and Time-Cost
Trade-off
Copyright 2009 John Wiley & Sons, Inc. 9-134
What is a Project? Project
unique, one-time operational activity or effort Examples
constructing houses, factories, shopping malls, athletic stadiums or arenas
developing military weapons systems, aircrafts, new ships launching satellite systems constructing oil pipelines developing and implementing new computer systems planning concert, football games, or basketball tournaments introducing new products into market
Copyright 2009 John Wiley & Sons, Inc. 9-135
Project Elements
Objective Scope Contract requirements Schedules Resources Personnel Control Risk and problem analysis
Copyright 2009 John Wiley & Sons, Inc. 9-136
Project Management Process
Project planning Project scheduling Project control Project team
made up of individuals from various areas and departments within a company
Matrix organization a team structure with members from functional areas,
depending on skills required Project Manager
most important member of project team
Copyright 2009 John Wiley & Sons, Inc. 9-137
Project Scope
Scope statementa document that provides an understanding,
justification, and expected result of a project Statement of work
written description of objectives of a project Work breakdown structure
breaks down a project into components, subcomponents, activities, and tasks
Copyright 2009 John Wiley & Sons, Inc. 9-138
Work Breakdown Structure for Computer Order Processing System ProjectWork Breakdown Structure for Computer Order Processing System Project
Copyright 2009 John Wiley & Sons, Inc. 9-139
Organizational Breakdown Structure a chart that shows which organizational units are
responsible for work items Responsibility Assignment Matrix
shows who is responsible for work in a project
Copyright 2009 John Wiley & Sons, Inc. 9-140
Project Scheduling
StepsDefine activitiesSequence activitiesEstimate timeDevelop schedule
TechniquesGantt chartCPMPERTMicrosoft Project
Copyright 2009 John Wiley & Sons, Inc. 9-141
Gantt Chart
Graph or bar chart with a bar for each project activity that shows passage of time
Provides visual display of project schedule
Slack amount of time an activity can be delayed
without delaying the project
Copyright 2009 John Wiley & Sons, Inc. 9-142
| | | | |Activity
Design house and obtain financing
Lay foundation
Order and receive materials
Build house
Select paint
Select carpet
Finish work
00 22 44 66 88 1010MonthMonth
MonthMonth11 33 55 77 99
Example of Gantt Chart
Copyright 2009 John Wiley & Sons, Inc. 9-143
Project Control
Time management Cost management Quality management Performance management
Earned Value Analysis a standard procedure for numerically measuring a
project’s progress, forecasting its completion date and cost and measuring schedule and budget variation
Communication Enterprise project management
Copyright 2009 John Wiley & Sons, Inc. 9-144
CPM/PERT
Critical Path Method (CPM) DuPont & Remington-Rand (1956) Deterministic task times Activity-on-node network construction
Project Evaluation and Review Technique (PERT) US Navy, Booz, Allen & Hamilton Multiple task time estimates Activity-on-arrow network construction
Copyright 2009 John Wiley & Sons, Inc. 9-145
Project Network
Activity-on-node (AON) nodes represent activities,
and arrows show precedence relationships
Activity-on-arrow (AOA) arrows represent activities
and nodes are events for points in time
Event completion or beginning of
an activity in a project
1 32
BranchBranch
NodeNode
Copyright 2009 John Wiley & Sons, Inc. 9-146
AOA Project Network for a House
3322 00
11
33
11 1111
