Networks

1
Networks

• Adding to our Project

2
PERT and CPM

• PERT
• Program Evaluation and Review Technique
• Activity on Arrow (arc)
• CPM
• Critical Path Method
• Activity on Node
• See Chapter 6
• Note that it prefers the AoN, we will still do
  AoA
• Spend more time with the conceptual in the chapter

3
Network Diagrams

• Describe work in terms of sequences, Activities
  and events
• All derive from simple logic diagrams
• Must know
• Activities
• Dependencies
• Durations

4
AoN vs. AoA

• Activity on Node
• Activity represented by a node
• Arrows show precedence
• Finish to Start
• Start to Start
• Finish to Finish

5
AoN vs. AoA

• Activity on Arrow (Arc)
• Activity represented by an arrow
• Arrows and Dummys show precedence
• Finish to Start
• Start to Start
• Finish to Finish

6
Steps

• Some trial and error!
• Start with activity that has no predecessors
• Add nodes for activities with start predecessor
• And so-on and so-on

7
Slack

• Difference in the latest allowable date and the
  earliest possible date
• Activities with slack are where we can manage!

8
Standard Labeling

• EF Early Finish
• Earliest possible Finish date of event
• LF Late Finish
• Latest possible Finish date for an event without
  extending the due date for a project
• S LF - EF
• Time we can wait (time we can manage!)

9
Standard Labeling

• ES Early Start
• Earliest possible Start date of event
• LS Late Start
• Latest possible Start date for an event without
  extending the due date for a project
• S LS - ES
• Time we can wait (time we can manage!)

10
Depiction on Chart
Name or Identification
Early Start
Early Finish
A(8,10)
2(15,17)
Duration
Late Finish
Late Start
11
Example

• Activity Predecessor Duration
• A -- 3
• B -- 2
• C A 3
• D A 7
• E B 5
• F C 6
• G D,E 5

12
Draw the Network

• Activity on Arrow

A
S
B
13
Draw the Network

• Activity on Arrow

C
A
D
S
B
E
14
Draw the Network

• Activity on Arrow

C
A
F
D
F
S
B
G
E
15
Steps Front Pass

• All numbers at start are 0
• Front Pass
• Early Start (ES) is the Highest of the Early
  Finishes for all predecessors
• Early Finish (EF) for an activity
• ES for an activity its own duration
• EF/LF for finish is always the same

16
Steps Back Pass

• All numbers at Finish are equal to the highest
  early finish of predecessors
• We will find late start and late finish
• Late Finish (LF) for an activity
• Lowest of late starts of all successors
• Late start (LS) is LF its own duration

17
Slack

• Slack LF EF
• Slack LS ES
• These should be the same
• Critical Path is where slack is 0

18
Depiction on Chart
Name or Identification
Early Start
Early Finish
A(8,10)
2(15,17)
Duration
Late Finish
Late Start
19
Draw the Network

• You make the call!

C(3,6) 3(6,9)
A(0,3) 3(0,3)
F(6,12) 6(9,15)
D(3,10) 7(3,10)
F
S
G(10,15) 5(10,15)
B(0,2) 2(2,5)
E(2,7) 5(5,10)
20
Cost

• Duration of activities can be affected by
  resources expended
• The expected range of cost varies
• There is a relationship that can be defined by a
  function
• We will stick to linear relationships

21
Crash

• We define these relationships
• Range between costs at normal time and the
  fastest possible time (Crash)
• Normal time/Crash time TN/TC
• Normal Cost/Crash Cost CN/CC
• Cost Slope

CC - CN Cost slope TC - TN
22
Cost Slope
Activity TN TC CN CC A 8 5 9
18
CC - CN Cost slope TC TN
18 - 9 5
8 -3
Cost of Activity
18
9
5
8
Duration of activity
23
Cost Slope

• Slope of -3 means?
• For every day (unit of time) that you speed up
  and activity it will cost you 3
• Each activity can be sped up
• It costs money!
• Where do we want to spend our money??

24
Assignment

• Do a network of your project.
• Activity listing with
• Durations (normal/crash)
• Predecessors
• Costs (normal/crash
• ES, EF, LS, LF for normal durations
• Suggest a cost savings step in your project