Chapter 7 Project Management

Learning Objectives  Understand how to plan, monitor, and control

projects using PERT/CPM.  Determine earliest start, earliest finish, latest

start, latest finish, and slack times for each activity.

 Identify critical activities and critical path.  Understand impact of variability in activity

times.

Project Management

  Used to manage large complex projects

  Has three phases: 1.  Project planning 2.  Project scheduling 3.  Project controlling

Phase 1: Project Planning

1.  What is the project goal or objective? 2.  What are the activities (or tasks) involved? 3.  How are activities linked? 4.  How much time required for each activity? 5.  What resources are required for each

activity?

Phase 2: Project Scheduling 1.  When will the entire project be completed? 2.  What is the scheduled start and end time for

each activity? 3.  Which are the “critical” activities? 4.  Which are the noncritical activities? 5.  How late can noncritical activities be without

delaying the project? 6.  After accounting for uncertainty, what is the

probability of completing the project by a specific deadline?

Project Controlling  Control of large projects involves close

monitoring of schedules, resources, and budgets.  Questions to be answered:

  At any particular date or time, is project on schedule, behind schedule, or ahead of schedule?

  At any particular date or time, is money spent on project equal to, less than, or greater than budgeted amount?

  Are there enough resources available to finish project on time?

  If project is to be finished in shorter amount of time, what is best way to accomplish this at least cost?

7.2 Project Networks

  Once project mission or goal has been clearly specified, first issues to address deal with project planning.

  Identify activities that constitute project, precedence relationships between these activities, and time and other resources required for each activity.

  These activities and precedence relationships are demonstrated graphically in an activity network

Identifying Activities

 Subdivides a large project into smaller units  Each activity should have a clearly defined

starting point and ending point  Each activity is clearly distinguishable from

every other activity  Each activity can be a project in itself

Work Breakdown Structure (WBS) Divides the project into its various

subcomponents and defines hierarchical levels of detail

Level 1 Project 2 Major tasks in project 3 Subtasks in major tasks 4 Activities to be completed

Example Work Breakdown Structure

Identify for Each Activity:

 Which other activities must be completed previously (predecessors)

 Time required for completion  Resources required

This completes the project planning phase.

Project Scheduling Phase

Commonly used techniques:

 Programme Evaluation and Review Technique (PERT)

 Critical Path Method (CPM)

Project Management Example: General Foundry Inc.

 Has 16 weeks to install a complex air filter system on its smokestack

 May be forced to close if not completed within 16 weeks due to environmental regulations

 Has identified 8 activities

Activities, Precedence Relationships and Estimated Time

Drawing the Project Network

 AON – Activity on Node networks show each activity as a node and arcs show the immediate predecessor activities

 AOA – Activity on Arc networks show each activity as an arc, and the nodes represent the starting and ending points

We will use the AON method

AON Network for General Foundry Both A and B have no predecessors; thus both start the project and we need a dummy start.

If there was only one activity without an immediate predecessor, it would be the only start and we would not need a dummy start.

Dummy Start

AON Network for General Foundry C comes after A so it is drawn next.

D comes after BOTH A and B so it is drawn next with 2 arrows; one from each predecessor activity preceding it.

Both E and F come after C (individually), so we draw these two activities.

G comes after both D and E so it is drawn next with 2 arrows; one from each predecessor preceding it.

H comes after both F and G so it is drawn next with 2 arrows. It is the ONLY terminal activity, so there is no dummy.

Determining the Project Schedule  Some activities can be done simultaneously so

project duration should be less than 25 weeks (sum of times of all activities = 25)

 Critical path analysis is used to determine project duration

 The critical path is the longest time path through the network and the SHORTEST time for project completion.

 Once project network has been drawn to show all activities and precedence relationships, determine project schedule.   This includes the earliest time an activity can start

(ES) and finish (EF) without violating the precedence relationships. All precedence relationships must be honoured.

 After we have determined ALL the ES and EF, we must now determine the latest time an activity can start LS, and finish LF, without delaying the project beyond its earliest possible finish.