1 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
Copyright 2009 John Wiley & Sons, Inc. 9-147
Concurrent ActivitiesConcurrent Activities
2 3
Lay foundationLay foundation
Order materialOrder material
(a)(a) Incorrect precedence Incorrect precedence relationshiprelationship
(b)(b) Correct precedence Correct precedence relationshiprelationship
3
42
DummyDummyLay Lay foundationfoundation
Order materialOrder material
11
22 00
Copyright 2009 John Wiley & Sons, Inc. 9-148
AON Network for House Building Project
13
22
43
31 5
1
61
71Start
Design house and obtain financing
Order and receive materials Select paint
Select carpet
Lay foundations Build house
Finish work
Copyright 2009 John Wiley & Sons, Inc. 9-149
13
22
43
31 5
1
61
71Start
Critical Path
Critical pathCritical path Longest path Longest path
through a networkthrough a network Minimum project Minimum project
completion timecompletion time
A:A: 1-2-4-71-2-4-73 + 2 + 3 + 1 = 9 months 3 + 2 + 3 + 1 = 9 months
B:B: 1-2-5-6-71-2-5-6-73 + 2 + 1 + 1 + 1 = 8 months3 + 2 + 1 + 1 + 1 = 8 months
C:C: 1-3-4-71-3-4-73 + 1 + 3 + 1 = 8 months3 + 1 + 3 + 1 = 8 months
D:D: 1-3-5-6-71-3-5-6-73 + 1 + 1 + 1 + 1 = 7 months3 + 1 + 1 + 1 + 1 = 7 months
Copyright 2009 John Wiley & Sons, Inc. 9-150
Activity Start Times
13
22
43
31 5
1
61
71Start
Start at 3 monthsStart at 6 months
Start at 5 months
Finish at 9 months
Finish
Copyright 2009 John Wiley & Sons, Inc. 9-151
Mode Configuration
1 0 3
3 0 3
Activity number
Activity duration
Earliest start
Latest start
Earliest finish
Latest finish
Copyright 2009 John Wiley & Sons, Inc. 9-152
Forward Pass
Start at the beginning of CPM/PERT network to determine the earliest activity times
Earliest Start Time (ES) earliest time an activity can start ES = maximum EF of immediate predecessors
Earliest finish time (EF) earliest time an activity can finish earliest start time plus activity time
EF= ES + t
Copyright 2009 John Wiley & Sons, Inc. 9-153
Earliest Activity Start and Finish Times
1 0 3
1
2 3 5
2
3 3 4
1 5 5 6
1
4 5 8
3
6 6 7
1
7 8 9
1
Start
Design house and obtain financing
Select pain
Lay foundations
Select carpet
Build house
Finish work
Order and receive materials
Copyright 2009 John Wiley & Sons, Inc. 9-154
Backward Pass
Determines latest activity times by starting at the end of CPM/PERT network and working forward
Latest Start Time (LS) Latest time an activity can start without delaying
critical path time
LS= LF - t Latest finish time (LF)
latest time an activity can be completed without delaying critical path time
LS = minimum LS of immediate predecessors
Copyright 2009 John Wiley & Sons, Inc. 9-155
Latest Activity Start and Finish Times
1 0 3
1 0 3
2 3 5
2 3 5
3 3 4
1 4 5 5 5 6
1 6 7
4 5 8
3 5 8
6 6 7
1 7 8
7 8 9
1 8 9
Start
Design house and obtain financing
Select pain
Lay foundations
Select carpet
Build house
Finish work
Order and receive materials
Copyright 2009 John Wiley & Sons, Inc. 9-156
* Critical Path* Critical Path
00009999999988888888*7*7*7*7
111177778888666677776666
111166667777555566665555
00008888888855555555*4*4*4*4
111144445555333344443333
00005555555533333333*2*2*2*2
00003333333300000000*1*1*1*1
Slack SSlack SEFEFLFLFESESLSLSActivityActivity
Activity Slack
Copyright 2006 John Wiley & Sons, Inc. 9-157
Probabilistic Time Estimates
Beta distribution a probability distribution traditionally used in
CPM/PERT
aa = optimistic estimate = optimistic estimatemm = most likely time estimate = most likely time estimateb b = pessimistic time estimate= pessimistic time estimate
wherewhere
Mean (expected time):Mean (expected time): tt = =aa + 4 + 4mm + + bb66
