MBA Course Lecture for Supply Chain Management System

1. Project Scheduling
(PERT/CPM)
Network Diagram

2. • The most critical element in the project management
process, especially during the implementation phase
• Source of most conflict and problems
• Frequently the single most important criterion for the success
of a project is that it be finished on time
• Time is also a measure of progress that is very visible
• It is an absolute with little flexibility. You can spend less money
or use fewer people but you cannot slow down or stop the
passage of time
Project Scheduling
• Sequencing & allotting time to all project activities

3. • Define the activities that must be performed to complete the
project
• Sequence the activities in the order in which they must be
completed
• Estimate the time required to complete each activity
• Develop the schedule based on this sequencing and time
estimates of the activities
Developing Project Schedule

4. • The process of project planning and control is greatly aided by the
use of techniques that help project managers to handle its
complexity and time-based nature
⁻ Gantt chart
⁻ Network Analysis Techniques-
1. PERT
2. CPM
Network Planning

5. A graph or bar chart with a bar for each project activity that shows the
passage of time.
• Simplest
• Excellent visual impact
• Easy to understand
Gantt Chart

6. Gantt Chart
• Fail to reveal certain relationships among activities that can be
crucial to project managers e.g., critical & non-critical activities.
• If one of the early activities suffers a delay, managers need to easily
determine which later activities would result in a delay.
• Conversely, some activities may safely be delayed without affecting
the overall project schedule.
• On more complex projects it is used in conjunction with a network
diagram.

7. Gantt Chart

8. A network of activity and event relationships that graphically
portrays the sequential relations between the tasks in a project
Network Technique
PERT -- Program Evaluation and Review Technique
CPM -- Critical Path Method
• Probabilistic activity time
• Research & Development
• Deterministic activity time
• Construction/Production/Market Survey
This approach helps in project planning, scheduling, monitoring, & controlling.

9. Developing the Project Network
• The Project Network Defined
- Is a graphic flow chart depicting the project activities that must be
completed, the logical sequences, the interdependencies of the
activities to be completed, and the times for the activities to start
and finish along with the longest path(s) through the network—
the critical path.
- Provides the basis for scheduling labor and equipment.
- Enhances communication among project stakeholders.
9

10. Developing the Project Network
• The Project Network Defined (cont.)
- Provides an estimate of project duration.
- Provides the basis for budgeting the cash flow.
- Identifies which activities are “critical” and should not be delayed.
- Highlights which activities to consider for compressing the project
duration.
- Helps managers get and stay on the project plan.
10

11. • Activity- Individual job or work effort requiring labor, resources and time, and is
subject to management control.
• Precedence relationship- The sequential relationship of project activities to
each other
• Slack- The amount of time an activity can be delayed without delaying the
project
• Critical activity- Any delay with this activity will cause a delay to the entire
project
• Non-critical activity- Delay doesn’t have an impact on the entire project.
• Event- Moments in time that occur at the start or finish of an activity.
Represented by a circle. Consumes no time and resources.
Some terminologies

12. Constructing a Project Network
• Terminology
- Parallel activities: activities that can take place at the same time, if desired.
- Burst activity: an activity that has more than one activity immediately
following it (more than one dependency arrow flowing from it)
- Merge activity: an activity that has more than one activity immediately
preceding it (more than one dependency arrow flowing to it)
- Path: a sequence of connected, dependent activities
- Critical path: the path with the longest duration through the network
12

13. Constructing a Project Network
• Two approaches
- Activity-on-Node (AON) uses a node to depict an activity.
- Activity-on-Arrow (AOA) uses an arrow to depict an activity.
13

14. Basic Rules to Follow in Developing Project Networks
1. Networks flow typically from left to right.
2. An activity cannot begin until all preceding connected activities
have been completed.
3. Arrows on networks indicate precedent and flow and can cross
over each other.
4. Each activity should have a unique identification number.
14

