Question

(3) Determine the critical path and critical time of the network shown below. Use the critical path method (the table of ES, EF, etc.).
(3) Determine the critical path and critical time of the network shown below. Use the critical path method (the table of ES, EF, etc.). po Problem . Example a 100 For all starting activities, ES is taken as 0. Activities 1-2, 1-3 gets ES of O. Find EF-ES +time. Activity Time ES E F LS L F Total Slack 1-2 DO 5-6 2-4 and 2-6 cannot start unless 1-2 is finished. ES of 2-4 and 2-6 is 4 = EF of 1-2). 3-4 and 3-5 cannot start unless 1-3 is finished. ES of 3-4 and 3-5 is 3 (EF of 1-3). Activity Time ES EF LS LF 1-2 1-3 The visual method can be used for small projects to determine the critical path, critical time, the critical activities. But it cannot give any further information on the project. Total Slack For large projects a more formal method is used known as the critical path method (CPM), is commonly used. This is the method that should be used for solving project network problem L 3-5 4-6 5-6 Let's define some parameters first: Early start is the earliest time an activity can start (ES). Early finish is the earliest time an activity can finish (EF-ES + activity time). Late start is the latest time an activity must start without delaying the project (LS) Late finish is the latest time an activity must finish without delaying the project (LFLS+ activity time) Total slack is the difference between late start and early start or difference between late finish and early finish (TSLS-ES or TS LF-EF). 4-6 cannot start unless 2-4 and 3-4 are finished. ES of 4-6 is 10 (= EF of 2-4). EF of 3-4 is 8 and EF of 2-4 is 10. Activity 4-6 cannot start unless both 3-4 and 2-4 are done. 5-6 cannot start unless 3-5 is finished. ES of 5-6 is 10 EF of 3-5). Activity Time ES E F LS L LF Total Slack 0 1-3 1-2 Consider an example to understand and use the CPM concepts. 2.4 Example using critical path method Apply the critical path method on the project network given before. The times are in days. To apply the CPM method we should draw a blank table with the column headings as shown the table below. Explanation is given before cach table. Calculated cells are given in bold. 4-6 5-6 6 10 126

Answer 1

Sol:

Sol: 2012 Activity 1-21 ES 0 2 12 Time 12 8 + 3 IF 12 20 16 IF(Total Slack) 11 w S 0 14 12 236 LF 12 22 16 29 I - s 2-5 w 12-17 2-5 3-6 [4.6 5.7 16 7 178] osloon I w 18 9 4 6 16 21 34 38 34 16 34 30 29 38 34 34 38 444 38 44 8 0 jo EL = EF = is - LE: TEL: Earliest Shaut Time Earliest Finish Time (Est Time) Latest Start Time (LF- Time) Latest Finish Time Total Float / Total Slack (LF-EF/LS-ES) TS . The The entical path is critical time is 1-2-4-6-7-8 44