Variance:Variance: 22 = =bb - - aa66
22
Copyright 2006 John Wiley & Sons, Inc. 9-158
Examples of Beta DistributionsExamples of Beta Distributions
PP(t
ime)
(tim
e)
PP(t
ime)
(tim
e)
PP(t
ime)
(tim
e)
TimeTimeaa mmtt bbaa mm tt bb
m m = = tt
TimeTime
TimeTimebbaa
Copyright 2006 John Wiley & Sons, Inc. 9-159
Project Network with Probabilistic Time Estimates: Example
Start Finish23,6,9
31,3,5
16,8,10
52,3,4
63,4,5
42,4,12
72,2,2
83,7,11
92,4,6
10
1,4,7
11
1,10,13
Equipment installation
System development
Position recruiting
Equipment testing and modification
Manual testing
Job Training
Orientation
System training
System testing
Final debugging
System changeover
Copyright 2006 John Wiley & Sons, Inc. 9-160
Activity Time EstimatesActivity Time Estimates
1 1 66 88 1010 88 0.440.44 22 33 66 99 66 1.001.00 33 11 33 55 33 0.440.44 44 22 44 1212 55 2.782.78 55 22 33 44 33 0.110.11 66 33 44 55 44 0.110.11 77 22 22 22 22 0.000.00 88 33 77 1111 77 1.781.78 99 22 44 66 44 0.440.441010 11 44 77 44 1.001.001111 11 1010 1313 99 4.004.00
TIME ESTIMATES (WKS)TIME ESTIMATES (WKS) MEAN TIMEMEAN TIME VARIANCEVARIANCE
ACTIVITYACTIVITY aa mm bb tt бб22
Copyright 2006 John Wiley & Sons, Inc. 9-161
Activity Early, Late Times, Activity Early, Late Times, and Slackand Slack
ACTIVITYACTIVITY tt бб ESES EFEF LSLS LFLF SS
11 88 0.440.44 00 88 11 99 11 22 66 1.001.00 00 66 00 66 00 33 33 0.440.44 00 33 22 55 22 4 4 55 2.782.78 88 1313 1616 2121 88 5 5 33 0.110.11 66 99 66 99 00 66 44 0.110.11 33 77 55 99 22 77 22 0.000.00 33 55 1414 1616 1111 88 77 1.781.78 99 1616 99 1616 00 99 44 0.440.44 99 1313 1212 1616 331010 44 1.001.00 1313 1717 2121 2525 881111 99 4.004.00 1616 2525 1616 2525 00
Copyright 2006 John Wiley & Sons, Inc. 9-162
Start Finish
1 0 8
8 1 9
3 0 3
3 2 5
4 8 13
5 16 21
6 3 7
4 5 9
7 3 5
2 14 16
9 9 13
4 12 16
10 13 17
1 0 3
2 0 6
6 0 6 5 6 9
3 6 9
8 9 16
7 9 16
11 16 25
9 16 25
Critical Path
Earliest, Latest, and Slack
Copyright 2006 John Wiley & Sons, Inc. 9-163
2 = б22 + б5
2 + б82 + б11
2
= 1.00 + 0.11 + 1.78 + 4.00
= 6.89 weeks
Total project variance
Copyright 2006 John Wiley & Sons, Inc. 9-164
Probabilistic Network Analysis
Determine probability that project is Determine probability that project is completed within specified timecompleted within specified time
wherewhere == ttpp = project mean time = project mean time
== project standard deviationproject standard deviationx =x = proposed project timeproposed project timeZ =Z = number of standard deviations xnumber of standard deviations x
is from meanis from mean
ZZ = =xx - -
Copyright 2006 John Wiley & Sons, Inc. 9-165
Normal Distribution Of Project Time
= = ttpp TimeTimexx
Z
ProbabilityProbability
Copyright 2006 John Wiley & Sons, Inc. 9-166
Southern Textile Example
What is the probability that the project is completed What is the probability that the project is completed within 30 weeks?within 30 weeks?
22 = 6.89 weeks= 6.89 weeks
= 6.89= 6.89
= 2.62 weeks= 2.62 weeks
ZZ ==
==
= 1.91= 1.91
xx - - 30 - 2530 - 252.622.62
From Table A.1, (appendix A) a From Table A.1, (appendix A) a ZZ score of 1.91 corresponds to a score of 1.91 corresponds to a probability of 0.4719. Thus probability of 0.4719. Thus PP(30) = 0.4719 + 0.5000 = 0.9719(30) = 0.4719 + 0.5000 = 0.9719
= 25= 25 Time (weeks)Time (weeks)xx = 30 = 30
PP((xx 30 weeks) 30 weeks)
Copyright 2006 John Wiley & Sons, Inc. 9-167
Southern Textile Example
= 25= 25 Time Time (weeks)(weeks)
xx = 22 = 22
PP((xx 22 weeks) 22 weeks)
What is the probability that the project is completed What is the probability that the project is completed within 22 weeks?within 22 weeks?
