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1




Project Management
2



OBJECTIVES

 Definition of Project Management
 Work Breakdown Structure

 Project Control Charts

 Structuring Projects

 Critical Path Scheduling
3



    Project Management
           Defined
   Project is a series of related jobs usually
    directed towards some major output and
    requiring a significant period of time to
    perform
   Project Management are the management
    activities of planning, directing, and
    controlling resources (people, equipment,
    material) to meet the technical, cost, and time
    constraints of a project
4

        Introduction to Project
             Management
   Definition of Project Management
    – A project can be defined as a group of tasks – which helps in
      achieving an objective
    – A Project : undertaken to solve a problem.
    – Project Management – the process of planning, directing and
      controlling resources to meet the technical, cost and time
      considerations of a project.
    – Project Management – as a Conversion Process.
5


    The Definition of a “PROJECT”
•   Purpose – Usually a one-time activity with a well-defined
    set of desired end result.
•   Life Cycle- From a slow beginning they progress to a
    buildup of size, then peak, finally terminate.
•   Interdependencies- Projects always interact with the
    parent organization’s standard, ongoing operations.
•   Uniqueness - Every Project has some elements that
    are unique. (No two Construction or R & D projects are
    precisely alike.)
6


    Project Vs. Routine Activities
   Project is a one time activity
   It involves large investments
   No revenue till the project is completed
   High degree & Wide variety of skills are used.
   Involves experts from various divisions of the company,
    consultants & a number of contractors.
   A systematic approach to problem solving – special
    techniques used.
   Usage of special purpose equipments – in some cases
   Deals     with   planning,     scheduling,    controlling
    simuttaneously with the objective of timely completion of
    the project.
7




Pure Project
A pure project is where a self-contained team
works full-time on the project

Structuring Projects / Pure
    Project: Advantages
   The project manager has full authority
    over the project
   Team members report to one boss
   Shortened communication lines
   Team pride, motivation, and commitment
    are high
8




    Structuring Projects / Pure
      Project: Disadvantages
 Duplication of resources
 Organizational goals and policies

  are ignored
 Lack of technology transfer
 Team members have no functional

  area "home"
9




     Functional Project
  A functional project is housed within
  a functional division
                              President


 Research and
                            Engineering              Manufacturing
 Development

Project Project Project   Project Project Project   Project Project Project
  A       B       C         D       E       F         G       H        I

               Example, Project “B” is in the functional
               area of Research and Development.
10


    Structuring Projects
       Functional Project :
         Advantages
 A team member can work on
  several projects
 Technical expertise is maintained

  within the functional area
 The functional area is a “home”

  after the project is completed
 Critical mass of specialized

  knowledge
Structuring Projects                11


       Functional Project:
       Disadvantages

 Aspects of the project that are not
  directly related to the functional
  area get short-changed
 Motivation of team members is

  often weak
 Needs of the client are secondary

  and are responded to slowly
12



 Matrix Project / Organisation
          Structure

                               President

            Research and
                         Engineering Manufacturing Marketing
            Development


Manager
Project A

Manager
Project B

Manager
Project C
13



        Structuring Projects /
           Matrix: Advantages


   Enhanced communications between functional
    areas
   Pinpointed responsibility
   Duplication of resources is minimized
   Functional “home” for team members
   Policies of the parent organization are followed
14




     Structuring Projects /
      Matrix: Disadvantages

   Too many bosses

   Depends on project manager’s
    negotiating skills

   Potential for sub-optimization
15


                    Gantt Chart

Vertical Axis:
Always Activities   Horizontal bars used to denote length
or Jobs             of time for each activity or job.

   Activity 1
   Activity 2
   Activity 3
   Activity 4
   Activity 5
   Activity 6

                      Time     Horizontal Axis: Always Time
16

 Work Breakdown Structure
A work breakdown structure defines the hierarchy of
project tasks, subtasks, and work packages

 Level Program


   1     Project 1       Project 2


   2          Task 1.1        Task 1.2


   3                 Subtask 1.1.1       Subtask 1.1.2


   4           Work Package 1.1.1.1        Work Package 1.1.1.2
17



           Networ k Dia g rams




1/2/3/4/5 are Events
A/B/C/D/E are Activities.
18


Networ k Dia g rams
19



    Network-Planning Models

   A project is made up of a sequence of activities that
    form a network representing a project
   The path taking longest time through this network of
    activities is called the “critical path”
   The critical path provides a wide range of scheduling
    information useful in managing a project
   Critical Path Method (CPM) helps to identify the
    critical path(s) in the project networks
20


