1. Project Scheduling: PERT/CPM n Managers are often responsible for planning, scheduling and controlling projects that consist of numerous separate jobs or tasks performed by a variety of individuals or departments. n Project managers must schedule and coordinate the activities that make up the project to ensure the project is completed on time. n A complicating factor is the interdependence of the activities Some activities must be completed before others can be started. Some activities must be completed before others can be started.

2. PERT/CPM n PERT Program Evaluation and Review Technique Program Evaluation and Review Technique Developed by U.S. Navy for Polaris missile project Developed by U.S. Navy for Polaris missile project Developed to handle uncertain activity times Developed to handle uncertain activity times n CPM Critical Path Method Critical Path Method Developed by Du Pont & Remington Rand Developed by Du Pont & Remington Rand Developed for industrial projects for which activity times generally were known Developed for industrial projects for which activity times generally were known n Todays project management software packages have combined the best features of both approaches.

3. PERT/CPM n PERT and CPM have been used to plan, schedule, and control a wide variety of projects: R&D of new products and processes R&D of new products and processes Construction of buildings and highways Construction of buildings and highways Maintenance of large and complex equipment Maintenance of large and complex equipment Design and installation of new systems Design and installation of new systems

4. PERT/CPM n PERT/CPM is used to plan the scheduling of individual activities that make up a project. n Projects may have as many as several thousand activities. n A complicating factor in carrying out the activities is that some activities depend on the completion of other activities before they can be started.

5. PERT/CPM n Project managers rely on PERT/CPM to help them answer questions such as: What is the total time to complete the project? What is the total time to complete the project? What are the scheduled start and finish dates for each specific activity? 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? Which activities are critical and must be completed exactly as scheduled to keep the project on schedule? How long can noncritical activities be delayed before they cause an increase in the project completion time? How long can noncritical activities be delayed before they cause an increase in the project completion time?

6. PERT/CPM n First step: develop a list of the activities that make up the project. n Then identify the immediate predecessor - the activities that must be completed immediately prior to the start of that activity. n Estimate the activity time for each activity

7. Shopping Center Project Activity Activity Description Immediate Predecessor Activity Time A Prepare architectural drawings --5 B Identify potential new tenants --6 C Develop prospectus for new tenants A4 D Select contractor A3 E Prepare building permits A1 F Obtain approval for building permits E4 G Perform construction D,F14 H Finalize contracts with tenants B,C12 I Tenants move in G,H2 Total51

8. Draw Project Network Start B A E D C F G HI Finish

9. Determining the Critical Path (forward pass) n Find the earliest start time and a latest start time for all activities in the network ES – earliest start time for an activity ES – earliest start time for an activity EF = earliest finish time for an activity EF = earliest finish time for an activity T = activity time T = activity time n EF = ES + t Activity A: ES = 0, t = 5, EF = 5 Activity A: ES = 0, t = 5, EF = 5 n An activity cannot be started until all immediately preceding activities have been finished. n ES = the largest of the earliest finish times for all its immediate predecessors.

10. Determining the Critical Path n Activity B: ES = 0, EF = ES + t = 0 + 6 = 6 n Activity C: earliest finish time for activity A is 5, so the earliest start time for activity C must be 5 ES = 5, t = 4 ES = 5, t = 4 EF = ES + t = 5 + 4 = 9 EF = ES + t = 5 + 4 = 9 n Activity H: Both B and C are predecessors. ES = the largest of the earliest finish times for activities B and C ES = the largest of the earliest finish times for activities B and C EF = 6 for activity B, and EF = 9 for activity C, t = 12 EF = 6 for activity B, and EF = 9 for activity C, t = 12 Thus ES for H is 9Thus ES for H is 9 EF (for H): ES + t = 9 + 12 = 21 EF (for H): ES + t = 9 + 12 = 21

11. Critical Path (forward pass) A 0 5 5 C 5 9 4 STARTH 9 21 12

12. Forward pass ActivityESEF A05 B06 C59 D58 E56 F610 G1024 H921 I2426

13. n Thus, the project can be completed in 26 weeks.

14. Backward Pass n Begin the backward pass with a latest finish time of 26 for activity I n Once the latest finish time is known, the latest start time can be computed: LS = latest start time for an activity LS = latest start time for an activity LF = latest finish time for an activity LF = latest finish time for an activity n Beginning with activity I, LF = 26, t = 2 n LS = LF – t = 26 – 2 = 24 I 24(ES) 26(EF) 2 (t) 24(LS) 26(LF)

15. Backward Pass Activity Time (t) ESEFLSLF A50505 B606612 C459812 D358710 E15656 F4610610 G1410241024 H129211224 I224262426

16. SLACK n Slack is the length of time an activity can be delayed without increasing the project completion time. n Slack = LS – ES = LF = EF n Activity C: LS – ES = 8 – 5 = 3 weeks Thus activity C can be delayed up to 3 weeks and the entire project can still be completed in 26 weeks Thus activity C can be delayed up to 3 weeks and the entire project can still be completed in 26 weeks n Activity E: LS – ES = 5 – 5 = 0 Activity E has no slack. This activity cannot be delayed without increasing the completion time for the entire project. Activity E has no slack. This activity cannot be delayed without increasing the completion time for the entire project. Activity E is a critical activity, and on the critical path. Activity E is a critical activity, and on the critical path.

17. Critical Path n Critical activities are those with zero slack n Activities with zero slack are on the critical path.

18. Critical Path ActivityESLSEFLFSlackLS-ES Critical Path? A00550Yes B066126No C589123No D578102No E55660Yes F6610100Yes G101024240Yes H91221243No I242426260Yes

19. Project Network n A project network can be constructed to model the precedence of the activities. n The nodes of the network represent the activities. n The arcs of the network reflect the precedence relationships of the activities. n A critical path for the network is a path consisting of activities with zero slack.

20. Example: Franks Fine Floats Franks Fine Floats is in the business of building elaborate parade floats. Frank and his crew have a new float to build and want to use PERT/CPM to help them manage the project. The table on the next slide shows the activities that comprise the project. Each activitys estimated completion time (in days) and immediate predecessors are listed as well. Frank wants to know the total time to complete the project, which activities are critical, and the earliest and latest start and finish dates for each activity.

21. Example: Franks Fine Floats Immediate Completion Immediate Completion Activity Description Predecessors Time (days) Activity Description Predecessors Time (days) A Initial Paperwork --- 3 A Initial Paperwork --- 3 B Build Body A 3 B Build Body A 3 C Build Frame A 2 C Build Frame A 2 D Finish Body B 3 D Finish Body B 3 E Finish Frame C 7 E Finish Frame C 7 F Final Paperwork B,C 3 F Final Paperwork B,C 3 G Mount Body to Frame D,E 6 G Mount Body to Frame D,E 6 H Install Skirt on Frame C 2 H Install Skirt on Frame C 2