Project Planning, Scheduling and Control

1
Project Planning, Scheduling and Control

• Project a set of partially ordered,
  interrelated activities that must be completed to
  achieve a goal.

2
Network Models

• PERT Program Evaluation and Review Technique
• probabilistic features
• CPM Critical Path Method
• cost/time trade-offs

project scheduler
3
Objectives

• Planning, scheduling, and control of complex
  projects
• Find critical activities to manage resources
  (management by exception)
• Determine flexibility of non-critical activities
  (slack)
• Estimate earliest completion time of project
• Determine time cost trade-offs

4
Business and Industry a taxonomy
Service Industry
Distribution Industry
Producing Industry
Raw materials
Continuous Processing
Discrete Products
Mining Drilling Farming
Chemicals Food Refinery
Construction Manufacturing
Batch Mass Processing Production
5
Production Systems
Gosh. Can you tell us more about these?

• Job shops
• Flow shops
• Batch production
• Mass production
• Cellular manufacturing
• Project Shop
• Continuous Processing

6
Project Shop

• single product in fixed location
• material and labor brought to the site
• usually job shop/flow shop associated
• functionalized production system
• examples include construction and shipbuilding

7
The Elements of Project Scheduling

• Project Definition. Statement of project, goals,
  and resources required.
• Activity Definitions. Content and requirements of
  each activity.
• Project Scheduling. Specification of starting and
  ending times of all activities.
• Project Monitoring. Keeping track of the progress
  of the project.

8
Definitions

• Activity an effort (task) that requires
  resources and takes a certain amount of time.
• Event a specific accomplishment or milestone
  (the start or finish of an activity).
• Project a collection of activities and events
  leading to a definable goal.
• Network a graphical representation of a project
  depicting the precedence relationships among the
  activities and events.
• Critical Activity an activity that if delayed
  will hold up the scheduled completion of a
  project.
• Critical Path the sequence of critical
  activities that forms a continuous path from the
  start of a project to its completion.

9
Framework for Analysis

• Analyze project in terms of activities and events
• Determine sequence (precedence) of activities
  (develop network)
• Assign estimates of time, cost, and resources to
  all activities
• Identify the critical path
• monitor, evaluate, and control progress of project

10
Network Representation

• Projects may be represented as networks with
• Arrows representing activities.
• Nodes representing completion of a set of
  activities (milestones).
• Pseudo activities may be required to satisfy
  precedence relationships.

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Network Development
Activities have duration and may have precedence.
1
2
3
Define activities in terms of their beginning and
ending events. e.g. Activity 1-2 must precede
Activity 2-3
12
Network Development (continued)
2
Event 1 is start of project Activities 1-2, 1-3,
and 1-4 have no predecessors and may start
simultaneously
1
3
4
13
Network Development (continued)
n-3
Event n is the end of the project. Activities
(n-3 n, (n-2) n, and (n-1) - n must be
completed for the project to be completed.
n-2
n
n-1
14
Network Development (continued)
7
5
6
8
9
Activities 6-7, 6-8, and 6-9 cannot start until
activity 5-6 has been completed.
15
Network Development (continued)
5
8
9
6
7
Activities 5-8, 6-8, and 7-8 must be
completed before activity 8-9 may begin.
16
Network Development (continued)
9
5
8
10
6
11
7
Activities 5-8, 6-8, and 7-8 must be
completed before activity 8-9, 8-10, or 8-11 may
begin.
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Dummy activity
A C A D B D
W R O N G
dummy has no resources and no duration
18
Project Networks

• Collection of nodes and arcs
• Depicted graphically
• Events are uniquely numbered
• Arcs are labeled according to their beginning and
  ending events
• Ending events always have higher numbers than
  beginning events
• Two activities cannot have the same beginning and
  ending events
• Activity lengths have no significance

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Our Very Own Exampleproduct development
activity description precedence A design
promotion campaign - B initial
pricing - C product design - D promotion
cost analysis A E manufacture
prototype C F test and redesign E G final
pricing B,D,F H market test G
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product development
2
D
A
B
1
6
7
5
G
H
C
F
3
4
E
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Notation

• i-j an activity of a project
• di-j the duration of activity i-j
• Ei the earliest time event i can occur
• ESi-j the earliest start time of activity i-j
• EFi-j the earliest finish time of activity i-j
• LSi-j the latest start time of activity i-j
• LFi-j the latest finish time of activity i-j
• Li the latest time event i can occur