22 = 6.89 weeks= 6.89 weeks
= 6.89= 6.89
= 2.62 weeks= 2.62 weeks
ZZ ==
==
= -1.14= -1.14
xx - - 22 - 2522 - 252.622.62
From Table A.1 (appendix A) a From Table A.1 (appendix A) a ZZ score of -1.14 corresponds to a score of -1.14 corresponds to a probability of 0.3729. Thus probability of 0.3729. Thus PP(22) = 0.5000 - 0.3729 = 0.1271(22) = 0.5000 - 0.3729 = 0.1271
Copyright 2006 John Wiley & Sons, Inc. 9-168
Project Crashing Crashing
reducing project time by expending additional resources
Crash time an amount of time an activity is reduced
Crash cost cost of reducing activity time
Goal reduce project duration at minimum cost
Copyright 2006 John Wiley & Sons, Inc. 9-169
112
28
412
34 5
4
64
74
Project Crashing: Example
Copyright 2006 John Wiley & Sons, Inc. 9-170
Project Crashing: Example (cont.)$7,000 –
$6,000 –
$5,000 –
$4,000 –
$3,000 –
$2,000 –
$1,000 –
–| | | | | | |
0 2 4 6 8 10 12 14 Weeks
Normal activity
Normal time
Normal cost
Crash time
Crashed activity
Crash cost
Slope = crash cost per week
Copyright 2006 John Wiley & Sons, Inc. 9-171
Normal Activity and Crash Data
TOTALTOTALNORMALNORMAL CRASHCRASH ALLOWABLEALLOWABLE CRASHCRASH
TIMETIME TIMETIME NORMALNORMAL CRASHCRASH CRASH TIMECRASH TIME COST PERCOST PERACTIVITYACTIVITY (WEEKS)(WEEKS) (WEEKS)(WEEKS) COSTCOST COSTCOST (WEEKS)(WEEKS) WEEKWEEK
11 1212 77 $3,000$3,000 $5,000$5,000 55 $400$400
22 88 55 2,0002,000 3,5003,500 33 500500
33 44 33 4,0004,000 7,0007,000 11 3,0003,000
44 1212 99 50,00050,000 71,00071,000 33 7,0007,000
55 44 11 500500 1,1001,100 33 200200
66 44 11 500500 1,1001,100 33 200200
77 44 33 15,00015,000 22,00022,000 11 7,0007,000
$75,000$75,000 $110,700$110,700
Copyright 2006 John Wiley & Sons, Inc. 9-172
112
28
34 5
4
64
74
$400
$500
$3000
$7000
$200$200
$70012
4Project Duration:36 weeks
FROM …
17
28
34 5
4
64
74
$400
$500
$3000
$7000
$200$200
$70012
4
Project Duration:31 weeksAdditional Cost:$2000
TO…
Copyright 2009 John Wiley & Sons, Inc. 9-173
Crashing costs increase as project Crashing costs increase as project duration decreasesduration decreases
Indirect costs increase as project Indirect costs increase as project duration increasesduration increases
Reduce project length as long as Reduce project length as long as crashing costs are less than indirect crashing costs are less than indirect costscosts
Time-Cost Relationship
Copyright 2009 John Wiley & Sons, Inc. 9-174
Time-Cost TradeoffC
ost
($)
Co
st (
$)
Project durationProject duration
CrashingCrashing TimeTime
Minimum cost = optimal project timeMinimum cost = optimal project timeTotal project costTotal project cost
Indirect costIndirect cost
Direct costDirect cost
■ The Elements of Project Management
■ CPM/PERT Networks
■ Probabilistic Activity Times
■ Microsoft Project
■ Project Crashing and Time-Cost Trade-Off
■ Formulating the CPM/PERT Network as a Linear Programming Model
Chapter Topics
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
■ Network representation is useful for project analysis.
■ Networks show how project activities are organized and are used to determine time duration of projects.
