Chapter 16 –

Project Management

Operations Management

by

R. Dan Reid & Nada R. Sanders

2nd Edition © Wiley 2005 PowerPoint Presentation by R.B. Clough - UNH

Project Management Applications

 

What is a project?

  Any endeavor with objectives With multiple activities   With defined precedent relationships With a specific time period for completion

Examples?

   A major event like a wedding Any construction project Designing a political campaign

Five Project Life Cycle Phases

    

Conception:

identify the need

Feasibility analysis or study:

benefits, and risks costs

Planning:

who, how long, what to do?

Execution:

doing the project

Termination:

ending the project

Network Planning Techniques



Program Evaluation & Review Technique (PERT):

 Developed to manage the Polaris missile project  Many tasks pushed the boundaries of science & engineering (tasks’ duration = probabilistic) 

Critical Path Method (CPM):

 Developed to coordinate maintenance projects in the chemical industry  A complex undertaking, but individual tasks are routine (tasks’ duration = deterministic)

Both PERT and CPM

    Graphically display the precedence relationships & sequence of activities Estimate the project’s duration Identify critical activities that cannot be delayed without delaying the project Estimate the amount of slack associated with non-critical activities

Network Diagrams



Activity-on-Node (AON):

 

Uses nodes to represent the activity Uses arrows to represent precedence relationships

Step 1-Define the Project:

Cables By Us

is bringing a new product on line to be manufactured in their current facility in some existing space. The owners have identified 11 activities and their precedence relationships. Develop an AON for the project.

Activity

H I J K A B C D E F G

Description

Develop product specifications Design manufacturing process Source & purchase materials Source & purchase tooling & equipment Receive & install tooling & equipment Receive materials Pilot production run Evaluate product design Evaluate process performance Write documentation report Transition to manufacturing

Immediate Predecessor

None A A B D C E & F G G H & I J

Duration (weeks)

4 6 3 6 14 5 2 2 3 4 2

Step 2- Diagram the Network for Cables By Us

Step 3 (a)- Add Deterministic Time Estimates and Connected Paths

Step 3 (a) (

Continued

): Calculate the Path Completion Times

 

Paths

ABDEGHJK ABDEGIJK

Path duration

40 41 ACFGHJK 22 ACFGIJK 23 The longest path (ABDEGIJK) limits the project’s duration (project cannot finish in less time than its longest path)

ABDEGIJK is the project’s critical path

Some Network Definitions

      All

activities Slack

on the

critical path

defines how long have

zero slack non-critical activities delayed without delaying the project

can be

Slack

= the activity’s

late finish minus its early finish

(or its

late start minus its early start

) Earliest Start (

ES

) = the earliest finish of the immediately preceding activity Earliest Finish (

EF

) = is the

ES plus

the

activity time

Latest Start (

LS

) and Latest Finish (

LF

) depend on whether or not the activity is on the critical path

ES, EF Network

LS, LF Network

Calculating Slack

Activity

A B C D E F G H I J K

Late Finish

4 10 25 16 30 30 32 35 35 39 41

Early Finish

4 10 7 16 30 12 32 34 35 39 41

Slack (weeks)

0 0 18 0 0 18 0 1 0 0 0

A B C D H I J K E F G 0

Earliest Start Gantt Chart

5 10 15 20 25 30 35 40 45

A B C D H I J K E F G 0

Latest Start Gantt Chart

5 10 15 20 25 30 35 40 45

Revisiting

Cables By Us

Using Probabilistic Time Estimates

Activity

H I J K A B C D E F G

Description

Develop product specifications Design manufacturing process Source & purchase materials Source & purchase tooling & equipment Receive & install tooling & equipment Receive materials Pilot production run Evaluate product design Evaluate process performance Write documentation report Transition to manufacturing

Optimistic time

2 3 2 4 12 2 2 2 2 2 2

Most likely time

4 7 3 7 16 5 2 3 3 4 2

Pessimistic time

6 10 5 9 20 8 2 4 5 6 2

Using Beta Probability Distribution to Calculate Expected Time Durations  

A typical beta distribution is shown below, note that it has definite end points The expected time for finishing each activity is a weighted average Exp.