  Prerequisites for Critical
     Path Methodology


A project must have:

 well-defined jobs or tasks whose
 completion marks the end of the project;

 independent jobs or tasks;

 and tasks that follow a given sequence.
Types of Critical Path
                                                             21



             Methods
   CPM with a Single Time Estimate
     – Used when activity times are known with certainty
     – Used to determine timing estimates for the project,
       each activity in the project, and slack time for
       activities
   CPM with Three Activity Time Estimates
     – Used when activity times are uncertain
     – Used to obtain the same information as the Single
       Time Estimate model and probability information
   Time-Cost Models
     – Used when cost trade-off information is a major
       consideration in planning
     – Used to determine the least cost in reducing total
       project time
22



    Steps in the CPM with
    Single Time Estimate

 1. Activity Identification
 2. Activity Sequencing and Network

  Construction
 3. Determine the critical path

    – From the critical path all of the project
      and activity timing information can be
      obtained
23

          CPM with Single Time
               Estimate
      Consider the following consulting project:
Activity                           Designation Immed. Pred. Time (Weeks)
Assess customer's needs                A          None            2
Write and submit proposal               B          A              1
Obtain approval                         C          B              1
Develop service vision and goals       D           C              2
Train employees                         E          C              5
Quality improvement pilot groups        F         D, E            5
Write assessment report                G           F              1

Develop a critical path diagram and determine
the duration of the critical path and slack times
for all activities.
24


         First draw the network
Act.      Imed. Pred. Time

   A          None     2
   B          A        1
   C          B        1
   D          C        2
   E          C        5
   F          D,E      5
                                    D(2)
   G          F        1


       A(2)          B(1)    C(1)          F(5)   G(1)



                                    E(5)
25

Determine early starts and early
         finish times

                                 ES=4
                                 EF=6

  ES=0      ES=2          ES=3   D(2)
                                        ES=9    ES=14
  EF=2      EF=3          EF=4          EF=14   EF=15

 A(2)       B(1)          C(1)          F(5)    G(1)
                                 ES=4
                                 EF=9
  Hint: Start with ES=0
  and go forward in the          E(5)
  network from A to G.
Determine                                          26


 late starts                 Hint: Start with LF=15
  and late                   or the total time of the
                             project and go
finish times          ES=4
                             backward in the
                      EF=6
                             network from G to A.
 ES=0   ES=2   ES=3   D(2)
                               ES=9       ES=14
 EF=2   EF=3   EF=4   LS=7     EF=14      EF=15
                      LF=9
 A(2)   B(1)   C(1)             F(5)       G(1)
                      ES=4
 LS=0   LS=2   LS=3   EF=9     LS=9        LS=14
 LF=2   LF=3   LF=4            LF=14       LF=15
                      E(5)

                      LS=4
                      LF=9
27


   Critical Path & Slack
                     ES=4
                             Slack=(7-4)=(9-6)= 3 Wks
                     EF=6

ES=0   ES=2   ES=3   D(2)
                             ES=9      ES=14
EF=2   EF=3   EF=4   LS=7    EF=14     EF=15
                     LF=9
A(2)   B(1)   C(1)          F(5)        G(1)
                     ES=4
LS=0   LS=2   LS=3   EF=9    LS=9       LS=14
LF=2   LF=3   LF=4           LF=14      LF=15
                     E(5)

                     LS=4   Duration=15 weeks
                     LF=9
28
       Program Evaluation & Review
            Technique (PERT)
   PERT is Event oriented & CPM is Activity oriented.
   PERT is used to deal unit uncertainty.
   PERT has 3 time estimates – Optimistic time
                                    – Most likely time.
                                 – Pessimistic time.
   PERT has one or more activities follow a probability
    distribution – taking into account the uncertainty of the
    situation.
   PERT network provides a measure of the probability of
    project completion by the scheduled date.
   The probability concept – Only associated with PERT
    and not CPM.
     (time estimates in CPM are deterministic & not
     probabilistic)
29




Example 2. CPM with Three
 Activity Time Estimates

        Immediate
  Task Predecesors Optimistic Most Likely Pessimistic
   A      None         3          6           15
   B      None         2          4           14
   C        A          6         12           30
   D        A          2          5            8
   E        C          5         11           17
   F        D          3          6           15
   G        B          3          9           27
   H       E,F         1          4            7
    I      G,H         4         19           28
30