■ Network techniques used are:
▪ CPM (Critical Path Method)
▪ PERT (Project Evaluation and Review Technique)
■ Developed independently during late 1950’s.
Overview
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Elements of Project Management
■ Management is generally perceived as concerned with planning, organizing, and control of an ongoing process or activity.
■ Project Management is concerned with control of an activity for a relatively short period of time after which management effort ends.
■ Primary elements of Project Management to be discussed: Project Planning Project Team Project Control
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Elements of Project ManagementProject Planning
■ Objectives
■ Project Scope
■ Contract Requirements
■ Schedules
■ Resources
■ Personnel
■ Control
■ Risk and Problem AnalysisCopyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
■ Project team typically consists of a group of individuals from various areas in an organization and often includes outside consultants.
■ Members of engineering staff often assigned to project work.
■ Project team may include workers.
■ Most important member of project team is the project manager.
■ Project manager is often under great pressure because of uncertainty inherent in project activities and possibility of failure. Potential rewards, however, can be substantial.
■ Project manager must be able to coordinate various skills of team members into a single focused effort.
Elements of Project ManagementThe Project Team
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Figure 8.1 The project management process
The Project Management Process
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Elements of Project ManagementScope Statement
■ Document providing common understanding of project.
■ Justification describing the factors giving rise to need for project.
■ Expected results and what constitutes success.
■ List of necessary documents and planning reports.
■ Statement of work (SOW) - a planning document for individuals, team members, groups, departments, subcontractors and suppliers, describing what are required for successful completion on time.
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Elements of Project ManagementWork Breakdown Structure (WBS) (1 of 2)
■ WBS breaks down project into major components (modules).
■ Modules are further broken down into activities and, finally, into individual tasks.
■ Identifies activities, tasks, resource requirements and relationships between modules and activities.
■ Helps avoid duplication of effort.
■ Basis for project development, management , schedule, resources and modifications.
■ Approaches for WBS development:1. Top down process 2. Brainstorm entire projectCopyright © 2010 Pearson Education,
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Figure 8.2 WBS for Computer Order-processing System Project
Elements of Project ManagementWork Breakdown Structure (2 of 2)
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Elements of Project ManagementResponsibility Assignment Matrix (1 of 2)
■ Project manager assigns work elements to organizational units, departments, groups, individuals or subcontractors.
■ Uses an organizational breakdown structure (OBS).
■ OBS is a table or a chart showing which organizational units are responsible for work items.
■ OBS leads to the responsibility assignment matrix (RAM)
■ RAM shows who is responsible for doing the necessary work in the project
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Elements of Project ManagementResponsibility Assignment Matrix (2 of 2)
Figure 8.3 A responsibility assignment matrix
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Elements of Project ManagementProject Scheduling■ Project Schedule evolves from planning documents,
with focus on timely completion.
■ Critical element in project management – source of most conflicts and problems.
■ Schedule development steps:1. Define activities, 2. Sequence
activities,3. Estimate activity times, 4. Construct
schedule.
■ Gantt chart and CPM/PERT techniques can be useful.
■ Computer software packages available, e.g. Microsoft Project.
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Elements of Project ManagementGantt Chart (1 of 2)
■ Popular, traditional technique, also known as a bar chart -developed by Henry Gantt (1914).
■ Direct precursor of CPM/PERT for monitoring work progress.
■ A visual display of project schedule showing activity start and finish times and where extra time is available.
■ Suitable for projects with few activities and precedence relationships.
■ Drawback: precedence relationships are not always discernible.
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Elements of Project ManagementGantt Chart (2 of 2)
Figure 8.4 A Gantt chart
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Elements of Project ManagementProject Control■ Process of ensuring progress toward successful
completion.
■ Monitoring project to minimize deviations from project plan and schedule.
■ Corrective actions necessary if deviations occur.
■ Key elements of project control Time management Cost management Performance management Earned value analysis.Copyright © 2010 Pearson Education,
Inc. Publishing as Prentice Hall
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
■ A branch reflects an activity of a project.
■ A node represents the beginning and end of activities, referred to as events.
■ Branches in the network indicate precedence relationships.
■ When an activity is completed at a node, it has been realized.
