Introduction to Project Scheduling BA 341 Lean Operations Dr Bogdan Bichescu 1 Goal Want to identify and use effective tools for planning scheduling and monitoring project progress What should we focus on in projects Common Inputs to Project Scheduling List of project tasks subtasks work packages and activities Logical sequence of activities in the project Activity durations Resources involved and their availability Usually presented as Work breakdown structure WBS Precedence tables Activities Work Packages Subtasks Major Tasks Project Work Breakdown Structure Producing a Documentary DVD Precedence Table Activity Description A B C D E F G Script writing Schedule shoots Script approval Revise script Shooting Editing Cover Design Predecessor Duration A A B C D E 10 7 5 7 11 3 5 Common Formats for Project Schedules Gantt charts How do we find the project duration Common Formats for Project Schedules Project Network Diagrams A 10 Start 0 C 5 F 3 End 0 D 7 G 5 B 7 E 11 Activity Name Duration Finding Project Duration using the Network Diagram One alternative is to identify all possible paths through the project Project duration is given by longest path critical path No Path 1 Start A C F End 2 Start A D G End 3 Start B E G End Critical Path Start B E G End Duration 18 22 23 23 Finding Project Duration using the Network Diagram Using the Critical Path Method CPM 0 10 A 10 1 0 11 0 C 5 15 20 10 17 Start 0 0 10 15 Earliest Start 15 18 Time ES Earliest Finish F 3 Time EF 20 23 23 23 End 0 D 7 0 11 18 0 7 B 7 0 7 18 23 Latest Start Time LS Latest Finish 18 23 Time LF Activity Name Duration G 5 7 18 E 11 7 Slack LS ES LF EF 23 23 18 The Project Schedule is Using the Critical Path Method CPM The Project Schedule is according to MS Project 11 Sensitivity Analysis Assuming that all activities start at their earliest times find the impact on project scheduling if Activity C takes 7 days Activity G is delayed to 9 days Activity D now takes 8 days Estimating task durations CPM assumes durations are deterministic Is this realistic Most likely How is it done in practice Probability Do your normal cautious estimating Add a generous safety margin Then double it 50 of probability Median Optimistic Pessimistic Time Program Evaluation and Review Technique PERT Similar to CPM but able to incorporate duration uncertainty Let for each project task a optimistic time estimate b pessimistic time estimate m most likely time estimate Then compute for each project task ET Expected Time a 4m b 6 2 Variance b a 6 2 Let s revisit our DVD project Activity Optimistic a Most Likely m Pessimistic b ET Variance a 4m b 6 2 b a 6 2 A B C D E F G 2 7 4 2 9 2 2 10 7 5 7 11 3 5 12 7 12 12 19 4 8 9 7 6 7 12 3 5 2 78 0 00 1 78 2 78 2 78 0 11 1 00 The Project Schedule is for ET Using PERT 0 9 A 9 3 0 12 0 15 C 6 15 21 9 Start 0 0 9 16 Earliest Start 15 18 Time ES Earliest Finish F 3 Time EF 21 24 24 24 End 0 D 7 0 12 19 0 7 B 7 0 7 24 24 19 24 Latest Start Time LS Latest Finish 19 24 Time LF Activity Name Duration G 5 7 19 E 12 7 19 Slack LS ES LF EF Critical Path Longest Path or Path with Least Slack Can now answer additional questions The probability of finishing the project in 26 days 2 Z D TE CP First compute where D the desired project completion time TE expected completion time i e the length of the critical path sum of ETs for critical activities CP2 variance of the critical path sum of variances of critical activities In our example D 26 TE 24 and CP2 0 2 78 1 3 78 Then Z 2624 sqrt 3 78 1 0287 This corresponds to 84 8 using a normal Find The project duration corresponding to 95 confidence 2 Z D T E CP Start from same equation 2 D T Z but now solve for D E CP According to a normal distribution table a Z of 1 65 corresponds to 95 probability Thus D 24 1 65 sqrt 3 78 27 21 days