15. 5. An activity identification number must be greater than that of any
activities that precede it.
6. Looping is not allowed.
7. Conditional statements are not allowed.
8. Where there are multiple starts, a common start node can be used
to indicate a clear project beginning on the network. Similarly, a
single project end node can be used to indicate a clear ending.
15
Basic Rules to Follow in Developing Project Networks

16. Activity-on-Node
(AON)/CPM/PDM
Fundamentals
16

17. Network Information (Automated Warehouse)
17

18. Automated Warehouse—Partial Network
18

19. Automated Warehouse—Completed Network
19

20. Network Computation Process
• Forward Pass—Earliest Times
• How soon can the activity start? (early start—ES)
• How soon can the activity finish? (early finish—EF)
• How soon can the project finish? (expected time—TE)
• Backward Pass—Latest Times
• How late can the activity start? (late start—LS)
• How late can the activity finish? (late finish—LF)
• Which activities represent the critical path? (critical path—CP)
• How long can the activity be delayed? (slack or float—SL)
20

21. Network Information (Automated Warehouse)
21

22. Activity-on-Node Network
22

23. Activity-on-Node Network Forward Pass
23
Activit
y
Prede
cesso
r
Durati
on
A - 10
B A 5
C A 25
D B 20
E C 50
F C 15
G D 35
H E,F,G 15

24. Forward Pass Computation
• Add activity times along each path in the network (ES + Duration =
EF).
• Carry the early finish (EF) to the next activity where it becomes its
early start (ES) unless…
• The next succeeding activity is a merge activity, in which case the
largest early finish (EF) number of all its immediate predecessor
activities is selected.
24

25. Activity-on-Node Network Backward Pass
25
Activit
y
Prede
cesso
r
Durati
on
A - 10
B A 5
C A 25
D B 20
E C 50
F C 15
G D 35
H E,F,G 15

26. Backward Pass Computation
• Subtract activity times along each path starting with the project end
activity (LF – Duration = LS).
• Carry the late start (LS) to the next preceding activity where it
becomes its late finish (LF) unless…
• The next succeeding activity is a burst activity, in which case the
smallest late start (LS) number of all its immediate successor
activities is selected.
26

27. Forward and Backward Pass Completed with Slack Times
27
Activit
y
Prede
cesso
r
Durati
on
A - 10
B A 5
C A 25
D B 20
E C 50
F C 15
G D 35
H E,F,G 15

28. Determining Slack (or Float) Times
• Total Slack
• Tells us the amount of time an activity can be delayed and
not delayed the project.
• Is how long an activity can exceed its early finish date
without affecting the project end date or an imposed
completion date.
• Is simply the difference between the LS and ES (LS – ES
= SL) or between LF and EF (LF – EF = SL).
28

29. Determining Slack (or Float) Times
• Free Slack
• Is the amount of time an activity can be delayed without
delaying any immediately following (successor) activity.
• Is how long an activity can exceed its early finish date
without affecting the early start dates of any successor(s).
• Allows flexibility in scheduling scarce resources.
• Occurs only activity at the end of a chain of activities,
where you have a merge activity.
29

30. The Critical Path
• Is the network path(s) that has (have) the least slack in common.
• Is the longest path through the activity network.
• Is the shortest expected time in which the entire project can be completed.
• Is important because it impacts completion time.
• Is where you put best people on.
• Is where you pay extra attention when doing risk assessment.
• Is where you don’t look when other managers are asking to ‘borrow’ people or
equipment.
• Is where you look when you don’t have time to monitor all activities.
30

31. Network Logic Errors—Illogical Loop
31

32. Automated Warehouse Picking System Network
32

33. Automated Warehouse Picking System Gantt Chart
33

34. 1. Each defined activity is
shown by a unique branch
2. Branches show only the
relationship between different
activities; the length of the
branches have no significance
3. Branches direction indicates
the general progression in
time. The branch head
represents the point in time at
which an “activity
completion event” takes
place. In a similar manner
the branch tail represent the
point in time at which an
“activity start event” occurs
Activity on Arrow/PERT/ADM