   Example 2. Expected
    Time Calculations
                                           ET(A)= 3+4(6)+15
        Immediate Expected                                         6
Task   Predecesors    Time
 A        None           7                 ET(A)=42/6=7
 B        None       5.333
 C          A           14               Immediate
                                   Task Predecesors Optimistic Most Likely Pessimistic
 D          A            5          A      None         3          6           15
 E          C           11          B
                                    C
                                           None
                                             A
                                                        2
                                                        6
                                                                   4
                                                                   12
                                                                               14
                                                                               30
 F          D            7          D        A          2          5            8
                                    E        C          5          11          17
 G          B           11          F        D          3          6           15
 H         E,F           4          G        B          3          9           27
                                    H       E,F         1          4            7
  I        G,H          18           I      G,H         4          19          28

                Opt. Time + 4(Most Likely Time) + Pess. Time
Expected Time =
                                     6
31
       Ex. 2. Expected Time
           Calculations

        Immediate Expected                 ET(B)= 2+4(4)+14
Task   Predecesors    Time                                         6
 A        None           7
 B        None       5.333                 ET(B)=32/6=5.333
 C          A           14
 D          A            5               Immediate
 E          C           11         Task Predecesors Optimistic Most Likely Pessimistic
                                    A      None         3          6           15
 F          D            7          B      None         2          4           14
 G          B           11          C
                                    D
                                             A
                                             A
                                                        6
                                                        2
                                                                   12
                                                                   5
                                                                               30
                                                                                8
 H         E,F           4          E        C          5          11          17
                                    F        D          3          6           15
  I        G,H          18          G        B          3          9           27
                                    H       E,F         1          4            7
                                     I      G,H         4          19          28

                Opt. Time + 4(Most Likely Time) + Pess. Time
Expected Time =
                                     6
Ex 2. Expected Time                                                      32


             Calculations

        Immediate Expected                ET(C)= 6+4(12)+30
Task   Predecesors    Time
 A        None           7                                        6
 B        None       5.333
 C          A           14                ET(C)=84/6=14
 D          A            5
 E          C           11               Immediate
                                   Task Predecesors Optimistic Most Likely Pessimistic
 F          D            7          A      None         3          6           15
 G          B           11          B
                                    C
                                           None
                                             A
                                                        2
                                                        6
                                                                   4
                                                                   12
                                                                               14
                                                                               30
 H         E,F           4          D        A          2          5            8
                                    E        C          5          11          17
  I        G,H          18          F        D          3          6           15
                                    G        B          3          9           27
                                    H       E,F         1          4            7
                                     I      G,H         4          19          28

                Opt. Time + 4(Most Likely Time) + Pess. Time
Expected Time =
                                     6
33



          Example 2. Network

                           Duration = 54 Days
           C(14)   E(11)

A(7)                           H(4)
            D(5)   F(7)

                                           I(18)


  B                G(11)
(5.333)
34



     Example 2. Probability
          Exercise
What is the probability of finishing this project in
less than 53 days?



    p(t < D)
                D=53
                                                       t
                      TE = 54
                                          D - TE
                                   Z =
                                           ∑ σ cp 2
35


                                Pessim. - Optim. 2
       Activity variance, σ = (
                              2
                                                )
                                       6

        Task     Optimistic Most Likely Pessimistic Variance
         A           3          6           15          4
         B           2          4           14
         C           6         12           30         16
         D           2          5            8
         E           5         11           17          4
         F           3          6           15
         G           3          9           27
         H           1          4            7          1
         I           4         19           28         16

(Sum the variance along the critical            ∑ σ 2 = 41
path.)
36




         p(t < D)

                                                         t
                D=53                  TE = 54
                    D - TE          53- 54
          Z =                     =        = -.156
                    ∑σ   cp
                              2       41

p(Z < -.156) = .438, or 43.8 % (NORMSDIST(-.156)

There is a 43.8% probability that this project will be
completed in less than 53 weeks.
37


Ex 2. Additional Probability
         Exercise

   What is the probability that the
    project duration will exceed 56
    weeks?
38

    Example 2. Additional
      Exercise Solution

     p(t < D)

