Deterministic Planning 1

1
1.040/1.401Project ManagementSpring
2007Deterministic Planning Part I

Dr. SangHyun Lee
lsh_at_mit.edu
Department of Civil and Environmental
Engineering Massachusetts Institute of Technology
2
Project Management Phase
DESIGN PLANNING
DEVELOPMENT
OPERATIONS
CLOSEOUT
FEASIBILITY
Fin.Eval.
Organization
Risk
Estimating
PlanningScheduling
3
Outline

• Objective
• Bar Chart
• Network Techniques
• CPM

4
Objective

• What are some of the Different Representations
  for Deterministic Schedules ?
• What are some Issues to Watch for?

5
Outline

• Objective
• Bar Chart
• Network Techniques
• CPM

6
Gantt Chart Characteristics

• Bar Chart
• Henry L. Gantt
• World War I - 1917
• Ammunition Ordering and Delivery
• Activities Enumerated in the Vertical Axis
• Activity Duration Presented on the Horizontal
  Axis
• Easy to Read

7
Simple Gantt Chart
8
Gantt (Bar) Charts

• Very effective communication tool
• Very popular for representation of simpler
  schedules
• Can be cumbersome when have gt100 activities
• Key shortcoming No dependencies captured
• Most effective as reporting format rather than
  representation

9
Hierarchy of Gantt Charts
10
Activity Aggregation

• Hammock Activities
• A graphical arrangement which includes a summary
  of a group of activities in the project.
• Duration equal to longest sequence of
  activities

Source Shtub et al., 1994
11
Activity Aggregation

• Milestones
• A task with a zero duration that acts as a
  reference point marking a major project event.
  Generally used to mark beginning end of
  project, completion of a major phase, or a task
  for which the duration is unknown or out of
  control.
• Flag the start or the successful completion of a
  set of activities

Source Shtub et al., 1994
12
Outline

• Objective
• Bar Chart
• Network Techniques
• CPM

13
Network Scheduling

• A network is a graphical representation of a
  project plan, showing the inter-relationships of
  the various activities.
• When results of time estimates computations are
  added to a network, it may be used as a project
  schedule.

Activity on Node AON
Source Badiru Pulat, 1995
14
Advantages

• Communications
• Interdependency
• Expected Project Completion Date
• Task Starting Dates
• Critical Activities
• Activities with Slack
• Concurrency
• Probability of Project Completion

Source Badiru Pulat, 1995
15
Network - Definitions
Node (Activity)
Arc
D
A
Milestone
Merge Point
Finish
B
G
E
Dummy
H
F
C
Burst Point
I
Source Badiru Pulat, 1995
16
Network - Definitions
D
A
Finish
B
G
E
H
F
C
I

• Predecessor Activity of D
• Successor Activity of F

Source Badiru Pulat, 1995
17
Definitions (Contd)

• Activity
• Time and resource consuming effort with a
  specific time required to perform the task or a
  set of tasks required by the project
• Dummy
• Zero time duration event used to represent
  logical relationships between activities
• Milestone
• Important event in the project life cycle
• Node
• A circular representation of an activity and/or
  event

Source Badiru Pulat, 1995
18
Definitions (Contd)

• Arc
• A line that connects two nodes and can be a
  representation of an event or an activity
• Restriction / Precedence
• A relationship which establishes a sequence of
  activities or the start or end of an activity
• Predecessor Activity
• An activity that immediately precedes the one
  being considered
• Successor Activity
• An activity that immediately follows the one
  being considered
• Descendent Activity
• An activity restricted by the one under
  consideration
• Antecedent Activity
• An activity that must precede the one being
  considered

Source Badiru Pulat, 1995
19
Definitions (Contd)

• Merge Point
• Exists when two or more activities are
  predecessors to a single activity (the merge
  point)
• Burst Point
• Exists when two or more activities have a common
  predecessor (the burst point)
• Network
• Graphical portrayal of the relationship between
  activities and milestones in a project
• Path
• A series of connected activities between any two
  events in a network

Source Badiru Pulat, 1995
20
Outline

• Objective
• Bar Chart
• Network Techniques
• CPM

21
Critical Path Method (CPM)

• DuPont, Inc., and UNIVAC Division of Remington
  Rand
• Scheduling Maintenance Shutdowns in Chemical
  Processing Plants
• 1958
• Construction Projects
• Time and Cost Control
• Deterministic Times

22
CPM Objective

• Determination of the critical path the minimum
  time for a project

23
CPM Precedence

• Technical Precedence
• Caused by the technical relationships among
  activities (e.g., in conventional construction,
  walls must be erected before roof installation)
• Procedural Precedence
• Determined by organizational policies and
  procedures that are often subjective with no
  concrete justification
• Imposed Precedence
• E.g., Resource Imposed (Resource shortage may
  require one task to be before another)

Source Badiru Pulat, 1995
24
CPM AOA AON

• Activity-on-Arrow
• Activity-on-Node

Source Feigenbaum, 2002 Newitt, 2005
25
CPM Calculations

• Forward Pass
• Early Start Times (ES)
• Earliest time an activity can start without
  violating precedence relations
• Early Finish Times (EF)
• Earliest time an activity can finish without
  violating precedence relations

Source Hegazy, 2002 Hendrickson and
Au, 1989/2003
26
Forward Pass - Intuition

• Its 8am. Suppose you want to know the earliest
  time you can arrange to meet a friend after
  performing some tasks
• Wash hair (5 min)
• Boil water for tea (10 min)
• Eat breakfast (10 min)
• Walk to campus (5 min)
• What is the earliest time you could meet your
  friend?