35. 1
2
3
4 5
A
B
C
D
4. When a number of activities terminate
at one event, this indicates that no
activity starting from that event may start
before all activities have been completed

36. 5. Events are identified by numbers. An effort should be made
to have each event identified by a number higher that the
immediately preceding event.
6. Activities are identified by the numbers of their starting
events and ending events, and are specified by capital
letters

37. 7. Two or more activities are not allowed to share the same beginning and
ending events. In a situation like this in which two or more activities can
be done concurrently , a dummy activity is used to ensure that the proper
activity relationship are depicted by the network. Dummy activities have
no duration or costs.

38. 8. There should be one starting point and one finishing
point for the entire network
9. No looping is allowed

39. CPM & PERT – Convention

42. Activity Immediate
Predecessor
Duration
a. remove
furniture
none 1
a. Prepare
bed room
a 2
a. Paint bed
room
b 3
a. Prepare
kitchen
a 1
a. Paint
kitchen
d 2
a. Replace
furniture
c, e 1

43. Class Problems:
1. Activity Predecessor
A ----
B ----
C A, B
D B

45. Class Problems:
2. Activity Predecessor
A ----
B ----
C A, B
D A

46. Class Problems:
3. Activity Predecessor
A ----
B ----
C A, B
D A, B

47. Class Problems:
4. Activity Predecessor
A ----
B ----
C A, B
D A, B
E A

48. Class Problems:
5. Activity Predecessor
A ----
B ----
C A, B
D A, B
E A
F B

49. Class Problems:
6. Activity Predecessor
A ----
B ----
C A, B
D A, B
E A
F B
G C, D

53. Example
Activity Description Immediate
predecessor
Time (weeks)
A Build internal components -- 2
B Modify roof & floor -- 3
C Construct collection stack A 2
D Pour concrete & install frame A,B 4
E Build high temperature burner C 4
F Install pollution control system C 3
G Install air pollution device D,E 5
H Inspect & test F,G 2

55. Example – AON Network
2
A
2
H
3
B
5
G
4
E
4
D
3
F
2
C
START
Duration
Activity

56. Example – AON Forward Pass
2
2
A
0
2
15
H
13
3
3
B
0
5
13
G
8
4
8
E
4
4
7
D
3
3
7
F
4
2
4
C
2
START
LF Duration
Late Start
Activity
Early Start
Late Finish
Early Finish
0

57. Example – AON Backward Pass
2
2
0
2
A
0
15
2
13
15
H
13
4
3
1
3
B
0
13
5
8
13
G
8
8
4
4
8
E
4
8
4
4
7
D
3
13
3
10
7
F
4
4
2
2
4
C
2
START
LF Duration
Late Start
Activity
Early Start
Late Finish
Early Finish
0
0

58. Example – AON Total Float
2
2
0
2
A
0
15
2
13
15
H
13
4
3
1
3
B
0
13
5
8
13
G
8
8
4
4
8
E
4
8
4
4
7
D
3
13
3
10
7
F
4
4
2
2
4
C
2
START
LF Duration
Late Start
Activity
Early Start
Late Finish
Early Finish
0
0
TF=6
TF=0
TF=1
TF=0
TF=0
TF=1
TF=0
TF=0
Total Float=LF-EF or LS-ES

59. Example – AON Critical Path
2
2
0
2
A
0
15
2
13
15
H
13
4
3
1
3
B
0
13
5
8
13
G
8
8
4
4
8
E
4
8
4
4
7
D
3
13
3
10
7
F
4
4
2
2
4
C
2
START
LF Duration
Late Start
Activity
Early Start
Late Finish
Early Finish
0
0
TF=6
TF=0
TF=1
TF=0
TF=0
TF=1
TF=0
TF=0