                                                 t
                     TE = 54
                                  D=56
                D - TE          56 - 54
        Z =                   =         = .312
                ∑σ   cp
                          2        41


p(Z > .312) = .378, or 37.8 % (1-NORMSDIST(.312))
39


          Time-Cost Models
   Basic Assumption: Relationship
    between activity completion time
    and project cost

   Time Cost Models: Determine the
    optimum point in time-cost
    tradeoffs
    –   Activity direct costs
    –   Project indirect costs
    –   Activity completion times
40


         Networ k Crashing (Project
   Determine the timeCrashing) each activity in the
                       – cost ratio for
    network – this ratio represents the increase in cost for a
    unit decrease in time.
    Time – Cost Ratio = crash cost – normal cost
                        normal time – crash time
   Identify the activities on critical path & select that activity
    which has smallest time cost ratio – crash that activity to
    the extent possible.
   Observe any change in the critical path – any other path
    becomes critical – calculate time cost ratio in the new
    critical path.
   Repeat above steps – till the activities are crashed to
    reduce the present duration to the desired time period.
CPM Assumptions /                               41


          Limitations
   Project activities can be identified as entities
    (There is a clear beginning and ending point
    for each activity.)

    Project activity sequence relationships can be
    specified and networked

   Project control should focus on the critical
    path

   The activity times follow the beta distribution,
    with the variance of the project assumed to
    equal the sum of the variances along the
    critical path
42


    Question Bowl

Which of the following are examples
   of Graphic Project Charts?
b. Gantt
c. Bar
d. Milestone
e. All of the above
f. None of the above


Answer: d. All of the above
43


     Question Bowl

Which of the following are one of the
   three organizational structures of
   projects?
b. Pure
c. Functional
d. Matrix
e. All of the above
f. None of the above
Answer: d. All of the above
44


       Question Bowl
A project starts with a written description of the
   objectives to be achieved, with a brief statement
   of the work to be done and a proposed schedule
   all contained in which of the following?
b. SOW
c. WBS
d. Early Start Schedule
e. Late Start Schedule
f. None of the above



Answer: a. SOW (or Statement of Work)
45


       Question Bowl
     For some activities in a project there may
     be some leeway from when an activity can
     start and when it must finish. What is this
     period of time called when using the Critical
     Path Method?
b.   Early start time
c.   Late start time
d.   Slack time
e.   All of the above
f.   None of the above

 Answer: c. Slack time
46


      Question Bowl
How much “slack time” is permitted in the “critical
   path” activity times?
b. Only one unit of time per activity
c. No slack time is permitted
d. As much as the maximum activity time in the
   network
e. As much as is necessary to add up to the total
   time of the project
f. None of the above
Answer: b. No slack time is permitted (All
critical path activities must have zero slack
time, otherwise they would not be critical to
the project completion time.)
47


      Question Bowl

When looking at the Time-Cost Trade Offs in the
   Minimum-Cost Scheduling time-cost model,
   we seek to reduce the total time of a project
   by doing what to the least-cost activity
   choices?                Answer: a. Crashing
b. Crashing them           them (We “crash” the
c. Adding slack time       least-cost activity
d. Subtracting slack time times to seek a reduced
e. Adding project time     total time for the
f. None of the above       entire project and we
                           do it step-wise as
                           inexpensively as
                           possible.)

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Ch3 proj.mgt

  • 2. 2 OBJECTIVES  Definition of Project Management  Work Breakdown Structure  Project Control Charts  Structuring Projects  Critical Path Scheduling
  • 3. 3 Project Management Defined  Project is a series of related jobs usually directed towards some major output and requiring a significant period of time to perform  Project Management are the management activities of planning, directing, and controlling resources (people, equipment, material) to meet the technical, cost, and time constraints of a project
  • 4. 4 Introduction to Project Management  Definition of Project Management – A project can be defined as a group of tasks – which helps in achieving an objective – A Project : undertaken to solve a problem. – Project Management – the process of planning, directing and controlling resources to meet the technical, cost and time considerations of a project. – Project Management – as a Conversion Process.
  • 5. 5 The Definition of a “PROJECT” • Purpose – Usually a one-time activity with a well-defined set of desired end result. • Life Cycle- From a slow beginning they progress to a buildup of size, then peak, finally terminate. • Interdependencies- Projects always interact with the parent organization’s standard, ongoing operations. • Uniqueness - Every Project has some elements that are unique. (No two Construction or R & D projects are precisely alike.)
  • 6. 6 Project Vs. Routine Activities  Project is a one time activity  It involves large investments  No revenue till the project is completed  High degree & Wide variety of skills are used.  Involves experts from various divisions of the company, consultants & a number of contractors.  A systematic approach to problem solving – special techniques used.  Usage of special purpose equipments – in some cases  Deals with planning, scheduling, controlling simuttaneously with the objective of timely completion of the project.
  • 7. 7 Pure Project A pure project is where a self-contained team works full-time on the project Structuring Projects / Pure Project: Advantages  The project manager has full authority over the project  Team members report to one boss  Shortened communication lines  Team pride, motivation, and commitment are high
  • 8. 8 Structuring Projects / Pure Project: Disadvantages  Duplication of resources  Organizational goals and policies are ignored  Lack of technology transfer  Team members have no functional area "home"
  • 9. 9 Functional Project A functional project is housed within a functional division President Research and Engineering Manufacturing Development Project Project Project Project Project Project Project Project Project A B C D E F G H I Example, Project “B” is in the functional area of Research and Development.
  • 10. 10 Structuring Projects Functional Project : Advantages  A team member can work on several projects  Technical expertise is maintained within the functional area  The functional area is a “home” after the project is completed  Critical mass of specialized knowledge
  • 11. Structuring Projects 11 Functional Project: Disadvantages  Aspects of the project that are not directly related to the functional area get short-changed  Motivation of team members is often weak  Needs of the client are secondary and are responded to slowly
  • 12. 12 Matrix Project / Organisation Structure President Research and Engineering Manufacturing Marketing Development Manager Project A Manager Project B Manager Project C
  • 13. 13 Structuring Projects / Matrix: Advantages  Enhanced communications between functional areas  Pinpointed responsibility  Duplication of resources is minimized  Functional “home” for team members  Policies of the parent organization are followed
  • 14. 14 Structuring Projects / Matrix: Disadvantages  Too many bosses  Depends on project manager’s negotiating skills  Potential for sub-optimization
  • 15. 15 Gantt Chart Vertical Axis: Always Activities Horizontal bars used to denote length or Jobs of time for each activity or job. Activity 1 Activity 2 Activity 3 Activity 4 Activity 5 Activity 6 Time Horizontal Axis: Always Time
  • 16. 16 Work Breakdown Structure A work breakdown structure defines the hierarchy of project tasks, subtasks, and work packages Level Program 1 Project 1 Project 2 2 Task 1.1 Task 1.2 3 Subtask 1.1.1 Subtask 1.1.2 4 Work Package 1.1.1.1 Work Package 1.1.1.2
  • 17. 17 Networ k Dia g rams 1/2/3/4/5 are Events A/B/C/D/E are Activities.
  • 18. 18 Networ k Dia g rams
  • 19. 19 Network-Planning Models  A project is made up of a sequence of activities that form a network representing a project  The path taking longest time through this network of activities is called the “critical path”  The critical path provides a wide range of scheduling information useful in managing a project  Critical Path Method (CPM) helps to identify the critical path(s) in the project networks
  • 20. 20 Prerequisites for Critical Path Methodology A project must have: well-defined jobs or tasks whose completion marks the end of the project; independent jobs or tasks; and tasks that follow a given sequence.
  • 21. Types of Critical Path 21 Methods  CPM with a Single Time Estimate – Used when activity times are known with certainty – Used to determine timing estimates for the project, each activity in the project, and slack time for activities  CPM with Three Activity Time Estimates – Used when activity times are uncertain – Used to obtain the same information as the Single Time Estimate model and probability information  Time-Cost Models – Used when cost trade-off information is a major consideration in planning – Used to determine the least cost in reducing total project time
  • 22. 22 Steps in the CPM with Single Time Estimate  1. Activity Identification  2. Activity Sequencing and Network Construction  3. Determine the critical path – From the critical path all of the project and activity timing information can be obtained
  • 23. 23 CPM with Single Time Estimate Consider the following consulting project: Activity Designation Immed. Pred. Time (Weeks) Assess customer's needs A None 2 Write and submit proposal B A 1 Obtain approval C B 1 Develop service vision and goals D C 2 Train employees E C 5 Quality improvement pilot groups F D, E 5 Write assessment report G F 1 Develop a critical path diagram and determine the duration of the critical path and slack times for all activities.
  • 24. 24 First draw the network Act. Imed. Pred. Time A None 2 B A 1 C B 1 D C 2 E C 5 F D,E 5 D(2) G F 1 A(2) B(1) C(1) F(5) G(1) E(5)
  • 25. 25 Determine early starts and early finish times ES=4 EF=6 ES=0 ES=2 ES=3 D(2) ES=9 ES=14 EF=2 EF=3 EF=4 EF=14 EF=15 A(2) B(1) C(1) F(5) G(1) ES=4 EF=9 Hint: Start with ES=0 and go forward in the E(5) network from A to G.
  • 26. Determine 26 late starts Hint: Start with LF=15 and late or the total time of the project and go finish times ES=4 backward in the EF=6 network from G to A. ES=0 ES=2 ES=3 D(2) ES=9 ES=14 EF=2 EF=3 EF=4 LS=7 EF=14 EF=15 LF=9 A(2) B(1) C(1) F(5) G(1) ES=4 LS=0 LS=2 LS=3 EF=9 LS=9 LS=14 LF=2 LF=3 LF=4 LF=14 LF=15 E(5) LS=4 LF=9
  • 27. 27 Critical Path & Slack ES=4 Slack=(7-4)=(9-6)= 3 Wks EF=6 ES=0 ES=2 ES=3 D(2) ES=9 ES=14 EF=2 EF=3 EF=4 LS=7 EF=14 EF=15 LF=9 A(2) B(1) C(1) F(5) G(1) ES=4 LS=0 LS=2 LS=3 EF=9 LS=9 LS=14 LF=2 LF=3 LF=4 LF=14 LF=15 E(5) LS=4 Duration=15 weeks LF=9
  • 28. 28 Program Evaluation & Review Technique (PERT)  PERT is Event oriented & CPM is Activity oriented.  PERT is used to deal unit uncertainty.  PERT has 3 time estimates – Optimistic time – Most likely time. – Pessimistic time.  PERT has one or more activities follow a probability distribution – taking into account the uncertainty of the situation.  PERT network provides a measure of the probability of project completion by the scheduled date.  The probability concept – Only associated with PERT and not CPM. (time estimates in CPM are deterministic & not probabilistic)
  • 29. 29 Example 2. CPM with Three Activity Time Estimates Immediate Task Predecesors Optimistic Most Likely Pessimistic A None 3 6 15 B None 2 4 14 C A 6 12 30 D A 2 5 8 E C 5 11 17 F D 3 6 15 G B 3 9 27 H E,F 1 4 7 I G,H 4 19 28
  • 30. 30 Example 2. Expected Time Calculations ET(A)= 3+4(6)+15 Immediate Expected 6 Task Predecesors Time A None 7 ET(A)=42/6=7 B None 5.333 C A 14 Immediate Task Predecesors Optimistic Most Likely Pessimistic D A 5 A None 3 6 15 E C 11 B C None A 2 6 4 12 14 30 F D 7 D A 2 5 8 E C 5 11 17 G B 11 F D 3 6 15 H E,F 4 G B 3 9 27 H E,F 1 4 7 I G,H 18 I G,H 4 19 28 Opt. Time + 4(Most Likely Time) + Pess. Time Expected Time = 6
  • 31. 31 Ex. 2. Expected Time Calculations Immediate Expected ET(B)= 2+4(4)+14 Task Predecesors Time 6 A None 7 B None 5.333 ET(B)=32/6=5.333 C A 14 D A 5 Immediate E C 11 Task Predecesors Optimistic Most Likely Pessimistic A None 3 6 15 F D 7 B None 2 4 14 G B 11 C D A A 6 2 12 5 30 8 H E,F 4 E C 5 11 17 F D 3 6 15 I G,H 18 G B 3 9 27 H E,F 1 4 7 I G,H 4 19 28 Opt. Time + 4(Most Likely Time) + Pess. Time Expected Time = 6