time



optimistic



4



most likely

 

pessimisti c 6

Calculating Expected Task Times

Expected time



optimistic

 4 

most likely

 

pessimisti c

6

Activity

A B C D E F G H I J K

Optimistic time

2 3 2 4 12 2 2 2 2 2 2

Most likely time

4 7 3 7 16 5 2 3 3 4 2

Pessimistic time

6 10 5 9 20 8 2 4 5 6 2

Expected time

4 6.83

3.17

6.83

16 5 2 3 3.17

4 2

Network Diagram with Expected Activity Times

Estimated Path Durations through the Network

Activities on paths

ABDEGHJK ABDEGIJK ACFGHJK ACFGIJK

Expected duration

44.66

44.83

23.17

23.34

 ABDEGIJK is the expected critical path & the project has an expected duration of

44.83 weeks

Estimating the Probability of Completion Dates

    Using probabilistic time estimates offers the advantage of predicting the probability of project completion dates We have already calculated the expected time for each activity by making three time estimates Now we need to calculate the variance for each activity The variance of the beta probability distribution is:

σ 2

  

p



o 6

 

2

 where p=pessimistic activity time estimate o=optimistic activity time estimate

Project Activity Variance

Activity H I J K E F G A B C D Optimistic 2 2 2 2 12 2 2 2 3 2 4 Most Likely 3 3 4 2 16 5 2 4 7 3 7 Pessimistic 4 5 6 2 6 10 5 9 20 8 2 Variance 0.44

1.36

0.25

0.69

1.78

1.00

0.00

0.11

0.25

0.44

0.00

Variances of Each Path through the Network

Path Number 1 Activities on Path A,B,D,E,G,H,J,k Path Variance (weeks) 4.82

2 3 A,B,D,E,G,I,J,K A,C,F,G,H,J,K 4.96

2.24

4 A,C,F,G,I,J,K 2.38

Calculating the Probability of Completing the Project in Less Than a Specified Time  

When you know:

  The expected completion time Its variance

You can calculate the probability of completing the project in “X” weeks with the following formula: z



specified time



path expected time path standard time

  

D T



EF P σ P 2

  Where DT = the specified completion date

EF P = the expected completion time of the path σ P 2



variance of path

Example: Calculating the probability of finishing the project in 48 weeks   Use the z values in Appendix B to determine probabilities E.G. for path 1

z

  

48 weeks



44.66

weeks 4.82

  

1.52

Path Number 1 2 3 Activities on Path Path Variance (weeks) z-value A,B,D,E,G,H,J,k A,B,D,E,G,I,J,K A,C,F,G,H,J,K 4.82

4.96

2.24

1.5216

1.4215

16.5898

4 A,C,F,G,I,J,K 2.38

15.9847

Probability of Completion 0.9357

0.9222

1.000

1.000

Reducing the Time of a Project (crashing) A H I J K B C D E F G Activity Normal Time (wk) 4 2 3 4 2 6 3 6 14 5 2 Normal Cost ($) 8,000 30,000 6,000 24,000 60,000 5,000 6,000 4,000 4,000 4,000 5,000 Crash Time 3 2 2 2 2 5 3 4 12 4 2 Crash Cost ($) 11,000 35,000 6,000 28,000 72,000 6,500 6,000 4,000 5,000 6,400 5,000 Max. weeks of reduction 1 0 1 2 0 1 0 2 2 1 0 Reduce cost per week 3,000 5,000 0 2,000 6,000 1500 0 0 1,000 1,200 0

Crashing Example: Suppose the

Us

product project from 41 to 36

Cables By

project manager wants to reduce the new weeks.   

Crashing Costs are considered to be linear Look to crash activities on the critical path Crash the least expensive activities on the critical path first (based on cost per week)

    Crash

activity I

from 3 weeks to 2 weeks $1000 Crash

activity J

Crash

activity D

from 4 weeks to 2 weeks $2400 from 6 weeks to 4 weeks $4000

Recommend Crash Cost $7400



Will crashing 5 weeks return more than it costs?

Crashed Network Diagram

Chapter 16 HW Assignment

Problems 1 – 8, 13 - 16