2/21 Project Management• Roll call/ collect homework

• Go over homework(?)

• Project management: Critical Path Method

• Small groups

• Assign homework

• Discuss midterm exam

Project Modeling• Project: build a house.

– Various tasks to be accomplished to achieve this goal:

• get permits

• pour foundations

• install electrical systems

• install plumbing systems

• connect systems to public systems

• frame walls

• install flooring

Project Modeling: CPM

• How to organize? How to plan?

• How long will the entire project take?

• Critical Path Model - Terms– Activity on Node– predecessor– duration

Project Modeling: CPM

• How to organize? How to plan?

• How long will the entire project take?

• Critical Path Model - Terms– Activity on Node– predecessor– duration

Project Modeling: CPM

• How to organize? How to plan?

• How long will the entire project take?

• Critical Path Model - Terms– Activity on Node– predecessor– duration

As long as the longest (duration) series of activities takes -- also call the CRITICAL PATH.

Critical Path Method - Terms.• Activity on Node

Nodes: activities

Arc: precedence

Duration (EX: hrs., days)

StartA6

B8

Finish

Critical Path Method: Terms• “Activity A must be done before B can

begin.” - Activity A is a PREDECESSOR of B.

StartA6

B8

Finish

Arc: precedence

Nodes: activities

Critical Path Method: Terms• “Activities A and B must be done before C

can begin.” - A & B are PREDECESSORS of C.

Start

A6

B8

Finish

Arcs: predecessors

C5

Nodes: activities

Critical Path Method

• “Activity A must be done before C and B can begin.”

StartA6

B8

Finish

Arcs: predecessors

C5

Nodes: activities

EX: build a house• Project tasks:

– install landscaping– pour foundations– frame walls – install plumbing systems– get permits– install electrical systems– move in.

EX: build a house: tasks in order– get permits– pour foundations– frame walls – install plumbing systems– install electrical systems– install landscaping– move in.

EX: build a house: durations– get permits– pour foundations– frame walls – install plumbing systems– install electrical systems– install landscaping– move in.

Durations:26

5

4

6

9

3

EX: build a house: label activities– A: get permits– B: pour foundations– C: frame walls – D: install plumbing– E: install electrical – F: install landscaping– G: move in.

Durations:26

5

46

3

Durations:26

5

46

9

3

EX: build a house: create table– A: get permits– B: pour foundations– C: frame walls – D: install plumb.– E: install elec.– F: install landscaping – G: move in.

Durations:26

5

46

9

3

Act. Dur. Preds. Post.A 2 -- DB 6 -- C,FC 5 B DD 4 A,C EE 6 D GF 9 B GG 3 E,F

EX: build a house: create graphic CPM

start

A

B

C

D E

F

G finish

Act Dur Pre Post

A 2 - D

B 6 - C,F

C 5 B D

D 4 A,C E

E 6 D G

F 9 B G

G 3 E,F

EX: build a house: add in durations

start

A2

B6

C5

D4

E6

F9

G3

finish

Act Dur Pre Post

A 2 - D

B 6 - C,F

C 5 B D

D 4 A,C E

E 6 D G

F 9 B G

G 3 E,F

But what is the Critical Path?

The critical path is the path of activities that takes the longest amount of time; the path with the activities that cannot be altered time-wise without changing the overall project duration.

(We must tell the family when the house will be done -- how soon?)

start

A2

B6

C5

D4

E6

F9

G3

finish

What is the Critical Path?

start

A2

B6

C5

D4

E6

F9

G3

finish

Add up all the paths possible; see what path is the longest. That path is the critical path.

A-D-E-G = 12B-C-D-E-G = 24B-F-G = 18

Defining slack, ES, EF, LS, LF• Slack: how much extra time you have available for a

particular activity.• ES -- early start: the earliest possible time you could

begin a particular activity.• EF -- early finish: the earliest possible time you could

finish a particular activity.• LS -- late start: the latest possible time you could begin

a particular activity.• LF -- late finish: the latest possible time you could

finish a particular activity.

Calculating slack, ES, EF, LS, LF

• Slack = (time available) - (duration)

• ES = (calc. time at the beginning of the node)

• EF = ES + duration

• LS = LF - duration

• LF = (calc. time at the ending of the node)

Calculating slack

start

A2

B6

C5

D4

E6

F9

G3

finish

Any activity on the critical path has NO SLACK.Any others are based on when they meet the critical path.EX: Activity A requires two days, but there are 11 days available

( Activity A meets the critical path at “start” (0) and at D. 11 days have passed on the critical path before getting to D (B+C=11).

Calculating ES (Early Start)Early start is the earliest possible time the activity could start.EX: Activity A could start (at the earliest) at 0. Activity D could start (at the earliest) at 11 (CP – No slack) Activity F could start (at the earliest) at 6.

start

A2

B6

C5

D4

E6

F9

G3

finish

Calculating EF (Early Finish)Early finish is the earliest possible time the activity could finish.EF = ES + Duration.EX: Activity A could finish (at the earliest) at 2 (0 + 2). Activity D could finish (at the earliest) at 15 (11 + 4) (CP).

Activity F could finish (at the earliest) at 15 (6 + 9).

start

A2

B6

C5

D4

E6

F9

G3

finish

Calculating LF (Late Finish)Late finish is the latest possible time the activity could finish without

affecting the overall project time.EX: Activity A could finish (at the latest) at 11. Activity D could finish (at the latest) at 15 (Crit path – no slack).

Activity F could finish (at the latest) at 21.

start

A2

B6

C5

D4

E6

F9

G3

finish

Calculating LS (Late Start)Late start is the latest possible time the activity could start w/o

affecting the overall project time.LS = LF – Duration.EX: Activity A could start (at the latest) at 9 (11 – 2). Activity D could start (at the latest) at 11 (crit. path – no slack).

Activity F could start (at the latest) at 12 (21 – 9).

start

A2

B6

C5

D4

E6

F9

G3

finish

Labeling the CPM Basic model:

start

B 0 66 0 6

C 6 115 6 11

D 10 154 10 15

E 15 216 15 21

F 6 159 12 21

G 21 243 21 24

finish

Activity ES EF

Duration LS LF

A 0 22 9 11

Small Group Exercise• Installation of a computer system comprises

eight activities. Draw the network model, calculate the ES, EF, LS, LF, and slack for each activity.

Activity Immediate Predecessors

Duration

A - 3

B - 6

C A 2

D B, C 5

E D 4

F E 3

G B, C 9

H F, G 3

HomeworkCh. 10 #2 (just draw the CPM model in Excel)

Ch. 10 #4 (draw the CPM model in Excel, calculate the critical path.)

Ch. 10 #8 (draw the CPM model in Excel, calculate and label all activities with ES, EF, LS, LF. Calculate the critical path. Calculate the slack for each activity.)

Ch. 10 #9 (calculate the critical path, calculate the ES, EF, LS, LF, and slack for each activity)

About the Midterm Exam• Three versions – make sure you do the right one.

• NO COLLABORATIONCollaboration=Cheating

• When you open the spreadsheet, click on “Enable Macros” (if it comes up).

• The midterm is posted (by 9 p.m. Thursday) athttp://www.adbook.net/teach022/305/m.htm

• It is due by 9:00 p.m. on Saturday, Feb. 23rd.

• Read the directions very carefully!