  • 32. Ex 2. Expected Time 32 Calculations Immediate Expected ET(C)= 6+4(12)+30 Task Predecesors Time A None 7 6 B None 5.333 C A 14 ET(C)=84/6=14 D A 5 E C 11 Immediate Task Predecesors Optimistic Most Likely Pessimistic F D 7 A None 3 6 15 G B 11 B C None A 2 6 4 12 14 30 H E,F 4 D A 2 5 8 E C 5 11 17 I G,H 18 F D 3 6 15 G B 3 9 27 H E,F 1 4 7 I G,H 4 19 28 Opt. Time + 4(Most Likely Time) + Pess. Time Expected Time = 6
  • 33. 33 Example 2. Network Duration = 54 Days C(14) E(11) A(7) H(4) D(5) F(7) I(18) B G(11) (5.333)
  • 34. 34 Example 2. Probability Exercise What is the probability of finishing this project in less than 53 days? p(t < D) D=53 t TE = 54 D - TE Z = ∑ σ cp 2
  • 35. 35 Pessim. - Optim. 2 Activity variance, σ = ( 2 ) 6 Task Optimistic Most Likely Pessimistic Variance A 3 6 15 4 B 2 4 14 C 6 12 30 16 D 2 5 8 E 5 11 17 4 F 3 6 15 G 3 9 27 H 1 4 7 1 I 4 19 28 16 (Sum the variance along the critical ∑ σ 2 = 41 path.)
  • 36. 36 p(t < D) t D=53 TE = 54 D - TE 53- 54 Z = = = -.156 ∑σ cp 2 41 p(Z < -.156) = .438, or 43.8 % (NORMSDIST(-.156) There is a 43.8% probability that this project will be completed in less than 53 weeks.
  • 37. 37 Ex 2. Additional Probability Exercise  What is the probability that the project duration will exceed 56 weeks?
  • 38. 38 Example 2. Additional Exercise Solution p(t < D) t TE = 54 D=56 D - TE 56 - 54 Z = = = .312 ∑σ cp 2 41 p(Z > .312) = .378, or 37.8 % (1-NORMSDIST(.312))
  • 39. 39 Time-Cost Models  Basic Assumption: Relationship between activity completion time and project cost  Time Cost Models: Determine the optimum point in time-cost tradeoffs – Activity direct costs – Project indirect costs – Activity completion times
  • 40. 40 Networ k Crashing (Project  Determine the timeCrashing) each activity in the – cost ratio for network – this ratio represents the increase in cost for a unit decrease in time. Time – Cost Ratio = crash cost – normal cost normal time – crash time  Identify the activities on critical path & select that activity which has smallest time cost ratio – crash that activity to the extent possible.  Observe any change in the critical path – any other path becomes critical – calculate time cost ratio in the new critical path.  Repeat above steps – till the activities are crashed to reduce the present duration to the desired time period.
  • 41. CPM Assumptions / 41 Limitations  Project activities can be identified as entities (There is a clear beginning and ending point for each activity.)  Project activity sequence relationships can be specified and networked  Project control should focus on the critical path  The activity times follow the beta distribution, with the variance of the project assumed to equal the sum of the variances along the critical path
  • 42. 42 Question Bowl Which of the following are examples of Graphic Project Charts? b. Gantt c. Bar d. Milestone e. All of the above f. None of the above Answer: d. All of the above
  • 43. 43 Question Bowl Which of the following are one of the three organizational structures of projects? b. Pure c. Functional d. Matrix e. All of the above f. None of the above Answer: d. All of the above
  • 44. 44 Question Bowl A project starts with a written description of the objectives to be achieved, with a brief statement of the work to be done and a proposed schedule all contained in which of the following? b. SOW c. WBS d. Early Start Schedule e. Late Start Schedule f. None of the above Answer: a. SOW (or Statement of Work)
  • 45. 45 Question Bowl For some activities in a project there may be some leeway from when an activity can start and when it must finish. What is this period of time called when using the Critical Path Method? b. Early start time c. Late start time d. Slack time e. All of the above f. None of the above Answer: c. Slack time
  • 46. 46 Question Bowl How much “slack time” is permitted in the “critical path” activity times? b. Only one unit of time per activity c. No slack time is permitted d. As much as the maximum activity time in the network e. As much as is necessary to add up to the total time of the project f. None of the above Answer: b. No slack time is permitted (All critical path activities must have zero slack time, otherwise they would not be critical to the project completion time.)
  • 47. 47 Question Bowl When looking at the Time-Cost Trade Offs in the Minimum-Cost Scheduling time-cost model, we seek to reduce the total time of a project by doing what to the least-cost activity choices? Answer: a. Crashing b. Crashing them them (We “crash” the c. Adding slack time least-cost activity d. Subtracting slack time times to seek a reduced e. Adding project time total time for the f. None of the above entire project and we do it step-wise as inexpensively as possible.)

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