Constructing Networks
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1 Constructing Networks 1
2 Network Terms Project: Obtain a college degree (B.S.) Register 1 Attend class, study etc. 4 Years Receive diploma Event (Node) Activity (Arrow) Event (Node)
3 Activity Relationships
4 Activity Relationships 1 4
5 Activity Relationships A 1 B A & B can occur concurrently 5
6 Activity Relationships A must be done before C & D can begin A 1 4 C D B 6
7 Activity Relationships D A 1 4 C 7 B E B & C must be done before E can begin
8 Activity Relationships A must be done before C & D can begin A 1 4 C D B A & B can occur concurrently 8 E B & C must be done before E can begin
9 Dummy Activities Activities are defined often by beginning & ending events Example: Activity - Every activity must have unique pair of beginning & ending events Computer programs get confused Dummy activities maintain precedence Consume no time or resources 9
10 Dummy Activities Example 10
11 Incorrect 1- Dummy Activities - Example
12 Incorrect 1- Dummy Activities - Example Different activities; same designation 1
13 Dummy Activities Example Incorrect Correct : Dummy activity
14 Network Example You re a project manager for Bechtel. Construct the network. Activity Predecessors A -- B A C A D B E B F C G D 14 H E, F 1995 Corel Corp.
15 Network Solution 1 15
16 Network Solution 1 All networks start with 1 event. 16
17 Network Solution A 1 17
18 Network Solution A 1 Event 1 starts the project; Activity A, with no predecessors, comes from it. 18
19 Network Solution A 1 B 19
20 Network Solution A 1 B Activity B requires completion of A; arrow leaves Event. 0
21 Network Solution A 1 B C 4 1
22 Network Solution B A 1 C 4 Activity C requires completion of A; arrow leaves Event.
23 Network Solution B D 5 A 1 C 4
24 Network Solution B D 5 A 1 C 4 Activity D requires completion of B; arrow leaves Event. 4
25 Network Solution B D 5 1 A E C 4 6 5
26 Network Solution B D 5 1 A E C Activity E requires completion of B; arrow leaves Event.
27 Network Solution B D 5 1 A E C 4 F 6 7
28 Network Solution Activity F requires completion of C; B arrow leaves Event 4. A 1 D E 5 C 4 F 6 8
29 Network Solution In problem statement, Activity H requires B completion of E & F. A Therefore, E & F have 1 same ending event (Event 6). C 4 D F E 5 6 9
30 Network Solution B D 5 G 1 A E 7 C 4 F 6 0
31 Network Solution B D 5 G 1 A E 7 Activity G requires C completion of D; arrow leaves Event 5. 4 F 6 1
32 Network Solution B D 5 G 1 A E 7 C 4 F 6 H
33 Network Solution B D 5 G 1 A E 7 C Activity H requires completion of E & F; arrow leaves Event 6. 4 F 6 H
34 Network Solution B D 5 G 1 A E 7 Activity H ends C at Event 7 since a network has 1 ENDING event. 4 F 6 H 4
35 5 Critical Path Analysis
36 Critical Path Analysis Provides activity information Earliest (ES) & latest (LS) start Earliest (EF) & latest (LF) finish Slack (S): Allowable delay Identifies critical path Longest path in network Shortest time project can be completed Any delay on activities delays project Activities have 0 slack 6
37 Critical Path Analysis Example You re project manager for Cooper Homes. Draw the network. Find the ES, EF, LS, LF & critical path. Begin Event 7 Ending Event Description Activity Time (Wks) 1 Pour fdn. & frame Buy shrubs etc. 1- Roof - 4 Do interior work -4 4 Landscape -4 4
38 Network Solution 1 8
39 Network Solution Pour foundation & frame 1 6 wk. 9
40 Network Solution Pour foundation & frame 1 6 wk. wk. Buy shrubs etc. 40
41 Network Solution Pour foundation & frame 1 6 wk. Roof wk. wk. Buy shrubs etc. 41
42 Network Solution Pour foundation & frame 6 wk. 1 4 wk. Buy shrubs etc. Roof wk. Do interior work wk. 4
43 Network Solution Pour foundation & frame 6 wk. 1 4 wk. Buy shrubs etc. Roof wk. Do interior work wk. Landscape 4 wk. 4
44 Earliest Start & Finish Steps Begin at starting event & work forward ES = 0 for starting activities ES is earliest start EF = ES + Activity time EF is earliest finish ES = Maximum EF of all predecessors for non-starting activities 44
45 Activity 1- Earliest Start Solution 45
46 Activity 1- Earliest Start Solution Activity ES EF LS LF Slack
47 Activity 1- Earliest Start Solution Activity ES EF LS LF Slack For starting activities, ES =
48 Activity 1- Earliest Finish Solution Activity ES EF LS LF Slack EF = ES + Activity time
49 Activity 1- Earliest Start Solution Activity ES EF LS LF Slack For starting activities, ES =
50 Activity 1- Earliest Finish Solution Activity ES EF LS LF Slack EF = ES + Activity time
51 Activity - Earliest Start Solution Activity ES EF LS LF Slack For non-starting activities, ES = Max EF of all predecessors. 4
52 Activity - Earliest Finish Solution Activity ES EF LS LF Slack EF = ES + Activity time
53 Activity -4 Earliest Start Solution Activity ES EF LS LF Slack For non-starting activities, ES = Max EF of all predecessors. 4
54 Activity -4 Earliest Finish Solution Activity ES EF LS LF Slack EF = ES + Activity time
55 Activity -4 Earliest Start Solution Activity ES EF LS LF Slack For non-starting activities, ES = Max EF of all predecessors
56 Activity -4 Earliest Finish Solution Activity ES EF LS LF Slack EF = ES + Activity time
57 Latest Start & Finish Steps Begin at ending event & work backward LF = Maximum EF for ending activities LF is latest finish; EF is earliest finish LS = LF - Activity time LS is latest start LF = Minimum LS of all successors for non-ending activities 57
58 Activity -4 Latest Finish Solution 58
59 Activity -4 Latest Finish Solution Activity ES EF LS LF Slack For ending activities, LF = Maximum EF. 59
60 Activity -4 Latest Start Solution Activity ES EF LS LF Slack LS = LF- Activity time. 60
61 Activity -4 Latest Finish Solution Activity ES EF LS LF Slack For ending activities, LF = Maximum EF
62 Activity -4 Latest Start Solution Activity ES EF LS LF Slack LS = LF- Activity time
63 Activity - Latest Finish Solution Activity ES EF LS LF Slack For non-ending activities, LF = Min LS of all successors. 6
64 Activity - Latest Start Solution Activity ES EF LS LF Slack LS = LF- Activity time.
65 Activity 1- Latest Finish Solution Activity ES EF LS LF Slack For non-ending activities, LF = Min LS of all successors. 65
66 Activity 1- Latest Start Solution Activity ES EF LS LF Slack LS = LF- Activity time.
67 Activity 1- Latest Finish Solution Activity ES EF LS LF Slack For non-ending activities, LF = Min LS of all successors. 67
68 Activity 1- Latest Start Solution Activity ES EF LS LF Slack LS = LF- Activity time.
69 Slack Solution Activity ES EF LS LF Slack Slack = LF - EF = LS - ES.
70 Critical Path Solution Activity ES EF LS LF Slack Critical path has 0 slack: 1-, -, -4.
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