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Critical path and fw bw pass

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Martin Bailey

The document provides a step-by-step example of calculating the critical path of a project using forward and backward passes. It shows determining the early start, early finish, late start and late finish of activities on the critical and non-critical paths. Adding dependencies between activities can create additional paths to consider in determining the critical path.

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Step by Step Critical Path START dur=5 dur= 3 dur=6 FINISH Activity A Activity B Activity C A Simple Example of a Path The CRITICAL PATH is the string of activities that will delay the whole project if any one of them is delayed. http://www.headfirstlabs.com/PMP/criticalpath/HeadFirstPMP_CriticalPathDrill.pdf Great explanation, examples, and questions at: 1
Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C A Simple Example of a Path The Path is A -> B -> C 2
Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C A Simple Example of a Path The Path is A -> B -> C The Duration of the Path equals the sum of all the durations of the tasks in the path. 3
Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C A Simple Example of a Path The Path is A -> B -> C The Duration of the Path equals the sum of all the durations of the tasks in the path. Path Duration = Duration of A + Duration of B + Duration of C 4
Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C A Simple Example of a Path The Path is A -> B -> C The Duration of the Path equals the sum of all the durations of the tasks in the path. Path Duration = Duration of A + Duration of B + Duration of C Path Duration = 5 + 3 + 6 The answer is 14 5
Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Critical Path dur =6 dur =9 Activity D Activity E Note that the letters A,B,C,D,E are just labels. They have nothing to do with order The Critical Path is the longest path in duration. 6
Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Critical Path dur =6 dur =9 Activity D Activity E The Critical Path is the longest path in duration. How many paths are there? What are they? What are their Durations? 7
Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Critical Path dur =6 dur =9 Activity D Activity E The Critical Path is the longest path in duration. How many paths are there? What are they? What are their Durations? 2 A,B,C and D,E A,B,C = 14 D,E = 15 8
Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Critical Path dur =6 dur =9 Activity D Activity E The Critical Path is the longest path in duration. How many paths are there? What are they? What are their Durations? 2 A,B,C and D,E A,B,C = 14 D,E = 15 D,E is longer so it is the Critical Path 9
Step by Step Float START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Float or Slack dur =6 dur =9 Activity D Activity E The Critical Path is the longest path in duration. D,E is longer so it is the Critical Path A,B,C = 14 D,E = 15 To determine the FLOAT of a path, subtract the duration of a Path from the duration of the Critical Path FLOAT is the amount of time an activity can slip (or delay) without causing your project delays. Activities on the CRITICAL PATH have NO FLOAT. Slack or Float = 0 10
Step by Step Float START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Float or Slack dur =6 dur =9 Activity D Activity E The Critical Path is the longest path in duration. D,E is longer so it is the Critical Path A,B,C = 14 D,E = 15 FLOAT of A,B,C = D,E duration A,B,C duration 15 14 = 1 EACH activity in A,B,C of this example has a float of 1 FLOAT is the amount of time an activity can slip (or delay) without causing your project delays. Activities on the CRITICAL PATH have NO FLOAT. Slack or Float = 0 11
Forward & Backward Pass START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C Critical Path (CP) the longest path of activities to complete a project Early Start (ES) the earliest you can start an activity Early Finish (EF) the earliest you can finish and activity Late Start (LS) - the latest you can start an activity (without affecting CP) Late Finish (LF) - the latest you can finish an activity (without affecting CP) Knowing Early Start and Early Finish lets you know how much freedom you have to move the start dates of activities without causing problems Knowing Late Start and Late Finish lets you know how much play you have in scheduling activities 12
Calculating Forward Pass START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 ES EF Duration LS LF A Simple Example 13
Calculating Forward Pass START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 1 5 5 LS LF Example: Activity A Start = 0 ES = 0+ 1 = 1 EF = 1 + 5 1 = 5 A Simple Example 14