The Project NetworkCPM/PERT
Figure 8.5 Nodes and Branches
Activity-on-Arc (AOA) Network
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■ Network aids in planning and scheduling.
■ Time duration of activities shown on branches.
■ Activities can occur at the same time (concurrently).
■ A dummy activity shows a precedence relationship but reflects no passage of time.
■ Two or more activities cannot share the same start and end nodes.
The Project NetworkConcurrent Activities
Figure 8. 7 A Dummy Activity
The Project NetworkHouse Building Project Data
No. Activity Activity Predecessor Duration (Months)
1. Design house and - 3 obtain financing
2. Lay foundation 1 2
3. Order Materials 1 1
4. Build house 2, 3 3
5. Select paint 2, 3 1
6. Select carpet 5 1
7. Finish work 4, 6 1Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
The Project NetworkAOA Network for House Building Project
Figure 8.6 Expanded Network for Building a House Showing Concurrent Activities
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The Project NetworkAON Network for House Building ProjectActivity-on-Node (AON) Network A node represents an activity, with its label and time shown on the node The branches show the precedence relationships Convention used in Microsoft Project software
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Figure 8.8
The Project NetworkPaths Through a Network
Table 8.1Paths Through the House-Building
NetworkCopyright © 2010 Pearson Education,
Inc. Publishing as Prentice Hall
Path Events
A 1247
B 12567
C 1347
D 13567
The critical path is the longest path through the network; the minimum time the network can be completed. From Figure 8.8:
Path A: 1 2 4 7 3 + 2 + 3 + 1 = 9 months
Path B: 1 2 5 6 7 3 + 2 + 1 + 1 + 1= 8
months
Path C: 1 3 4 7 3 + 1 + 3 + 1 = 8 months
Path D: 1 3 5 6 7 3 + 1 + 1 + 1 + 1 = 7
months
The Project NetworkThe Critical Path
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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
The Project NetworkActivity Start Times
Figure 8.9 Activity start time
The Project NetworkActivity-on-Node Configuration
Figure 8.10 Activity-on-Node Configuration
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■ ES is the earliest time an activity can start: ES = Maximum (EF)
■ EF is the earliest start time plus the activity time: EF = ES + t
The Project NetworkActivity Scheduling : Earliest Times
Figure 8.11 Earliest activity start and finish times
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■ LS is the latest time an activity can start without delaying critical path time: LS = LF - t
■ LF is the latest finish time. LF = Minimum (LS)
The Project NetworkActivity Scheduling : Latest Times
Figure 8.12 Latest activity start and finish times
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Slack is the amount of time an activity can be delayed without delaying the project: S = LS – ES = LF - EF
Slack Time exists for those activities not on the critical path for which the earliest and latest start times are not equal.
Shared Slack is slack available for a sequence of activities.
The Project NetworkActivity Slack Time (1 of 2)
Table 8.2
*Critical path
Activity
LS ES LF EF Slack, S
*1 0 0 3 3 0
*2 3 3 5 5 0
3 4 3 5 4 1
*4 5 5 8 8 0
5 6 5 7 6 1
6 7 6 8 7 1
*7 8 8 9 9 0
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The Project NetworkActivity Slack Time (2 of 2)
Figure 8.13 Activity slack
■ Activity time estimates usually cannot be made with certainty.
■ PERT used for probabilistic activity times.
■ In PERT, three time estimates are used: most likely time (m), the optimistic time (a), and the pessimistic time (b).
■ These provide an estimate of the mean and variance of a beta distribution:
variance:
mean (expected time):
6b 4m a t
2
6a - b
v
Probabilistic Activity Times
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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Probabilistic Activity TimesExample (1 of 3)
Figure 8.14 Network for Installation Order Processing System
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Probabilistic Activity TimesExample (2 of 3)
Table 8.3 Activity Time Estimates for Figure 8.14
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Probabilistic Activity TimesExample (3 of 3)
Figure 8.15 Earliest and Latest Activity Times
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■ Expected project time is the sum of the expected times of the critical path activities.
■ Project variance is the sum of the critical path activities’ variances
■ The expected project time is assumed to be normally distributed (based on central limit theorem).
