Presentation on theme: "Chapter 9 Project Scheduling: PERT/CPM"— Presentation transcript:
1 Chapter 9 Project Scheduling: PERT/CPM Projects are usually complex, unique, expensive to implement and may have several thousand activities. Moreover, some activities depend on the completion of other activities before they can be started.Examples of projects include:R&D of new products and processesConstruction of buildings and highwaysMaintenance of large and complex equipmentDesign and installation of new systemsPERT/CPM is used to plan the scheduling of individual activities that make up a project.
2 PERT/CPM PERT Program Evaluation and Review Technique Developed by U.S. Navy for Polaris missile projectDeveloped to handle uncertain activity timesCPMCritical Path MethodDeveloped by DuPont & Remington RandDeveloped for industrial projects for which activity times are fixedToday’s project management software packages have combined the best features of both approaches.
3 PERT/CPMProject managers rely on PERT/CPM to help them answer questions such as:What is the total time to complete the project?What are the scheduled start and finish dates for each specific activity?Which activities are critical and must be completed exactly as scheduled to keep the project on schedule?How long can non-critical activities be delayed before they cause an increase in the project completion time?
4 Project NetworkA project network can be constructed to model the precedence of the activities.The nodes of the network represent the activities.The arcs of the network reflect the precedence relationships of the activities.A critical path for the network is a path consisting of activities with zero slack. It is also the path that takes the longest time to complete.
5 Example: Frank’s Fine Floats Frank’s Fine Floats is in the business of buildingelaborate parade floats. Frank ‘s crew has a new float tobuild and want to use PERT/CPM to help them managethe project.The table on the next slide shows the activities thatcomprise the project as well as each activity’s estimatedcompletion time (in days) and immediate predecessors.Frank wants to know the total time to complete theproject, which activities are critical, and the earliest andlatest start and finish dates for each activity.
6 Example: Frank’s Fine Floats Immediate CompletionActivity Description Predecessors Time (days)A Initial PaperworkB Build Body AC Build Frame AD Finish Body BE Finish Frame CF Final Paperwork B,CG Mount Body to Frame D,EH Install Skirt on Frame C
8 Earliest Start and Finish Times Step 1: Make a forward pass through the network as follows: For each activity i beginning at the Start node, compute:Earliest Start Time, ESi = the maximum of the earliest finish times of all activities immediately preceding activity i. (This is 0 for an activity with no predecessors.)Earliest Finish Time, EFi = (Earliest Start Time) + (Time to complete activity i ).The project completion time is the maximum of the Earliest Finish Times all the activities that end at the Finish node.
9 Example: Frank’s Fine Floats Earliest Start and Finish TimesB3 6D6 933G12 186F6 93A0 3StartFinish3E5 127C3 5H5 722HES EF2LS LF
10 Latest Start and Finish Times Step 2: Make a backwards pass through the network as follows: Move sequentially backwards from the Finish node to the Start node. For each activity, i, compute:Latest Finish Time, LFi = the minimum of the latest start times of all the successor activity/ies of node i. (For node last node/s, this is the project completion time or the largest earliest finish times of the nodes that end at the Finish node.)Latest Start Time, LSi = (Latest Finish Time) - (Time to complete activity i ).
12 Determining the Critical Path Step 3: Calculate the slack time for each activity by:Slack = (Latest Start) - (Earliest Start), or= (Latest Finish) - (Earliest Finish).B3 6D6 936 939 12G12 18612 18F6 9315 18A0 3StartFinish30 3E5 1275 12C3 5H5 723 5216 18
13 Example: Frank’s Fine Floats Activity Schedule including the Slack TimeActivity ES EF LS LF SlackA (critical)BC (critical)DE (critical)FG (critical)H
14 Example: Frank’s Fine Floats A critical path is a path of activities, from the Start node to the Finish node, with 0 slack times.B3 6D6 936 939 12G12 18612 18F6 9315 18A0 3StartFinish30 3E5 1275 12C3 5H5 723 5216 18Critical Path: A – C – E – GProject Completion Time: days
15 PERT/CPM Critical Path Procedure Step 1. Develop a list of the activities of the project.Step 2. Determine the immediate predecessor(s) for each activity in the project.Step 3. Estimate the completion time for each activity.Step 4. Draw a project network depicting the activities and immediate predecessors listed in steps 1 and 2.Step 5. Determine the earliest start and the earliest finish time for each activity by making a forward pass through the network.Step 6. Use backward pass through the network to identify the latest start and latest finish time for each activity.
16 PERT/CPM Critical Path Procedure Step 7. Use the difference between the latest start time and the earliest start time for each activity to determine the slack for each activity.Step 8. Find the activities with zero slack; these are the critical activities.Step 9. Use the information from steps 5 and 6 to develop the activity schedule for the project.
17 Classroom Exercise: ABC Associates Consider the following project:Activity Immed. Predec. Activity time (hours)ABC AD AE AF B,CG B,CH E,FI E,FJ D,HK G,Ii) Draw the project network diagram for ABC Associates.ii) Calculate the ES, EF, LS, LS and S for each activity.iii) Determine the critical path.iv) What is the project completion time?
19 Uncertain Activity Times for PERT Calculation of activity’s mean completion time and completion time variance.An activity’s mean completion time is:t = (a + 4m + b)/6a = the optimistic completion time estimateb = the pessimistic completion time estimatem = the most likely completion time estimateAn activity’s completion time variance is: 2 = ((b-a)/6)2
20 Example: ABC Associates Consider the following project:Immed. Optimistic Most Likely PessimisticActivity Predec. Time (Hr.) Time (Hr.) Time (Hr.)ABC AD AE AF B,CG B,CH E,FI E,FJ D,HK G,I
21 Example: ABC Associates Activity Expected Times and Variancest = (a + 4m + b)/6 2 = ((b-a)/6)2Activity Expected Time VarianceA /9B /9CD /9E /36F /9G /9H /9IJ /9K /9
22 Example: ABC Associates Critical Path (A-C-F-I-K); Project Completion time: 23 hours6 1115 2019 2220 235313 1914 200 66 712 1366113 186 99 1353418 230 45 99 1116 18542Important Note: The variance of the project completion time is the sum of the variances of the activities on the critical path.
23 Example: ABC Associates Probability the project will be completed within 24 hrs:Step 1: Calculate the variance of the project completion time 2 = 2A + 2C + 2F + 2I + 2K= 4/ / /9= 2 =Step 2: Calculate the standard normal, z = (X – m)/ ,where m = expected project completion time.z = ( )/ (24-23)/1.414 = .71Step 3: Calculate the probability from the standard normal distribution table (See Appendix A in the textbook):P(z < .71) = =
24 Example: ABC Associates i) What is the probability that the project will be completed with 25 hours?ii) What is the probability that the project will be completed between 20 and 25 hours?