Calculating Forward Pass START 1 5 dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 ES EF 3 LS LF Example: Activity B ES = EF = A Simple Example 15
Calculating Forward Pass START 1 5 dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 6 8 3 LS LF Example: Activity B ES = 5 + 1 = 6 EF = 6 + 3 -1 = 8 A Simple Example 16
Calculating Forward Pass START 1 5 dur=5 6 8 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 ES EF 6 LS LF Example: Activity C ES = EF = A Simple Example 17
Calculating Forward Pass START 1 5 dur=5 6 8 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 9 14 6 LS LF Example: Activity C ES = 8 + 1 = 9 EF = 9 + 6 1 = 14 A Simple Example 18
Calculating Backward Pass START 1 5 dur=5 6 8 dur=3 9 14 dur=6 FINISH Activity A Activity B Activity C LF = previous LS -1 LS = LF - duration + 1 ES EF 6 9 14 Example: Activity C Since we are beginning our calculations at the end, DO NOT subtract 1 LF = 14 LS = 14 6 + 1 = 9 A Simple Example 19
Calculating Backward Pass START 1 5 dur=5 6 8 dur=3 9 14 dur=6 9 14 FINISH Activity A Activity B Activity C LF = previous LS -1 LS = LF - duration + 1 ES EF 3 6 8 Example: Activity B LF = 9 1 = 8 LS = 8 3 + 1 = 6 A Simple Example 20
Calculating Backward Pass START 1 5 dur=5 6 8 dur=3 6 8 9 14 dur=6 9 14 FINISH Activity A Activity B Activity C LF = previous LS -1 LS = LF - duration + 1 ES EF 3 1 5 Example: Activity A LF = 6 1 = 5 LS = 5 -5 + 1= 1 A Simple Example 21
Calculating Backward Pass START 1 5 dur=5 1 5 6 8 dur=3 6 8 9 14 dur=6 9 14 FINISH Activity A Activity B Activity C A Simple Example Notice that on the Critical Path ES = LS and EF = LF 22
Forward & Backward with 2 Paths START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Since I have not changed the numbers, we have already determined that Duration of D,E = 15 and A,B,C = 14 Path D,E is the Critical Path, Do CRITICAL PATH calculations first 23
Forward & Backward with 2 Paths START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 7 15 dur =9 7 15 Activity D Activity E Since I have not changed the numbers, we have already determined that Duration of D,E = 15 and A,B,C = 14 Path D,E is the Critical Path, Activity D ES = Previous EF + 1 EF = ES + Duration - 1 ES = 0 + 1 = 1 EF = 1 + 6 1 = 6 Activity E ES = Previous EF + 1 EF = ES + Duration - 1 ES = 6 + 1 = 7 EF = 7 + 9 1 = 15 REMEMBER In the Critical Path ES = LS EF = LF 24
Forward & Backward with 2 Paths START 1 5 dur=5 6 8 dur=3 9 14 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 7 15 dur =9 7 15 Activity D Activity E Since I have not changed the numbers, we have already determined that Duration of D,E = 15 and A,B,C = 14 Path D,E is the Critical Path, Activity A ES = Previous EF + 1 EF = ES + Duration - 1 ES = 0 + 1 = 1 EF = 1 + 5 1 = 5 Activity C ES = Previous EF + 1 EF = ES + Duration - 1 ES = 8 + 1 = 9 EF = 9 + 6 1 = 14 Activity B ES = Previous EF + 1 EF = ES + Duration - 1 ES = 5 + 1 = 6 EF = 6 + 3 1 = 8 25
Forward & Backward with 2 Paths START 1 5 dur=5 6 8 dur=3 9 14 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 7 15 dur =9 7 15 Activity D Activity E Since I have not changed the numbers, we have already determined that Duration of D,E = 15 and A,B,C = 14 Path D,E is the Critical Path, Backward Pass of A,B,C Is where it gets interesting 26
Forward & Backward with 2 Paths START 1 5 dur=5 2 6 6 8 dur=3 7 9 9 14 dur=6 10 15 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 7 15 dur =9 7 15 Activity D Activity E Since I have not changed the numbers, we have already determined that Duration of D,E = 15 and A,B,C = 14 Path D,E is the Critical Path, Activity C LF = LF of Critical Path LS = LF - Duration +1 LF = 15 LS = 15 6 + 1= 10 Activity A LF = Previous LS - 1 LS = LF - Duration + 1 LF = 7 - 1= 6 LS = 6 - 5 + 1 = 2 Activity B LF = Previous LS - 1 LS = LF - Duration + 1 LF = 10 - 1= 9 LS = 9 - 3 + 1 = 7 27
Forward & Backward with 2 Paths START 1 5 dur=5 2 6 6 8 dur=3 7 9 9 14 dur=6 10 15 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 7 15 dur =9 7 15 Activity D Activity E What does it mean ? It means Activities on the Critical Path MUST start on time on day 1 Activity A can start on day 2 and we can still meet our schedule 28
Forward & Backward with Many Paths START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E How many paths are there? What are they? What are their Durations? 29
Forward & Backward with Many Paths START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E How many paths? What are they? What are their Durations? 3 A,B,C, D,E A,B,E A,B,C = 14 D,E = 15 A,B,E = 17 30
Forward & Backward with Many Paths START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E How many paths? What are they? What are their Durations? 3 A,B,C, D,E A,B,E A,B,C = 14 D,E = 15 A,B,E = 17 A,B,E is the longest, so A,B,E is the CRITICAL PATH 31
