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Project Scheduling: Lagging, Crashing and

Activity NetworksChapter 10

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1. Apply lag relationships to project activities.

2. Construct and comprehend Gantt charts. 3. Understand the trade-offs required in the

decision to crash project activities. 4. Develop activity networks using Activity-

on-Arrow techniques. 5. Understand the differences in AON and

AOA and recognize the advantages and disadvantages of each technique.

Learning Goals

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Lags in Precedence Relationships

The logical relationship between the start and finish of one activity and the start and finish of another activity.

Four logical relationships between tasks1. Finish to Start2. Finish to Finish3. Start to Start4. Start to Finish

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Most common type of sequencing Shown on the line joining the nodes

◦ Added during forward pass◦ Subtracted during backward pass

Finish-to-Start (FS) Lag

0 A 6Spec Design 6

6 B 11Design Check 5

15 C 22Blueprinting 7

Lag 4 days

This lag is not

the same as

activity slack

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Two activities share a similar completion point◦ The interior construction cannot happen until

wiring, plumbing, and HVAC installation are complete

Finish-to-Finish (FF) Lag

31 S 33Plumbing 2

33 T 39HVAC 3

39 U 45Interior Const. 6

30 R 36Wiring 6

Lag 3 days

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Often two or more activities must start at the same time

Start-to-Start (SS) Lag

31 S 33Plumbing 2

33 T 36HVAC 3

36 U 42Inspection 6

30 R 36Wiring 6

Lag 3

Logic must be maintained by both forward and backward pass

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Least common type of lag relationship Successor’s finish dependent on

predecessor’s start

Start-to-Finish (SF) Lag

22 S 28Plumbing 6

28 T 33HVAC 5

33 U 34Inspection 1

30 R 36Wiring 6

Lag 3

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Gantt Charts A graphical representation of the project schedule

that illustrates how work flows over time Shows activity start and end dates and durations Links project activities to a project schedule baseline Can be used as a tracking tool

Benefits of Gantt charts1. Easy to create, read, and comprehend2. Identify the project network and schedule baseline3. Allows for updating and control4. Useful to identify resource needs and assigning

resources to tasks

Example

Create a Gantt chart based on the activities listed in the table.

Task Time Predecessor

Z 8 --

Y 5 Z

X 8 Z

W 4 Y,X

V 5 W

U 3 W

T 6 V

S 7 U,T

R 9 S9

Gantt Chart Example from MSExcel

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Z

Y

X

W

V

U

T

S

R

0 5 10 15 20 25 30 35 40 45 50

Task Start DurationZ 0 8Y 8 5X 8 8W 16 4V 20 5U 20 3T 25 6S 31 7R 38 9

http://office.microsoft.com/en-us/excel/HA102382531033.aspx

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Sample Tracking Gantt Chart With Critical Path A-C-D-F-H

Critical path in red

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Crashing Projects

Accelerating a project by committing more resources.

Principal options for crashing Improving existing resources’ productivity Changing work methods used Increasing the quantity of resources

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The initial schedule may be too optimistic.

Market needs change and the project is in demand earlier than anticipated.

The project has slipped considerably behind schedule.

The contractual situation provides even more incentive to avoid schedule slippage.

Crashing Projects – Under What Conditions?

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Steps in Project Crashing

1. Compute the crash cost per time period. If crash costs are linear over time:

Crash costper period =

(Crash cost – Normal cost)

(Normal time – Crash time)

2. Using current activity times, find the critical path and identify the critical activities.

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3. If there is only one critical path, then select the activity on this critical path that

(a) can still be crashed, and (b) has the smallest crash cost per period.

4. If there is more than one critical path, then select one activity from each critical path such that

(a) each selected activity can still be crashed, and (b) the total crash cost of all selected activities is the

smallest.

Note: the same activity may be common to more than one critical path.

Steps in Project Crashing

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5. Update all activity times. 6. If the desired due date has been reached,

stop. If not, return to Step 2.