■ In example, expected project time (tp) and variance (vp) interpreted as the mean () and variance (2) of a normal distribution: = 25 weeks
2 = 62/9
= 6.9 (weeks)2
Probabilistic Activity TimesExpected Project Time and Variance
■ Using the normal distribution, probabilities are determined by computing the number of standard deviations (Z) a value is from the mean.
■ The Z value is used to find corresponding probability in Table A.1, Appendix A.
Probability Analysis of a Project Network (1 of 2)
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Probability Analysis of a Project Network (2 of 2)
Figure 8.16 Normal Distribution of Network Duration
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What is the probability that the new order processing system will be ready by 30 weeks?
µ = 25 weeks
2 = 6.9 = 2.63 weeksZ = (x-)/ = (30 -25)/2.63 = 1.90
Z value of 1.90 corresponds to probability of .4713 in Table A.1, Appendix A. Probability of completing project in 30 weeks or less: (.5000 + .4713) = .9713.
Probability Analysis of a Project NetworkExample 1 (1 of 2)
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Probability Analysis of a Project NetworkExample 1 (2 of 2)
Figure 8.17 Probability the Network Will Be Completed in 30 Weeks or Less
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■ A customer will trade elsewhere if the new ordering system is not working within 22 weeks. What is the probability that she will be retained?
Z = (22 - 25)/2.63 = -1.14
■ Z value of 1.14 (ignore negative) corresponds to probability of .3729 in Table A.1, appendix A.
■ Probability that customer will be retained is .1271
Probability Analysis of a Project NetworkExample 2 (1 of 2)
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Probability Analysis of a Project NetworkExample 2 (2 of 2)
Figure 8.18 Probability the Network Will Be Completed in 22 Weeks or Less
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CPM/PERT Analysis with QM for Windows & Excel QM (1 of 2)
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Exhibit 8.2
CPM/PERT Analysis with QM for Windows & Excel QM (2 of 2)
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Microsoft Project handles only AON networks.
Analysis with Microsoft Project (1 of 13)
Exhibit 8.3
Analysis with Microsoft Project (2 of 13)
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Exhibit 8.4
Analysis with Microsoft Project (3 of 13)
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Exhibit 8.5
Exhibit 8.6Copyright © 2010 Pearson Education,
Inc. Publishing as Prentice Hall
Analysis with Microsoft Project (4 of 13)
Figure 8.7Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Analysis with Microsoft Project (5 of 13)
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Analysis with Microsoft Project (6 of 13)
Figure 8.8
Exhibit 8.9Copyright © 2010 Pearson Education,
Inc. Publishing as Prentice Hall
Analysis with Microsoft Project (7 of 13)
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Analysis with Microsoft Project (8 of 13)
Exhibit 8.10
Exhibit 8.11Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Analysis with Microsoft Project (9 of 13)
Figure 8.12Copyright © 2010 Pearson Education,
Inc. Publishing as Prentice Hall
Analysis with Microsoft Project (10 of 13)
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Analysis with Microsoft Project (11 of 13)
Figure 8.13
Exhibit 8.14Copyright © 2010 Pearson Education,
Inc. Publishing as Prentice Hall
Analysis with Microsoft Project (12 of 13)
Exhibit 8.15Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Analysis with Microsoft Project (13 of 13)
■ Project duration can be reduced by assigning more resources to project activities.
■ However, doing this increases project cost.
■ Decision is based on analysis of trade-off between time and cost.
■ Project crashing is a method for shortening project duration by reducing one or more critical activities to a time less than normal activity time.
Project Crashing and Time-Cost Trade-Off Overview
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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Project Crashing and Time-Cost Trade-Off Example Problem (1 of 5)
Figure 8.19 The Project Network for Building a House
Project Crashing and Time-Cost Trade-Off Example Problem (2 of 5)
Figure 8.20
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Crash cost & crash time have a linear relationship:
$2000
5 $400 /
Total Crash Cost
Total Crash Time weekswk
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Table 8.4
Project Crashing and Time-Cost Trade-Off Example Problem (3 of 5)
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Figure 8.21 Network with Normal Activity Times and Weekly Crashing Costs
Project Crashing and Time-Cost Trade-Off Example Problem (4 of 5)
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Figure 8.22Revised Network with Activity 1 Crashed
Project Crashing and Time-Cost Trade-Off Example Problem (5 of 5)
As activities are crashed, the critical path may change and several paths may become critical.