Forward & Backward with Many Paths START 1 5 dur=5 6 8 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 9 17 dur =9 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E First Step: ES & EF of CRITICAL PATH Activity A ES = Previous EF + 1 EF = ES + Duration - 1 ES = 0 + 1 = 1 EF = 1 + 5 1 = 5 Activity B ES = Previous EF + 1 EF = ES + Duration - 1 ES = 5 + 1 = 6 EF = 6 + 3 1 = 8 Activity E ES = Previous EF + 1 EF = ES + Duration - 1 ES = 8 + 1 = 9 EF = 9 + 9 1 = 17 32
Forward & Backward with Many Paths START 1 5 dur=5 1 5 6 8 dur=3 6 8 dur=6 FINISH Activity A Activity B Activity C dur =6 9 17 dur =9 9 17 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E Second Step: LS & LF of CRITICAL PATH This is easy for the Critical Path LS = ES LF = EF 33
Forward & Backward with Many Paths START 1 5 dur=5 1 5 6 8 dur=3 6 8 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 3 8 9 17 dur =9 9 17 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E First Step: ES & EF of 2nd Longest Path D,E is 2nd longest CAUTION Do NOT change values you already calculated Activity D ES & EF ES = Previous EF + 1 EF = ES + Duration - 1 ES = 0 + 1 = 1 EF = 1 + 6 1 = 6 Activity D LS & LF LF = Previous LS - 1 LS = LF - Duration + 1 LF = 9 1 = 8 LS = 8 6 + 1 = 3 34
Forward & Backward with Many Paths START 1 5 dur=5 1 5 6 8 dur=3 6 8 9 14 dur=6 12 17 FINISH Activity A Activity B Activity C 1 6 dur =6 3 8 9 17 dur =9 9 17 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E Next Step: ES & EF of 3rd Longest Path A,B,C CAUTION Do NOT change values you already calculated Activity C ES & EF ES = Previous EF + 1 EF = ES + Duration - 1 ES = 8 + 1 = 9 EF = 9 + 6 1 = 14 Activity C LS & LF LF = LF of Critical Path LS = LF - Duration + 1 LF = 17 LS = 17 6 + 1 = 12 35
Forward & Backward with Many Paths START 1 5 dur=5 1 5 6 8 dur=3 6 8 9 14 dur=6 12 17 FINISH Activity A Activity B Activity C 1 6 dur =6 3 8 9 17 dur =9 9 17 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E Next Step: ES & EF of 3rd Longest Path A,B,C CAUTION Do NOT change values you already calculated Activity C ES & EF ES = Previous EF + 1 EF = ES + Duration - 1 ES = 8 + 1 = 9 EF = 9 + 6 1 = 14 Activity C LS & LF LF = LF of Critical Path LS = LF - Duration + 1 LF = 17 LS = 17 6 + 1 = 12 36
Forward & Backward with Many Paths START 1 5 dur=5 1 5 6 8 dur=3 6 8 9 14 dur=6 12 17 FINISH Activity A Activity B Activity C 1 6 dur =6 3 8 9 17 dur =9 9 17 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E What does it mean? Activity A Can start on day 1 or as late as Day 3 without affecting schedule Activity C Can start no earlier than day 9, but it can start as late as day 12 without affecting schedule The Critical Path is A,B,E 37
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 38 How many paths are there? What are they? What are their Durations?
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 39 How many paths are there? What are they? What are their Durations? It is easier to track the paths and then count them Do the easy ones first
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 40 How many paths are there? What are they? What are their Durations? A, B,C D,E Are there others?
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 41 How many paths are there? What are they? What are their Durations? A, B,C D,E D,B,C Any More?
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 42 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E Next step: compute duration
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 43 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E A,B,C = D,E = D,B,C = D,B,C = Next step: compute duration
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 44 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E A,B,C = D,E = D,B,C = D,B,C = Next step: compute duration
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 45 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E A,B,C=5+3+6 D,E=6+9 D,B,C=6+3+6 D,B,E=6+3+9 Next step: compute duration
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 46 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E A,B,C=14 D,E=15 D,B,C=15 D,B,E=18
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 47 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E A,B,C=14 D,E=15 D,B,C=15 D,B,E=18 I forgot a path
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 48 How many paths are there? What are they? What are their Durations? 4 5 A, B,C D,E D,B,C D,B,E A,B,E A,B,C=14 D,E=15 D,B,C=15 D,B,E=18 A,B,E = 5+3+9 = 17 I forgot a path
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 49 How many paths are there? What are they? What are their Durations? 5 A, B,C D,E D,B,C D,B,E A,B,E A,B,C=14 D,E=15 D,B,C=15 D,B,E=18 A,B,E = 17 Time to do Forward & Backward Pass on the Critical Path D,B,E is the longest. So D,B,E is the Critical Path
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 50 D,B,E is the longest. So D,B,E is the Critical Path Activity D ES = Previous EF + 1 EF = ES + Duration - 1 Activity B ES = Previous EF + 1 EF = ES + Duration - 1 Activity E ES = Previous EF + 1 EF = ES + Duration - 1
Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 51 D,B,E is the longest. So D,B,E is the Critical Path Activity D ES = Previous EF + 1 EF = ES + Duration 1 ES = 0 + 1 = 1 EF = 1 + 6 -1 = 6 Activity B ES = Previous EF + 1 EF = ES + Duration - 1 Activity E ES = Previous EF + 1 EF = ES + Duration - 1
Working together to Solve START dur=5 7 9 dur=3 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 52 D,B,E is the longest. So D,B,E is the Critical Path Activity D ES = Previous EF + 1 EF = ES + Duration 1 ES = 0 + 1 = 1 EF = 1 + 6 -1 = 6 Activity B ES = Previous EF + 1 EF = ES + Duration 1 ES = 6 + 1 = 7 EF = 7 + 3 1 = 9 Activity E ES = Previous EF + 1 EF = ES + Duration - 1
Working together to Solve START dur=5 7 9 dur=3 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 10 18 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 53 D,B,E is the longest. So D,B,E is the Critical Path Activity D ES = Previous EF + 1 EF = ES + Duration 1 ES = 0 + 1 = 1 EF = 1 + 6 -1 = 6 Activity B ES = Previous EF + 1 EF = ES + Duration 1 ES = 6 + 1 = 7 EF = 7 + 3 1 = 9 Activity E ES = Previous EF + 1 EF = ES + Duration 1 ES = 9 + 1 = 10 EF = 10 + 9 -1 = 18
Working together to Solve START dur=5 7 9 dur=3 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 10 18 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 54 D,B,E is the longest. So D,B,E is the Critical Path Time to compute LS & LF for the Critical Path
Working together to Solve START dur=5 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 55 D,B,E is the longest. So D,B,E is the Critical Path On the Critical Path LS = ES and LF = EF Because there is NO FLOAT on the Critical Path Next Step: Compute for next longest path
Working together to Solve START dur=5 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 56 D,B,E is the longest. So D,B,E is the Critical Path A,B,E is 2nd Longest
Working together to Solve START dur=5 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 57 D,B,E is the longest. So D,B,E is the Critical Path In A,B,E B & E are already done, so only compute A CAUTION Do NOT change values you already calculated Activity A ES = Previous EF + 1 EF = ES + Duration 1 Activity A LF = LF of Critical Path LS = LF - Duration + 1
Working together to Solve START 1 5 dur=5 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 58 D,B,E is the longest. So D,B,E is the Critical Path CAUTION Do NOT change values you already calculated Activity A ES = Previous EF + 1 EF = ES + Duration 1 ES = 0 + 1 = 1 EF = 1 + 5- 1 = 5 Activity A LF = Previous LS - 1 LS = LF - Duration + 1
Working together to Solve START 1 5 dur=5 2 6 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 59 D,B,E is the longest. So D,B,E is the Critical Path CAUTION Do NOT change values you already calculated Activity A ES = Previous EF + 1 EF = ES + Duration 1 ES = 0 + 1 = 1 EF = 1 + 5- 1 = 5 Activity A LF = Previous LS - 1 LS = LF - Duration + 1 LF = 7 - 1= 6 LS = 6 - 5 + 1 = 2
Working together to Solve START dur=5 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 60 D,B,E is the longest. So D,B,E is the Critical Path CAUTION Do NOT change values you already calculated Activity C ES = Previous EF + 1 EF = ES + Duration 1 Activity C LF = LF of Critical Path LS = LF - Duration + 1
Working together to Solve START dur=5 7 9 dur=3 7 9 10 15 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 61 D,B,E is the longest. So D,B,E is the Critical Path CAUTION Do NOT change values you already calculated Activity C ES = Previous EF + 1 EF = ES + Duration 1 ES = 9 + 1 = 10 EF = 10 + 6 -1 = 15 Activity C LF = LF of Critical Path LS = LF - Duration + 1
Working together to Solve START 1 5 dur=5 2 6 7 9 dur=3 7 9 10 15 dur=6 13 18 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 62 D,B,E is the longest. So D,B,E is the Critical Path CAUTION Do NOT change values you already calculated Activity C ES = Previous EF + 1 EF = ES + Duration 1 ES = 9 + 1 = 10 EF = 10 + 6 -1 = 15 Activity C LF = LF of Critical Path LS = LF - Duration + 1 LF = 18 LS = 18 6 + 1 = 13
What do we know from this? START 1 5 dur=5 2 6 7 9 dur=3 7 9 10 15 dur=6 13 18 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E 63 Project Length is 18 days Critical Path is D,B,E There is no float on D,B,E Tasks D, B, & E must start on time Task D must start on Day 1 There are 5 Paths Task A could start on Day 2 And NOT affect Schedule Task C could start on Day 13 And NOT affect Schedule ES, EF, LS & LF of each task A link to more on Critical Path and Forward & Backward Pass The Link

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Critical path and fw bw pass

  • 1. Step by Step Critical Path START dur=5 dur= 3 dur=6 FINISH Activity A Activity B Activity C A Simple Example of a Path The CRITICAL PATH is the string of activities that will delay the whole project if any one of them is delayed. http://www.headfirstlabs.com/PMP/criticalpath/HeadFirstPMP_CriticalPathDrill.pdf Great explanation, examples, and questions at: 1
  • 2. Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C A Simple Example of a Path The Path is A -> B -> C 2
  • 3. Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C A Simple Example of a Path The Path is A -> B -> C The Duration of the Path equals the sum of all the durations of the tasks in the path. 3
  • 4. Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C A Simple Example of a Path The Path is A -> B -> C The Duration of the Path equals the sum of all the durations of the tasks in the path. Path Duration = Duration of A + Duration of B + Duration of C 4
  • 5. Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C A Simple Example of a Path The Path is A -> B -> C The Duration of the Path equals the sum of all the durations of the tasks in the path. Path Duration = Duration of A + Duration of B + Duration of C Path Duration = 5 + 3 + 6 The answer is 14 5
  • 6. Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Critical Path dur =6 dur =9 Activity D Activity E Note that the letters A,B,C,D,E are just labels. They have nothing to do with order The Critical Path is the longest path in duration. 6
  • 7. Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Critical Path dur =6 dur =9 Activity D Activity E The Critical Path is the longest path in duration. How many paths are there? What are they? What are their Durations? 7
  • 8. Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Critical Path dur =6 dur =9 Activity D Activity E The Critical Path is the longest path in duration. How many paths are there? What are they? What are their Durations? 2 A,B,C and D,E A,B,C = 14 D,E = 15 8
  • 9. Step by Step Critical Path START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Critical Path dur =6 dur =9 Activity D Activity E The Critical Path is the longest path in duration. How many paths are there? What are they? What are their Durations? 2 A,B,C and D,E A,B,C = 14 D,E = 15 D,E is longer so it is the Critical Path 9
  • 10. Step by Step Float START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Float or Slack dur =6 dur =9 Activity D Activity E The Critical Path is the longest path in duration. D,E is longer so it is the Critical Path A,B,C = 14 D,E = 15 To determine the FLOAT of a path, subtract the duration of a Path from the duration of the Critical Path FLOAT is the amount of time an activity can slip (or delay) without causing your project delays. Activities on the CRITICAL PATH have NO FLOAT. Slack or Float = 0 10
  • 11. Step by Step Float START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C How to Determine the Float or Slack dur =6 dur =9 Activity D Activity E The Critical Path is the longest path in duration. D,E is longer so it is the Critical Path A,B,C = 14 D,E = 15 FLOAT of A,B,C = D,E duration A,B,C duration 15 14 = 1 EACH activity in A,B,C of this example has a float of 1 FLOAT is the amount of time an activity can slip (or delay) without causing your project delays. Activities on the CRITICAL PATH have NO FLOAT. Slack or Float = 0 11
  • 12. Forward & Backward Pass START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C Critical Path (CP) the longest path of activities to complete a project Early Start (ES) the earliest you can start an activity Early Finish (EF) the earliest you can finish and activity Late Start (LS) - the latest you can start an activity (without affecting CP) Late Finish (LF) - the latest you can finish an activity (without affecting CP) Knowing Early Start and Early Finish lets you know how much freedom you have to move the start dates of activities without causing problems Knowing Late Start and Late Finish lets you know how much play you have in scheduling activities 12
  • 13. Calculating Forward Pass START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 ES EF Duration LS LF A Simple Example 13
  • 14. Calculating Forward Pass START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 1 5 5 LS LF Example: Activity A Start = 0 ES = 0+ 1 = 1 EF = 1 + 5 1 = 5 A Simple Example 14
  • 15. Calculating Forward Pass START 1 5 dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 ES EF 3 LS LF Example: Activity B ES = EF = A Simple Example 15
  • 16. Calculating Forward Pass START 1 5 dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 6 8 3 LS LF Example: Activity B ES = 5 + 1 = 6 EF = 6 + 3 -1 = 8 A Simple Example 16
  • 17. Calculating Forward Pass START 1 5 dur=5 6 8 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 ES EF 6 LS LF Example: Activity C ES = EF = A Simple Example 17
  • 18. Calculating Forward Pass START 1 5 dur=5 6 8 dur=3 dur=6 FINISH Activity A Activity B Activity C ES = previous EF + 1 EF = ES + duration - 1 9 14 6 LS LF Example: Activity C ES = 8 + 1 = 9 EF = 9 + 6 1 = 14 A Simple Example 18
  • 19. Calculating Backward Pass START 1 5 dur=5 6 8 dur=3 9 14 dur=6 FINISH Activity A Activity B Activity C LF = previous LS -1 LS = LF - duration + 1 ES EF 6 9 14 Example: Activity C Since we are beginning our calculations at the end, DO NOT subtract 1 LF = 14 LS = 14 6 + 1 = 9 A Simple Example 19
  • 20. Calculating Backward Pass START 1 5 dur=5 6 8 dur=3 9 14 dur=6 9 14 FINISH Activity A Activity B Activity C LF = previous LS -1 LS = LF - duration + 1 ES EF 3 6 8 Example: Activity B LF = 9 1 = 8 LS = 8 3 + 1 = 6 A Simple Example 20
  • 21. Calculating Backward Pass START 1 5 dur=5 6 8 dur=3 6 8 9 14 dur=6 9 14 FINISH Activity A Activity B Activity C LF = previous LS -1 LS = LF - duration + 1 ES EF 3 1 5 Example: Activity A LF = 6 1 = 5 LS = 5 -5 + 1= 1 A Simple Example 21
  • 22. Calculating Backward Pass START 1 5 dur=5 1 5 6 8 dur=3 6 8 9 14 dur=6 9 14 FINISH Activity A Activity B Activity C A Simple Example Notice that on the Critical Path ES = LS and EF = LF 22
  • 23. Forward & Backward with 2 Paths START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Since I have not changed the numbers, we have already determined that Duration of D,E = 15 and A,B,C = 14 Path D,E is the Critical Path, Do CRITICAL PATH calculations first 23
  • 24. Forward & Backward with 2 Paths START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 7 15 dur =9 7 15 Activity D Activity E Since I have not changed the numbers, we have already determined that Duration of D,E = 15 and A,B,C = 14 Path D,E is the Critical Path, Activity D ES = Previous EF + 1 EF = ES + Duration - 1 ES = 0 + 1 = 1 EF = 1 + 6 1 = 6 Activity E ES = Previous EF + 1 EF = ES + Duration - 1 ES = 6 + 1 = 7 EF = 7 + 9 1 = 15 REMEMBER In the Critical Path ES = LS EF = LF 24
  • 25. Forward & Backward with 2 Paths START 1 5 dur=5 6 8 dur=3 9 14 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 7 15 dur =9 7 15 Activity D Activity E Since I have not changed the numbers, we have already determined that Duration of D,E = 15 and A,B,C = 14 Path D,E is the Critical Path, Activity A ES = Previous EF + 1 EF = ES + Duration - 1 ES = 0 + 1 = 1 EF = 1 + 5 1 = 5 Activity C ES = Previous EF + 1 EF = ES + Duration - 1 ES = 8 + 1 = 9 EF = 9 + 6 1 = 14 Activity B ES = Previous EF + 1 EF = ES + Duration - 1 ES = 5 + 1 = 6 EF = 6 + 3 1 = 8 25
  • 26. Forward & Backward with 2 Paths START 1 5 dur=5 6 8 dur=3 9 14 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 7 15 dur =9 7 15 Activity D Activity E Since I have not changed the numbers, we have already determined that Duration of D,E = 15 and A,B,C = 14 Path D,E is the Critical Path, Backward Pass of A,B,C Is where it gets interesting 26
  • 27. Forward & Backward with 2 Paths START 1 5 dur=5 2 6 6 8 dur=3 7 9 9 14 dur=6 10 15 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 7 15 dur =9 7 15 Activity D Activity E Since I have not changed the numbers, we have already determined that Duration of D,E = 15 and A,B,C = 14 Path D,E is the Critical Path, Activity C LF = LF of Critical Path LS = LF - Duration +1 LF = 15 LS = 15 6 + 1= 10 Activity A LF = Previous LS - 1 LS = LF - Duration + 1 LF = 7 - 1= 6 LS = 6 - 5 + 1 = 2 Activity B LF = Previous LS - 1 LS = LF - Duration + 1 LF = 10 - 1= 9 LS = 9 - 3 + 1 = 7 27
  • 28. Forward & Backward with 2 Paths START 1 5 dur=5 2 6 6 8 dur=3 7 9 9 14 dur=6 10 15 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 7 15 dur =9 7 15 Activity D Activity E What does it mean ? It means Activities on the Critical Path MUST start on time on day 1 Activity A can start on day 2 and we can still meet our schedule 28
  • 29. Forward & Backward with Many Paths START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E How many paths are there? What are they? What are their Durations? 29
  • 30. Forward & Backward with Many Paths START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E How many paths? What are they? What are their Durations? 3 A,B,C, D,E A,B,E A,B,C = 14 D,E = 15 A,B,E = 17 30
  • 31. Forward & Backward with Many Paths START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E How many paths? What are they? What are their Durations? 3 A,B,C, D,E A,B,E A,B,C = 14 D,E = 15 A,B,E = 17 A,B,E is the longest, so A,B,E is the CRITICAL PATH 31
  • 32. Forward & Backward with Many Paths START 1 5 dur=5 6 8 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 9 17 dur =9 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E First Step: ES & EF of CRITICAL PATH Activity A ES = Previous EF + 1 EF = ES + Duration - 1 ES = 0 + 1 = 1 EF = 1 + 5 1 = 5 Activity B ES = Previous EF + 1 EF = ES + Duration - 1 ES = 5 + 1 = 6 EF = 6 + 3 1 = 8 Activity E ES = Previous EF + 1 EF = ES + Duration - 1 ES = 8 + 1 = 9 EF = 9 + 9 1 = 17 32
  • 33. Forward & Backward with Many Paths START 1 5 dur=5 1 5 6 8 dur=3 6 8 dur=6 FINISH Activity A Activity B Activity C dur =6 9 17 dur =9 9 17 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E Second Step: LS & LF of CRITICAL PATH This is easy for the Critical Path LS = ES LF = EF 33
  • 34. Forward & Backward with Many Paths START 1 5 dur=5 1 5 6 8 dur=3 6 8 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 3 8 9 17 dur =9 9 17 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E First Step: ES & EF of 2nd Longest Path D,E is 2nd longest CAUTION Do NOT change values you already calculated Activity D ES & EF ES = Previous EF + 1 EF = ES + Duration - 1 ES = 0 + 1 = 1 EF = 1 + 6 1 = 6 Activity D LS & LF LF = Previous LS - 1 LS = LF - Duration + 1 LF = 9 1 = 8 LS = 8 6 + 1 = 3 34
  • 35. Forward & Backward with Many Paths START 1 5 dur=5 1 5 6 8 dur=3 6 8 9 14 dur=6 12 17 FINISH Activity A Activity B Activity C 1 6 dur =6 3 8 9 17 dur =9 9 17 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E Next Step: ES & EF of 3rd Longest Path A,B,C CAUTION Do NOT change values you already calculated Activity C ES & EF ES = Previous EF + 1 EF = ES + Duration - 1 ES = 8 + 1 = 9 EF = 9 + 6 1 = 14 Activity C LS & LF LF = LF of Critical Path LS = LF - Duration + 1 LF = 17 LS = 17 6 + 1 = 12 35
  • 36. Forward & Backward with Many Paths START 1 5 dur=5 1 5 6 8 dur=3 6 8 9 14 dur=6 12 17 FINISH Activity A Activity B Activity C 1 6 dur =6 3 8 9 17 dur =9 9 17 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E Next Step: ES & EF of 3rd Longest Path A,B,C CAUTION Do NOT change values you already calculated Activity C ES & EF ES = Previous EF + 1 EF = ES + Duration - 1 ES = 8 + 1 = 9 EF = 9 + 6 1 = 14 Activity C LS & LF LF = LF of Critical Path LS = LF - Duration + 1 LF = 17 LS = 17 6 + 1 = 12 36
  • 37. Forward & Backward with Many Paths START 1 5 dur=5 1 5 6 8 dur=3 6 8 9 14 dur=6 12 17 FINISH Activity A Activity B Activity C 1 6 dur =6 3 8 9 17 dur =9 9 17 Activity D Activity E Now to make it interesting A question on the test may be like this We have added a dependency between B & E What does it mean? Activity A Can start on day 1 or as late as Day 3 without affecting schedule Activity C Can start no earlier than day 9, but it can start as late as day 12 without affecting schedule The Critical Path is A,B,E 37
  • 38. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 38 How many paths are there? What are they? What are their Durations?
  • 39. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 39 How many paths are there? What are they? What are their Durations? It is easier to track the paths and then count them Do the easy ones first
  • 40. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 40 How many paths are there? What are they? What are their Durations? A, B,C D,E Are there others?
  • 41. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 41 How many paths are there? What are they? What are their Durations? A, B,C D,E D,B,C Any More?
  • 42. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 42 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E Next step: compute duration
  • 43. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 43 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E A,B,C = D,E = D,B,C = D,B,C = Next step: compute duration
  • 44. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 44 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E A,B,C = D,E = D,B,C = D,B,C = Next step: compute duration
  • 45. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 45 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E A,B,C=5+3+6 D,E=6+9 D,B,C=6+3+6 D,B,E=6+3+9 Next step: compute duration
  • 46. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 46 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E A,B,C=14 D,E=15 D,B,C=15 D,B,E=18
  • 47. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 47 How many paths are there? What are they? What are their Durations? 4 A, B,C D,E D,B,C D,B,E A,B,C=14 D,E=15 D,B,C=15 D,B,E=18 I forgot a path
  • 48. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this We have added a dependency between D & B 48 How many paths are there? What are they? What are their Durations? 4 5 A, B,C D,E D,B,C D,B,E A,B,E A,B,C=14 D,E=15 D,B,C=15 D,B,E=18 A,B,E = 5+3+9 = 17 I forgot a path
  • 49. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 49 How many paths are there? What are they? What are their Durations? 5 A, B,C D,E D,B,C D,B,E A,B,E A,B,C=14 D,E=15 D,B,C=15 D,B,E=18 A,B,E = 17 Time to do Forward & Backward Pass on the Critical Path D,B,E is the longest. So D,B,E is the Critical Path
  • 50. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 50 D,B,E is the longest. So D,B,E is the Critical Path Activity D ES = Previous EF + 1 EF = ES + Duration - 1 Activity B ES = Previous EF + 1 EF = ES + Duration - 1 Activity E ES = Previous EF + 1 EF = ES + Duration - 1
  • 51. Working together to Solve START dur=5 dur=3 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 51 D,B,E is the longest. So D,B,E is the Critical Path Activity D ES = Previous EF + 1 EF = ES + Duration 1 ES = 0 + 1 = 1 EF = 1 + 6 -1 = 6 Activity B ES = Previous EF + 1 EF = ES + Duration - 1 Activity E ES = Previous EF + 1 EF = ES + Duration - 1
  • 52. Working together to Solve START dur=5 7 9 dur=3 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 52 D,B,E is the longest. So D,B,E is the Critical Path Activity D ES = Previous EF + 1 EF = ES + Duration 1 ES = 0 + 1 = 1 EF = 1 + 6 -1 = 6 Activity B ES = Previous EF + 1 EF = ES + Duration 1 ES = 6 + 1 = 7 EF = 7 + 3 1 = 9 Activity E ES = Previous EF + 1 EF = ES + Duration - 1
  • 53. Working together to Solve START dur=5 7 9 dur=3 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 10 18 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 53 D,B,E is the longest. So D,B,E is the Critical Path Activity D ES = Previous EF + 1 EF = ES + Duration 1 ES = 0 + 1 = 1 EF = 1 + 6 -1 = 6 Activity B ES = Previous EF + 1 EF = ES + Duration 1 ES = 6 + 1 = 7 EF = 7 + 3 1 = 9 Activity E ES = Previous EF + 1 EF = ES + Duration 1 ES = 9 + 1 = 10 EF = 10 + 9 -1 = 18
  • 54. Working together to Solve START dur=5 7 9 dur=3 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 10 18 dur =9 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 54 D,B,E is the longest. So D,B,E is the Critical Path Time to compute LS & LF for the Critical Path
  • 55. Working together to Solve START dur=5 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 55 D,B,E is the longest. So D,B,E is the Critical Path On the Critical Path LS = ES and LF = EF Because there is NO FLOAT on the Critical Path Next Step: Compute for next longest path
  • 56. Working together to Solve START dur=5 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 56 D,B,E is the longest. So D,B,E is the Critical Path A,B,E is 2nd Longest
  • 57. Working together to Solve START dur=5 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 57 D,B,E is the longest. So D,B,E is the Critical Path In A,B,E B & E are already done, so only compute A CAUTION Do NOT change values you already calculated Activity A ES = Previous EF + 1 EF = ES + Duration 1 Activity A LF = LF of Critical Path LS = LF - Duration + 1
  • 58. Working together to Solve START 1 5 dur=5 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 58 D,B,E is the longest. So D,B,E is the Critical Path CAUTION Do NOT change values you already calculated Activity A ES = Previous EF + 1 EF = ES + Duration 1 ES = 0 + 1 = 1 EF = 1 + 5- 1 = 5 Activity A LF = Previous LS - 1 LS = LF - Duration + 1
  • 59. Working together to Solve START 1 5 dur=5 2 6 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 59 D,B,E is the longest. So D,B,E is the Critical Path CAUTION Do NOT change values you already calculated Activity A ES = Previous EF + 1 EF = ES + Duration 1 ES = 0 + 1 = 1 EF = 1 + 5- 1 = 5 Activity A LF = Previous LS - 1 LS = LF - Duration + 1 LF = 7 - 1= 6 LS = 6 - 5 + 1 = 2
  • 60. Working together to Solve START dur=5 7 9 dur=3 7 9 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 60 D,B,E is the longest. So D,B,E is the Critical Path CAUTION Do NOT change values you already calculated Activity C ES = Previous EF + 1 EF = ES + Duration 1 Activity C LF = LF of Critical Path LS = LF - Duration + 1
  • 61. Working together to Solve START dur=5 7 9 dur=3 7 9 10 15 dur=6 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 61 D,B,E is the longest. So D,B,E is the Critical Path CAUTION Do NOT change values you already calculated Activity C ES = Previous EF + 1 EF = ES + Duration 1 ES = 9 + 1 = 10 EF = 10 + 6 -1 = 15 Activity C LF = LF of Critical Path LS = LF - Duration + 1
  • 62. Working together to Solve START 1 5 dur=5 2 6 7 9 dur=3 7 9 10 15 dur=6 13 18 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E Now to make it even MORE interesting! A question on the test may be like this 62 D,B,E is the longest. So D,B,E is the Critical Path CAUTION Do NOT change values you already calculated Activity C ES = Previous EF + 1 EF = ES + Duration 1 ES = 9 + 1 = 10 EF = 10 + 6 -1 = 15 Activity C LF = LF of Critical Path LS = LF - Duration + 1 LF = 18 LS = 18 6 + 1 = 13
  • 63. What do we know from this? START 1 5 dur=5 2 6 7 9 dur=3 7 9 10 15 dur=6 13 18 FINISH Activity A Activity B Activity C 1 6 dur =6 1 6 10 18 dur =9 10 18 Activity D Activity E 63 Project Length is 18 days Critical Path is D,B,E There is no float on D,B,E Tasks D, B, & E must start on time Task D must start on Day 1 There are 5 Paths Task A could start on Day 2 And NOT affect Schedule Task C could start on Day 13 And NOT affect Schedule ES, EF, LS & LF of each task A link to more on Critical Path and Forward & Backward Pass The Link