27
CPM Calculations

• Backward Pass
• Late Start Times (LS)
• Latest time an activity can start without
  delaying the completion of the project
• Late Finish Times (LF)
• Latest time an activity can finish without
  delaying the completion of the project

Source Hegazy, 2002 Hendrickson and
Au, 1989/2003
28
Backward Pass - Intuition

• Your friend will arrive at 9am. You want to know
  by what time you need to start all things
• Wash hair (5 min)
• Boil water for tea (10 min)
• Eat breakfast (10 min)
• Walk to campus (5 min)
• What is the latest time you should start?

29
Slack or Float

• Its 8am, and you know that your friend will
  arrive at 9am. How much do you have as free time?
  
• Wash hair (5 min)
• Boil water for tea (10 min)
• Eat breakfast (10 min)
• Walk to campus (5 min)

30
CPM Example
Draw AON network
Source Badiru Pulat, 1995
31
Forward Pass
F 4
A 2
End
D 3
ES
EF
0
0
G 2
B 6
Start
E 5
C 4
Source Badiru Pulat, 1995
32
Forward Pass

2
6
F 4
0
2
11
11
A 2
2
5
End
D 3
9
11
0
6
0
0
G 2
B 6
Start
0
4
4
9
E 5
C 4
Source Badiru Pulat, 1995
33
Backward Pass

2
6
F 4
0
2
11
11
A 2
2
5
End
D 3
11
11
9
11
0
6
LS
LF
0
0
G 2
B 6
Start
0
4
4
9
E 5
C 4

• LF(k) MinLS(j) j S(k)
• LS(k) LF(k) D(k)

?
Source Badiru Pulat, 1995
34
Backward Pass

2
6
F 4
0
2
11
11
7
11
A 2
2
5
End
D 3
4
6
11
11
6
9
9
11
0
6
0
0
G 2
B 6
Start
9
11
0
0
3
9
0
4
4
9
E 5
C 4
0
4
4
9
Source Badiru Pulat, 1995
35
Slack or Float

• The amount of flexibility an activity possesses
• Degree of freedom in timing for performing task

2
6
4
F 4
0
2
11
11
7
11
A 2
End
2
5
D 3
4
6
11
11
6
9
9
11
0
0
G 2
B 6
0
6
Start
9
11
0
0
3
9
0
4
4
9
E 5
C 4
0
4
4
9
Source Hendrickson and Au, 1989/2003
36
Total Slack or Float

• Total Slack or Float (TS or TF)
• Max time can delay w/o delaying the project
• TS(k) LF(k) - EF(k) or LS(k) - ES(k)

2
6
TS 4
F 4
0
2
11
11
7
11
A 2
End
2
5
D 3
4
6
11
11
6
9
9
11
0
0
G 2
B 6
0
6
Start
9
11
0
0
3
9
0
4
4
9
E 5
C 4
0
4
4
9
37
Free Slack or Float

• Free Slack or Float (FS or FF)
• Max time can delay w/o delaying successors
• FS(k) MinES(j) - EF(k) j S(k)

?
2
6
F 4
0
2
11
11
7
11
A 2
End
2
5
D 3
4
6
11
11
FS 3
6
9
9
11
0
0
G 2
B 6
0
6
Start
9
11
0
0
3
9
0
4
4
9
E 5
C 4
0
4
4
9
38
Independent Slack or Float

• Independent Slack or Float (IF)
• Like Free float but assuming worst-case finish of
  predecessors
• IF(k) Max 0, ( Min(ES(j)) - Max(LF(i)) D(k)
  ) j S(k), i P(k)

?
?
IF 1
2
6
F 4
0
2
11
11
7
11
A 2
End
2
5
D 3
4
6
11
11
6
9
9
11
0
0
G 2
B 6
0
6
Start
9
11
0
0
3
9
0
4
4
9
E 5
C 4
0
4
4
9
39
CPM Analysis

Activity
Duration
ES
EF
LS
LF
TS
FS
IF
Critical
A
2
0
2
4
6
4
0
0
B
6
0
6
3
9
3
3
3
C
4
0
4
0
4
0
0
0
Yes
D
3
2
5
6
9
4
4
0
E
5
4
9
4
9
0
0
0
Yes
F
4
2
6
7
11
5
5
1
G
2
9
11
9
11
0
0
0
Yes
Adapted from Badiru Pulat, 1995
40
Critical Path

• The path with the least slack or float in the
  network
• Activities in that path critical activities
• For algorithm as described, at least one such
  path
• Must be completed on time or entire project
  delayed
• Determines minimum time required for project
• Consider near-critical activities as well!

41
Critical Path
If EFi ESj, then activity i is a critical
activity (here, activity i is an immediate
predecessor of activity j

2
6
F 4
0
2
11
11
7
11
A 2
End
2
5
D 3
4
6
11
11
6
9
9
11
0
0
G 2
B 6
0
6
Start
9
11
0
0
3
9
0
4
4
9
E 5
C 4
0
4
4
9
Source Badiru Pulat, 1995
42
Path Criticality

• Rank paths from more critical to less critical

minimum total float maximum total
float total float or slack in current path
43
Path Criticality - Example

• Calculate Path Criticality
• amin 0, amax 5
• Path 1 (5-0)/(5-0)(100 ) 100
• Path 2 (5-3)/(5-0)(100 ) 40
• Path 3 (5-4)/(5-0)(100 ) 20
• Path 4 (5-5)/(5-0)(100 ) 0

Source Badiru Pulat, 1995