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Exhibit
8.16
Project Crashing and Time-Cost Trade-Off Project Crashing with QM for Windows
Project Crashing and Time-Cost Trade-Off General Relationship of Time and Cost (1 of 2)
■ Project crashing costs and indirect costs have an inverse relationship.
■ Crashing costs are highest when the project is shortened.
■ Indirect costs increase as the project duration increases.
■ Optimal project time is at minimum point on the total cost curve.
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Project Crashing and Time-Cost Trade-Off General Relationship of Time and Cost (2 of 2)
Figure 8.23The Time-Cost Trade-Off
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General linear programming model with AOA convention:
Minimize Z = xi
subject to: xj - xi tij for all activities i j xi, xj 0
Where: xi = earliest event time of node ixj = earliest event time of node jtij = time of activity i j
The objective is to minimize the project duration (critical path time).
The CPM/PERT Network Formulating as a Linear Programming Model
i
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The CPM/PERT Network Example Problem Formulation and Data (1 of 2)
Figure 8.24Copyright © 2010 Pearson Education,
Inc. Publishing as Prentice Hall
Minimize Z = x1 + x2 + x3 + x4 + x5 + x6 + x7
subject to:
x2 - x1 12x3 - x2 8x4 - x2 4x4 - x3 0x5 - x4 4x6 - x4 12x6 - x5 4x7 - x6 4xi, xj 0
The CPM/PERT Network Example Problem Formulation and Data (2 of 2)
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Exhibit 8.17
The CPM/PERT Network Example Problem Solution with Excel (1 of 4)
B6:B12
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Exhibit 8.18
The CPM/PERT Network Example Problem Solution with Excel (2 of 4)
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Exhibit 8.19
The CPM/PERT Network Example Problem Solution with Excel (3 of 4)
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Exhibit 8.20
The CPM/PERT Network Example Problem Solution with Excel (4 of 4)
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Minimize Z = $400y12 + 500y23 + 3000y24 + 200y45 + 7000y46 + 200y56 + 7000y67
subject to:y12 5 y12 + x2 - x1 12 x7 30 y23 3 y23 + x3 - x2 8 xi, yij ≥ 0y24 1 y24 + x4 - x2 4y34 0 y34 + x4 - x3 0y45 3 y45 + x5 - x4 4y46 3 y46 + x6 - x4 12y56 3 y56 + x6 - x5 4y67 1 x67 + x7 - x6 4
xi = earliest event time of node Ixj = earliest event time of node jyij = amount of time by which activity i j is crashed
Project Crashing with Linear ProgrammingExample Problem – Model Formulation
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Objective is to minimize the cost of crashing
Project Crashing with Linear ProgrammingExcel Solution (1 of 3)
Exhibit 8.21
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Project Crashing with Linear ProgrammingExcel Solution (2 of 3)
Exhibit 8.22
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Project Crashing with Linear ProgrammingExcel Solution (3 of 3)
Exhibit 8.23
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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Given this network and the data on the following slide, determine the expected project completion time and variance, and the probability that the project will be completed in 28 days or less.
Example Problem Problem Statement and Data (1 of 2)
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Example ProblemProblem Statement and Data (2 of 2)
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6b 4m a t
2
6a - b
v
Example Problem Solution (1 of 4)
Step 1: Compute the expected activity times and variances.
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Example Problem Solution (2 of 4)
Step 2: Determine the earliest and latest activity times & slacks
Example Problem Solution (3 of 4)
Step 3: Identify the critical path and compute expected completion time and variance.
Critical path (activities with no slack): 1 3 5 7
Expected project completion time: tp = 9+5+6+4 = 24 days
Variance: vp = 4 + 4/9 + 4/9 + 1/9 = 5 (days)2
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Example Problem Solution (4 of 4)
Step 4: Determine the Probability That the Project Will be Completed in 28 days or less (µ = 24, = 5)
Z = (x - )/ = (28 -24)/5 = 1.79
Corresponding probability from Table A.1, Appendix A, is .4633 and P(x 28) = .4633 + .5 = .9633.
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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall