Constructing Networks 1
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)
Activity Relationships
Activity Relationships 1 4
Activity Relationships A 1 B A & B can occur concurrently 5
Activity Relationships A must be done before C & D can begin A 1 4 C D B 6
Activity Relationships D A 1 4 C 7 B E B & C must be done before E can begin
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
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
Dummy Activities Example 10
Incorrect 1- Dummy Activities - Example 1 4 - -4 11
Incorrect 1- Dummy Activities - Example 1 4 - -4 Different activities; same designation 1
Dummy Activities Example Incorrect Correct 1- - 1 4 1- - -4-4 4-5 1 4 5 1 - -4: Dummy activity
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.
Network Solution 1 15
Network Solution 1 All networks start with 1 event. 16
Network Solution A 1 17
Network Solution A 1 Event 1 starts the project; Activity A, with no predecessors, comes from it. 18
Network Solution A 1 B 19
Network Solution A 1 B Activity B requires completion of A; arrow leaves Event. 0
Network Solution A 1 B C 4 1
Network Solution B A 1 C 4 Activity C requires completion of A; arrow leaves Event.
Network Solution B D 5 A 1 C 4
Network Solution B D 5 A 1 C 4 Activity D requires completion of B; arrow leaves Event. 4
Network Solution B D 5 1 A E C 4 6 5
Network Solution B D 5 1 A E C 4 6 6 Activity E requires completion of B; arrow leaves Event.
Network Solution B D 5 1 A E C 4 F 6 7
Network Solution Activity F requires completion of C; B arrow leaves Event 4. A 1 D E 5 C 4 F 6 8
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
Network Solution B D 5 G 1 A E 7 C 4 F 6 0
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
Network Solution B D 5 G 1 A E 7 C 4 F 6 H
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
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
5 Critical Path Analysis
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
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 1-6 1 Buy shrubs etc. 1- Roof - 4 Do interior work -4 4 Landscape -4 4
Network Solution 1 8
Network Solution Pour foundation & frame 1 6 wk. 9
Network Solution Pour foundation & frame 1 6 wk. wk. Buy shrubs etc. 40
Network Solution Pour foundation & frame 1 6 wk. Roof wk. wk. Buy shrubs etc. 41
Network Solution Pour foundation & frame 6 wk. 1 4 wk. Buy shrubs etc. Roof wk. Do interior work wk. 4
Network Solution Pour foundation & frame 6 wk. 1 4 wk. Buy shrubs etc. Roof wk. Do interior work wk. Landscape 4 wk. 4
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
Activity 1- Earliest Start Solution 45
Activity 1- Earliest Start Solution Activity ES EF LS LF Slack 1-1- - -4-4 6 1 4 4 46
Activity 1- Earliest Start Solution Activity ES EF LS LF Slack 1-0 1- - -4-4 For starting activities, ES = 0. 47 6 1 4 4
Activity 1- Earliest Finish Solution Activity ES EF LS LF Slack 1-0 6 1- - -4-4 48 + 6 EF = ES + Activity time. 6 1 4 4
Activity 1- Earliest Start Solution Activity ES EF LS LF Slack 1-0 6 1-0 - -4-4 For starting activities, ES = 0. 49 6 1 4 4
Activity 1- Earliest Finish Solution Activity ES EF LS LF Slack 1-0 6 1-0 - -4-4 50 + EF = ES + Activity time. 6 1 4 4
Activity - Earliest Start Solution Activity ES EF LS LF Slack 1-0 6 1-0 - 6-4 -4 51 6 1 4 For non-starting activities, ES = Max EF of all predecessors. 4
Activity - Earliest Finish Solution Activity ES EF LS LF Slack 1-0 6 1-0 - 6 8-4 -4 5 + EF = ES + Activity time. 6 1 4 4
Activity -4 Earliest Start Solution Activity ES EF LS LF Slack 1-0 6 1-0 - 6 8-4 6-4 5 6 1 4 For non-starting activities, ES = Max EF of all predecessors. 4
Activity -4 Earliest Finish Solution Activity ES EF LS LF Slack 1-0 6 1-0 - 6 8-4 6 9-4 54 + EF = ES + Activity time. 6 1 4 4
Activity -4 Earliest Start Solution Activity ES EF LS LF Slack 1-0 6 1-0 - 6 8-4 6 9-4 8 For non-starting activities, ES = Max EF of all predecessors. 55 6 1 4 4
Activity -4 Earliest Finish Solution Activity ES EF LS LF Slack 1-0 6 1-0 - 6 8-4 6 9-4 8 1 + 4 EF = ES + Activity time. 56 6 1 4 4
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
Activity -4 Latest Finish Solution 58
Activity -4 Latest Finish Solution Activity ES EF LS LF Slack 1-0 6 1-0 - 6 8-4 6 9 6 1 4 4-4 8 1 1 For ending activities, LF = Maximum EF. 59
Activity -4 Latest Start Solution Activity ES EF LS LF Slack 1-0 6 1-0 - 6 8-4 6 9 6 1 4 4-4 8 1 8 1-4 LS = LF- Activity time. 60
Activity -4 Latest Finish Solution Activity ES EF LS LF Slack 1-0 6 1-0 - 6 8-4 6 9 1-4 8 1 8 1 For ending activities, LF = Maximum EF. 61 6 1 4 4
Activity -4 Latest Start Solution Activity ES EF LS LF Slack 1-0 6 1-0 - 6 8-4 6 9 9 1-4 8 1 8 1 6 LS = LF- Activity time. 6 1 4-4
Activity - Latest Finish Solution Activity ES EF LS LF Slack 1-0 6 6 1-0 1 4-6 8 8-4 6 4 9 9 1-4 8 1 8 1 For non-ending activities, LF = Min LS of all successors. 6
Activity - Latest Start Solution Activity ES EF LS LF Slack 1-0 6 6 1-0 1 4-6 8 6 8 - -4 6 4 9 9 1-4 8 1 8 1 64 LS = LF- Activity time.
Activity 1- Latest Finish Solution Activity ES EF LS LF Slack 1-0 6 6 1-0 8 1 4-6 8 6 8-4 6 4 9 9 1-4 8 1 8 1 For non-ending activities, LF = Min LS of all successors. 65
Activity 1- Latest Start Solution Activity ES EF LS LF Slack 1-0 6 6 1-0 5 8 1 4 - - 6 8 6 8-4 6 4 9 9 1-4 8 1 8 1 66 LS = LF- Activity time.
Activity 1- Latest Finish Solution Activity ES EF LS LF Slack 1-0 6 6 6 1-0 5 8 1 4-6 8 6 8-4 6 4 9 9 1-4 8 1 8 1 For non-ending activities, LF = Min LS of all successors. 67
Activity 1- Latest Start Solution Activity ES EF LS LF Slack 1-0 6 0 6 6-6 1-0 5 8 1 4-6 8 6 8-4 6 4 9 9 1-4 8 1 8 1 68 LS = LF- Activity time.
Slack Solution Activity ES EF LS LF Slack 1-0 6 0 6 0 1-0 5 8 5-6 8 6 8 0-4 6 9 9 1-4 8 1 8 1 0 69 Slack = LF - EF = LS - ES.
Critical Path Solution Activity ES EF LS LF Slack 1-0 6 0 6 0 1-0 5 8 5-6 8 6 8 0-4 6 9 9 1-4 8 1 8 1 0 70 Critical path has 0 slack: 1-, -, -4.