Project Management CPM Method Tutorial-p1 Objectives and Information Step 1. Developing the Network Step 2. Determining the Duration Step 3. Determining the Critical Path (s) part 2 Developed by: Alex J. Ruiz-Torres, Ph.D.

Objectives and Information

Objectives and Information There are two goals when analyzing a project plan using the CPM method. 1. Determine the duration of the project 2. Determine the critical path activities. In other words, the activities that determine the duration. From a management perspective, the activities that need to be managed with more attention as any delay will delay the project. Delay in activities that are not in a critical path will (up to a point) not have an effect on the duration of the project.

Objectives and Information The project information that must be already defined: Set of Activities Activity duration Precedence relationships Example Activity Code Time (Weeks) Predecessors Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y

Step 1. Developing the Network

Step 1. Developing the Network We use a Network representation of the project. Nodes to represent the activities Arcs to represent the relationships We draw left to right. Activity D Activity M this means activity D must be complete before activity M can be started

Step 1. Developing the Network Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y Left to right Z Z has no predecessors, so to the “extreme” left

Step 1. Developing the Network Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y Left to right R Z R goes after Z, so to its right

Step 1. Developing the Network Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y Left to right R Z U goes after Z, so to its right U

Step 1. Developing the Network Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y Left to right U Z Given no relationship between R and U, their position is not relevant. R

Step 1. Developing the Network Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y Left to right U Z Arcs are added to indicate the U and R can only start after Z is completed. R

Step 1. Developing the Network Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y U X Z X and Y starts after U and R are finished, so to their right R Y

Step 1. Developing the Network Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y U X Z X can start after both R and U are finished R Y

Step 1. Developing the Network Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y U X Z Y can start after both R and U are finished R Y

Step 1. Developing the Network Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y U X Z A A can start after both X and Y are finished R Y

Step 2. Determining the Duration

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y We draw a box next to each node ES EF LS LF ES EF LS LF U X ES EF LS LF ES EF LS LF Z A R Y ES EF LS LF ES EF LS LF

Step 2. Determining the Duration ES = Early Start: earliest time by which an activity can start for the estimated Duration EF = Early Finish: earliest time by which an activity can end for the estimated Duration LS = Late Start: latest time by which an activity can start for the estimated Duration LF = Late Finish: latest time by which an activity can end for the estimated Duration ES EF LS LF Z

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y We always start at time 0. ES =0 for all activities with no predecessors. WE ‘MOVE’ from LEFT to RIGHT ES EF LS LF ES EF LS LF U X 0 EF LS LF ES EF LS LF Z A R Y ES EF LS LF ES EF LS LF

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y EF = ES + Activity Time ES =0 + 3 for Activity Z ES EF LS LF ES EF LS LF U X 0 3 LS LF ES EF LS LF Z A R Y ES EF LS LF ES EF LS LF

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y The Earliest Activity U can start depends on the time activity Z is finished. Same for R 3S EF LS LF ES EF LS LF U X 0 3 LS LF ES EF LS LF Z A R Y 3S EF LS LF ES EF LS LF

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y At this time we do not know when X starts as we have yet to determine when U and R are completed. 3S EF LS LF ?S EF LS LF U X 0 3 LS LF ES EF LS LF Z A R Y 3S EF LS LF ES EF LS LF

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y The EF for Activity U is ES + Time, thus 3 + 7 The EF for Activity R is its ES + Time, thus 3 + 5 3S10 LS LF ES EF LS LF U X 0 3 LS LF ES EF LS LF Z A R Y 3S 8 LS LF ES EF LS LF

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y The Earliest Activity X can start is when both U and R are finished. In other words the maximum of the EF’s. The max (8, 10) = 10. 3S10 LS LF 10 EF LS LF U X 0 3 LS LF ES EF LS LF Z A R Y 3S 8 LS LF ES EF LS LF

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y Same for Y. 3S10 LS LF 10 EF LS LF U X 0 3 LS LF ES EF LS LF Z A R Y 3S 8 LS LF 10 EF LS LF

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y EF = ES + Activity Time For X, 10 + 6 For Y, 10 + 9 3S10 LS LF 10 16 LS LF U X 0 3 LS LF ES EF LS LF Z A R Y 3S 8 LS LF 10 19 LS LF

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y 3S10 LS LF 10 16 LS LF U X 0 3 LS LF 19 EF LS LF Z A ES of Activity A depends on EF of X and Y. Max of 16 and 19 = 19 R Y 3S 8 LS LF 10 19 LS LF

Step 2. Determining the Duration Code Time Pred. Z 3 - R 5 U 7 X 6 R, U Y 9 A 4 X, Y 3S10 LS LF 10 16 LS LF U X 0 3 LS LF 19 23 LS LF EF = ES + Activity Time 19 + 4 = 23 Largest EF of the Network = Project Duration = 23 Weeks Z A R Y 3S 8 LS LF 10 19 LS LF

End of part 1 Part 2 will demonstrate how the determine the critical path.