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Our Very Own Exampleproduct development
activity precedence duration (days) A
(1-2) - 17 B (1-5) - 7 C (1-3) - 33 D
(2-5) A 6 E (3-4) C 40 F (4-5) E 7 G
(5-6) B,D,F 12 H (6-7) G 48
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product development forward pass
2
D(6)
ES4-5 73 EF4-5 80
E5 80
A(17)
B(7)
1
6
7
5
G(12)
H(48)
C(33)
F(7)
3
ES2-5 17 ES3-4 33
4
ES5-6 80 EF5-6 92 E6 92
E1 0
E(40)
EF2-5 23 EF3-4 73
ES1-2 0 ES1-5 0 ES1-3 0
EF1-2 17 EF1-5 7 EF1-3 33
E2 17 E5 7 E3 33
ES6-7 92 EF6-7 140 E7 140
E4 73
24
product development backward pass
2
LF2-5 80 LS2-5 74
L7 140 LF6-7 140 LS6-7 92
D(6)
A(17)
B(7)
1
6
7
5
G(12)
H(48)
C(33)
F(7)
LF4-5 80 LS4-5 73
3
4
L6 92 LF5-6 92 LS5-6 80
L1 0
E(40)
L4 73
LF1-2 74 LF1-5 80 LF1-3 33
LS1-2 57 LS1-5 73 LS1-3 0
LF3-4 73 LS3-4 33
L2 74 L3 33
L5 80
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Activity Slack
Si-j LSi-j ESi-j
Activity LS ES Slack 1-2 57 0 57 1-5 73 0 73 1-
3 0 0 0 2-5 74 17 57 3-4 33 33 0 4-5 73 73 0 5
-6 80 80 0 6-7 92 92 0
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Critical Path Method

• An analytical tool that provides a schedule that
  completes the project in minimum time subject to
  the precedence constraints. In addition, CPM
  provides
• Starting and ending times for each activity
• Identification of the critical activities (i.e.,
  the ones whose delay necessarily delay the
  project).
• Identification of the non-critical activities,
  and the amount of slack time available when
  scheduling these activities.

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critical path
2
D(6)
A(17)
B(7)
1
6
7
5
G(12)
H(48)
C(33)
F(7)
3
4
E(40)
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Critical Path Activities

• focus management attention
• increase resources
• eliminate delays
• eliminate critical activities
• overlap critical activities
• break activity into smaller tasks
• outsource or subcontract

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Critical Path by LP
earliest start times
latest start times
30
Activity Durations
uniform
triangular
beta
a
b
31
More Activity Durations
let a optimistic time b pessimistic
time m most likely time
uniform triangular beta
32
activity durationsproduct development
beta
activity a m b A (1-2) 6 18 24 17 9 3 B
(1-5) 6 6 12 7 1 1 C (1-3) 24 30 54 33 25 5 D
(2-5) 6 6 6 6 0 0 E (3-4) 24 36 72 40 64 8 F
(4-5) 6 6 12 7 1 1 G (5-6) 6 12 18 12 4 2 H
(6-7) 36 48 60 48 16 4
note based upon a 6 day workweek
33
critical path analysisproduct development
beta
activity a m b C (1-3) 24 30 54 33 25 5 E
(3-4) 24 36 72 40 64 8 F (4-5) 6 6 12 7 1 1 G
(5-6) 6 12 18 12 4 2 H (6-7) 36 48 60 48 16 4 sum
140 110
34
Probability Statements
Probability project will be completed by day 150
is given by
35
Resource Constraints
Activity ES Duration staffing 1-2 0 17 5 1-5 0
7 7 1-3 0 33 10 2-5 17 6 4 3-4 33 40 6 4-5
73 7 3 5-6 80 12 5 6-7 92 48 6
36
Resource Profile early start schedule
30 25 20 15 10 5
1-5
1-2
2-5
1-3
3-4
5-6
4-5
0 10 20 30 40 50 60 70 80
37
Late Start Staffing
Activity ES Duration staffing 1-2 57 17 5 1-5
73 7 7 1-3 0 33 10 2-5 74 6 4 3-4 33 40 6 4
-5 73 7 3 5-6 80 12 5 6-7 92 48 6
38
Resource Profile late start schedule
30 25 20 15 10 5
2-5
1-2
1-5
1-3
3-4
5-6
4-5
0 10 20 30 40 50 60 70 80
39
Time Costing Methods

• Suppose that projects can be expedited by
  reducing the time required for critical
  activities. Doing so results in an increase in
  some costs and a decrease in others. The goal is
  to determine the optimal number of days to
  schedule the project to minimize total cost.
• Assume that there is a linear time/cost
  relationship for each activity.

40
Time-Cost Trade-offs
crash cost
normal cost
time
crash time
normal time
41
Heuristic Crashing
/ day
time cost activity normal crash normal
crash k C (1-3) 33 25 10 20 1.25 E
(3-4) 40 31 22 35 1.44 F (4-5)
7 5 8 12 2.0 G (5-6) 12 9 17
30 4.33 H (6-7) 48 40 30
48 2.25
42
An LP approach
let yi-j number of time units activity i-j is
crashed K indirect cost per day
43
The End

• Backups Follow

44
Forward Pass
If i-j not an activity
set ESi-j Ei EFi-j Ei di-j Ej max Ej ,
EFi-j
set Ei 0 i1 j2
If i-j is an activity
j lt n
set j j 1
j gt n
i i 1 j 2
i lt n
i n
stop
45
Backward Pass
If i-j not an activity
set LFi-j Li LSi-j Li - di-j Lj min Lj ,
LFi-j
set Li En i1 jn
If i-j is an activity
i lt n
set i i 1
i n
j j - 1 i 1
j gt 0
j 0
stop