 We then determine the slack for each activity

7.3 Determining The Project Schedule

Critical Path Time Computations   To find the critical path, calculate two distinct starting and

ending times for each activity:   ES = Earliest time at which an activity can start,

assuming all predecessors have been completed.

  EF = Earliest time at which an activity can be finished.

  LS = Latest time at which an activity can start so as to not delay completion time of entire

project.   LF = Latest time by which an activity has to finish so as to not delay the completion time of

entire project.

Forward Pass  Identifies earliest times (ES and EF)

 ES Rule: All immediate predecessors must be done before an activity can begin

  If only 1 immediate predecessor, then ES = EF of predecessor

  If >1 immediate predecessors, then ES = Max {all predecessor EF’s}

EF = ES + activity time.

Forward Pass: Earliest Start & Finish Times

  In doing the forward pass, we go from start to finish: go with the flow of arrows

  ES and EF only; ES before EF   ES of an activity = Max {EF of all its

immediate predecessors}   EF = ES + time

ES EF

LS LF

Activity Time Node Notation:

Forward Pass: Earliest Start & Finish Times

  ES of both A and B we set at 0 for both activities start the project.

  EFA = 2; and EFB = 3   ESC = 2 which = EFA. EFC = 5   ESD = max {EFA,EFB} = max {2, 3} = 3. EFD

= 7   ESE and ESF = EFC = 4. EFE = 8; EFE = 7   ESG = max {EFD,EFE} = 8. EFD = 13   ESH = max {EFF,EFG} = 13. EFD = 15

Forward Pass: Earliest Start and Finish Times

Backward Pass   Identifies latest times (LS and LF)   LF Rule (we do not delay the project):

 If an activity is an immediate predecessor for a single activity, its LF equals the LS of the activity that immediately follows it, then

LF = LS of immediate follower  If activity is the immediate predecessor

to more than one activity, then LF = Min {LS of all immediate followers}   LS = LF – activity time

Backward Pass: Latest Start & Finish Times

  LFH = 15. Only terminal activity. LSH = 13   LFF = 13; LFG = 13; LSF = 10; LSG = 8   LFD = 8; LFE = 8; LSD = 4; LSE = 4   LFC = min {LSE, LSF} = min {4, 10} = 4. LSC

= 2   LFB = LSD = 4; LSB = 1   LFA = min {LSC, LSD} = min {2, 4} = 2. LSA =

0   LFSTART = min {LSA, LSB} = 0 = LSSTART

Backward Pass: Latest Start and Finish Times

Slack Time and Critical Path(s)  Slack is the length of time an activity can

be delayed without delaying the project Slack = LS – ES or LF – EF

 Activities with 0 slack are Critical Activities  The Critical Path is a continuous path

through the network from start to finish that include only critical activities. There are NO gaps or breaks between activities.

Project Schedule and Slack Times

Critical Path and Slack Times The critical Path is A→ C → E → G → H

Expected time is 15 weeks

Total Slack Time vs. Free Slack Time  Total slack time is shared by more than 1

activity Example: A 1 week delay in activity B will leave 0 slack for activity D

 Free slack time is associated with only 1 activity Example: Activity F has 6 week of free slack time

Variability in Activity Times

  Activity times are usually estimates that are subject to uncertainty

  Approaches to variability: 1.  Build “buffers” into activity times 2.  PERT – probability based 3.  Computer simulation

PERT Analysis  Uses 3 time estimates for each activity

Optimistic time (a) Pessimistic time (b) Most likely time (m)

 These estimates are used to calculate an expected value and variance for each activity (based on the Beta distribution)

Expected Time E[T] and Variance V[T]

Project Variance and Standard Deviation  Project variance (σp

2) is the sum of the variances of the CRITICAL activities only = ∑ (variances of all critical path activities) σp

2 = 0.11 + 0.11 + 1.0 + 1.78 + 0.11 = 3.11

 Project standard deviation (σp) = SQRT (Project variance) σp = SQRT ( 3.11) = 1.76

Probability of Project Completion  What is the probability of finishing the

project within 16 weeks?  Assumptions:

  Project duration is normally distributed   Activity times are independent

 Normal distribution parameters: µp = expected completion time= 15 weeks σp = proj standard deviation = 1.76 weeks

Normal Probability Calculations

This means 16 weeks is 0.57 standard deviations above the mean of 15 weeks.