Steps in Project Crashing

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Time-Cost Tradeoffs for Crashing Activities

| | |1 2 3 Time (Weeks)

$34,000 —

$33,000 —

$32,000 —

$31,000 —

$30,000 —

—

Activity Cost

Crash Point

Normal Point

Crash Time Normal Time

Crash Cost

Normal Cost

Crash Cost/Wk = Crash Cost – Normal CostNormal Time – Crash Time

=$34,000 – $30,000

3 – 1

= = $2,000/Wk$4,0002 WksHow far do you

need to speedup the process?

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Formula Slope = crash cost – normal cost normal time – crash time

 Example – calculating the cost of crashing

Suppose: Normal activity duration = 8 weeksNormal cost = $14,000

Crashed activity duration = 5 weeksCrashed cost = $23,000 The activity cost slope =  

23,000 – 14,000 or, $9,000 = $3,000 per week 8 – 5 3

Crashing Activities – An Example

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Managerial Considerations

Determine activity fixed and variable

costs The crash point is the fully expedited

activity Optimize time-cost tradeoffs Shorten activities on the critical path Cease crashing when

◦ the target completion time is reached◦ the crash cost exceeds the penalty cost

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Crash Example

Activity Pred Normal Time Min Time

Normal Cost

Crash Cost

A -- 14 9 500 1500

B A 5 2 1000 1600

C A 10 8 2000 2900

D B, C 8 5 1000 2500

E D 6 5 1600 1900

F D 9 6 1500 3000

G E, F 7 4 600 1800

H G 15 11 1600 3600

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What is the lowest cost to complete this project in 53 weeks? Times are in weeks and costs in dollars.

Crash Example

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Activities represented by arrows Event nodes easy to flag Forward and backward pass

logic similar to AON Two activities may not begin

and end at common nodes Dummy activities may be

required

Activity on Arrow (AOA) Networks

Event label

Earliest Event Time (ES)

Latest Event Time (LF)

Task Description

Duration

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Sample AOA Network Diagram

1 2

3

4

A

B

C

111 2

3

4

A

B

C

222

333

444

A

B

C

Figure 10.18

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Activity on Arrow (AOA) Network

AH

F

E

D

C

B

K

G

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A Comparison of AON and AOA Network Conventions

Activity on Activity Activity onNode (AON) Meaning Arrow (AOA)

A comes before B, which comes before C

(a) A B CBA C

A and B must both be completed before C can start

(b)

A

CC

B

A

B

B and C cannot begin until A is completed

(c)

B

A

CA

B

C

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A Comparison of AON and AOA Network Conventions

Activity on Activity Activity onNode (AON) Meaning Arrow (AOA)

C and D cannot begin until both A and B are completed

(d)

A

B

C

D B

A C

D

C cannot begin until both A and B are completed; D cannot begin until B is completed. A dummy activity is introduced in AOA

(e)

CA

B D

Dummy activity

A

B

C

D

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A Comparison of AON and AOA Network Conventions

Activity on Activity Activity onNode (AON) Meaning Arrow (AOA)

B and C cannot begin until A is completed. D cannot begin until both B and C are completed. A dummy activity is again introduced in AOA.

(f)

A

C

DB A B

C

D

Dummy activity

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1. Please give examples of circumstances in which a project would employ lag relationships between activities using:

1. Finish to start2. Finish to finish3. Start to start4. Start to finish

2. The advantage of Gantt Charts lies in their linkage to the project schedule baseline. Explain this concept.

3. What are the advantages in the use of Gantt charts over PERT diagrams? In what ways might PERT diagrams be advantageous?

4. Under what circumstances might you wish to crash a project?

Discussion Questions

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5. In crashing a project, we routinely focus on those activities that lie on the critical path, not activities with slack time. Explain why this is the case.

6. What are some of the advantages in the use of AOA notation as opposed to AON? Under what circumstances does it seem better to apply AON methodology in network development? Explain the concept of a “dummy variable.” Why are they employed in AOA notation? Why is there no need to use dummy variables in an AON network?

7. Explain the concept of a “dummy variable.” Why are they employed in AOA notation? Why is there no need to use dummy variables in an AON network?

Discussion Questions