60.  Critical Path: A-C-E-G-H; Path time, TP1 = 15 weeks
 Non critical Path: A-C-F-H; TP2 = 9 weeks
 Non critical Path: A-D-G-H; TP3 = 13 weeks
 Non critical Path: B-D-G-H; TP4 = 14 weeks
Example – AON: Critical & Noncritical Path

61.  Activity B & D share their total slack/float
 Typically, when two or more non-critical activities appear
successively in a path, they share total slack
Example – AON: Total Slack & Shared Slack

62. Variability in Activity Time
Activity Optimistic time
(a)
Most likely
(m)
Pessimistic
time (b)
A 1 2 3
B 2 3 4
C 1 2 3
D 2 4 6
E 1 4 7
F 1 2 9
G 3 4 11
H 1 2 3

63. Example – AOA: Network
2 4
6 7
5
3
1
A
2
C
2 F
3
5
G
D
4
B
3
H
2
E
4

64. Example – AOA: Backward Pass
2
2 4 4
13
13 15 15
8
8
3
4
0
0
A
2
C
2 F
3
5
G
D
4
B
3
H
2
E
4
EET
LET
EET: Earliest event time
LET: Latest event time

65. Example – AOA: Total Float
2
2 4 4
13
13 15 15
8
8
3
4
0
0
A
2
C
2 F
3
5
G
D
4
B
3
H
2
E
4
TF=0
TF=0
TF=1
TF=0
TF=1
TF=0
TF=6
TF=0
EET: Earliest event time
LET: Latest event time
TF: LET(suc) - Duration – EET
FF: EET(suc) - Duration – EET

66. Example – AOA: Critical Path
2
2 4 4
13
13 15 15
8
8
3
4
0
0
A
2
C
2 F
3
5
G
D
4
B
3
H
2
E
4
TF=0
TF=0
TF=1
TF=0
TF=1
TF=0
TF=6
TF=0
EET: Earliest event time
LET: Latest event time
TF: LET(suc) - Duration – EET
FF: EET(suc) - Duration – EET

67. Variability in Activity Time
Expected time, 𝑡 =
𝑎+4𝑚+𝑏
6
Variance, 𝜎2 =
(𝑏−𝑎)
6
2

68. Variability in Activity Time (contd.)
Activity Optimistic time
(a)
Most likely
(m)
Pessimistic
time (b)
Expected time
𝒕 =
𝒂 + 𝟒𝒎 + 𝒃
𝟔
Variance
(𝒃 − 𝒂)
𝟔
𝟐
A 1 2 3 2 0.11
B 2 3 4 3 0.11
C 1 2 3 2 0.11
D 2 4 6 4 0.44
E 1 4 7 4 1.00
F 1 2 9 3 1.78
G 3 4 11 5 1.78
H 1 2 3 2 0.11

69. PERT makes 2 assumptions:
1.Total project completion time follows normal distribution
2.Activity times are statistically independent

70. Probability of On Time Completion
𝑧 =
𝐷−𝜇𝑐
𝜎𝑐
;
𝜇𝑐 = 𝑡ℎ𝑒 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑟𝑜𝑗𝑒𝑐𝑡
𝐷 = 𝑡ℎ𝑒 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑝𝑟𝑜𝑗𝑒𝑐𝑡 𝑐𝑜𝑚𝑝𝑙𝑒𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒
𝜎𝑐
2 = 𝑡ℎ𝑒 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑝𝑎𝑡ℎ
𝑍 = 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎 𝑛𝑜𝑟𝑚𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
Here,
𝐷 = 16 𝑤𝑒𝑒𝑘𝑠
𝜇𝑐 = 15 𝑤𝑒𝑒𝑘𝑠
𝜎𝑐 = 0.11 + 0.11 + 1 + 1.78 + 0.11 = 1.76
𝑍 = 0.57
Probability = 71.57% (from Z table)

72. Thank you!