Z(0.57) = 0.2157. Add 0.5 to get 0.7157

Prob (proj completion < 16 weeks) = 0.7157

Project Duration for a Given Probability •  What time must be set to ensure a 99%

chance of completion within that time?

•  This is the inverse transformation.

•  The Z value that corresponds to an area of 0.49 is 2.33

•  Project duration = σZ + µ (σ = 1.76; Μ = 15) •  Time = 1.76*2.33 + 15 •  Time = 19.1008 weeks

Consider The Following Projects   Draw The Project Networks   Determine the Expected Times and Variances   Determine the activity schedule (ES, EF, LS, LF, Slack)   Identify the critical activities   State the critical paths   What times must be set such that there is a guaranteed

90% (and 99%) time of completion?   What is the probability that project 1 will be completed

within 20 (and also 24) days?   What is the probability that project 2 will be done

within 70 (and also between 72 and 80; also between 60 and 75) days?

Activity Immediate

Predecessors a m b A -- 2 4 7 B A 3 6 10 C A 1 2 3 D B 2 4 6 E B 2 3 5 F B, C 3 4 6 G B 1 2 4 H F 2 3 4 I F, H 1 1.5 2 J I 2 3 4 K D, E 4 7 10

PRO

JECT 1

Activity Immediate

Predecessors a m b A – 8 10 12 B – 6 7 9 C – 3 3 4 D A 10 20 30 E C 6 7 8 F B, D, E 9 10 11 G B, D, E 6 7 10 H F 14 15 16 I F 10 11 13 J G, H 6 7 8 K I, J 4 7 8 L G, H 1 2 4

PRO

JECT 2

Activity Immediate Predecessors A – B – C A D B E B F B, C G B H F I F, H J I K D, E

PRO

JECT 3

PRO

JECT 4

Activity Immediate Predecessors

(a) (m) (b) A – 3 6 8 B A 5 8 10 C A 5 6 8 D B, C 1 2 4 E D 7 11 17 F D 7 9 12 G D 6 8 9 H F, G 3 4 7 I E, F, H 3 5 7

PRO

JECT 5

Activity Predecessors Normal Time A 5 B 6 C A 4 D A, B 3 E B 5 F C, D 2 G E 4 H E, G 2 I F, H 3 J G 2 K I, J 5

Activity on Node (AON) Network •  Arcs represent precedence relationships between

activities. •  There is only one activity (A) that does not have any

predecessor. Begin immediately, no dummy start. •  Draw one node for A. Also the start of the project

Project 1

A

•  Activities B and C have activity A as their only predecessor. Draw two arrows from A to B and C.

A B

C

Activity on Node (AON) Network •  Activities D, E, F and G have activity B as their

predecessor. Draw arrows from B to all of these. F also has C has a predecessor so draw an arrow from C to F. Notice where we put F so C can be clearly attached (arrows CAN cross).

Project 1

A B

C

D

E

G

F

Activity on Node (AON) Network •  Both activities H and I come after activity F. Activity

I also comes after activity H. Draw arrows from F to H and I and draw an arrow from H (newly drawn) to I

Project 1

A B

C

D

E

G

F

H

I

Activity on Node (AON) Network •  Activity J comes after activity I. Draw an arrow from

both I to J.

Project 1

A B

C

D

E

G

F

H

I

J

Activity on Node (AON) Network

•  Activities D and E precede Activity K. Draw arrows from both D and E to K.

Project 1

K

A B

C

D

E

G

F

H

I

J

Activity on Node (AON) Network •  All activities have been drawn, but we must clearly

identify the finish of the project. Notice that activities G, J and K have no successor activities, therefore they are all terminal (finish) activities. All these must be represented at the finish (dummy)

Project 1

A B

C

D

E

G

F

H

I

K

J

Finish