1.040/1.401 Project Management Spring 2007 Deterministic Planning Part I

1. 1.040/1.401Project ManagementSpring 2007Deterministic Planning Part I Dr. SangHyun Lee lsh@mit.edu Department of Civil and Environmental Engineering Massachusetts Institute of Technology

2. Project Management Phase DESIGN PLANNING DEVELOPMENT OPERATIONS CLOSEOUT FEASIBILITY Fin.&Eval. Organization Risk Estimating Planning&Scheduling

3. Outline • Objective • Bar Chart • Network Techniques • CPM

4. Objective • What are some of the Different Representations for Deterministic Schedules ? • What are some Issues to Watch for?

5. Outline • Objective • Bar Chart • Network Techniques • CPM

6. Gantt Chart Characteristics • Bar Chart • Henry L. Gantt • World War I - 1917 • Ammunition Ordering and Delivery • Activities Enumerated in the Vertical Axis • Activity Duration Presented on the Horizontal Axis • Easy to Read

7. Simple Gantt Chart

8. Gantt (Bar) Charts • Very effective communication tool • Very popular for representation of simpler schedules • Can be cumbersome when have >100 activities • Key shortcoming: No dependencies captured • Most effective as reporting format rather than representation

9. Hierarchy of Gantt Charts

10. Activity Aggregation • Hammock Activities • A graphical arrangement which includes a summary of a group of activities in the project. • Duration equal to longest sequence of activities Source: Shtub et al., 1994

11. Activity Aggregation • Milestones • A task with a zero duration that acts as a reference point marking a major project event. Generally used to mark: beginning & end of project, completion of a major phase, or a task for which the duration is unknown or out of control. • Flag the start or the successful completion of a set of activities Source: Shtub et al., 1994

12. Outline • Objective • Bar Chart • Network Techniques • CPM

13. Activity on Arrow AOA Activity A Activity A Activity B Event i Event j Network Scheduling • A network is a graphical representation of a project plan, showing the inter-relationships of the various activities. • When results of time estimates & computations are added to a network, it may be used as a project schedule. Activity on Node AON Source: Badiru & Pulat, 1995

14. Advantages • Communications • Interdependency • Expected Project Completion Date • Task Starting Dates • Critical Activities • Activities with Slack • Concurrency • Probability of Project Completion Source: Badiru & Pulat, 1995

15. Start Network - Definitions Node (Activity) Arc A D Milestone Merge Point Finish B G E Dummy H F C Burst Point I Source: Badiru & Pulat, 1995

16. Start Network - Definitions A D Finish B G E H F C I • Predecessor Activity of D • Successor Activity of F Source: Badiru & Pulat, 1995

17. Definitions (Cont’d) • Activity • Time and resource consuming effort with a specific time required to perform the task or a set of tasks required by the project • Dummy • Zero time duration event used to represent logical relationships between activities • Milestone • Important event in the project life cycle • Node • A circular representation of an activity and/or event Source: Badiru & Pulat, 1995

18. Definitions (Cont’d) • Arc • A line that connects two nodes and can be a representation of an event or an activity • Restriction / Precedence • A relationship which establishes a sequence of activities or the start or end of an activity • Predecessor Activity • An activity that immediately precedes the one being considered • Successor Activity • An activity that immediately follows the one being considered • Descendent Activity • An activity restricted by the one under consideration • Antecedent Activity • An activity that must precede the one being considered Source: Badiru & Pulat, 1995

19. Definitions (Cont’d) • Merge Point • Exists when two or more activities are predecessors to a single activity (the merge point) • Burst Point • Exists when two or more activities have a common predecessor (the burst point) • Network • Graphical portrayal of the relationship between activities and milestones in a project • Path • A series of connected activities between any two events in a network Source: Badiru & Pulat, 1995

20. Outline • Objective • Bar Chart • Network Techniques • CPM

21. Critical Path Method (CPM) • DuPont, Inc., and UNIVAC Division of Remington Rand • Scheduling Maintenance Shutdowns in Chemical Processing Plants • ~1958 • Construction Projects • Time and Cost Control • Deterministic Times

22. CPM Objective • Determination of the critical path: the minimum time for a project

23. CPM Precedence • Technical Precedence • Caused by the technical relationships among activities (e.g., in conventional construction, walls must be erected before roof installation) • Procedural Precedence • Determined by organizational policies and procedures that are often subjective with no concrete justification • Imposed Precedence • E.g., Resource Imposed (Resource shortage may require one task to be before another) Source: Badiru & Pulat, 1995

24. Arrow Finish Event Clear & Grub Start Form Footings Excavate Footings Fabricate Footings Forms at Site Workshop 1 Mobilize 7 3 2 4 6 Dummy Activity Fabricate Rebar Footings Activity 5 8 Fabricate Forms Footings Fabricate Rebar Footings Excavate Footings Form Footings Start Dummy Activity Arc Clear & Grub Mobilize Finish CPM: AOA & AON • Activity-on-Arrow • Activity-on-Node Source: Feigenbaum, 2002 Newitt, 2005

25. CPM Calculations • Forward Pass • Early Start Times (ES) • Earliest time an activity can start without violating precedence relations • Early Finish Times (EF) • Earliest time an activity can finish without violating precedence relations Source: Hegazy, 2002 Hendrickson and Au, 1989/2003

26. Forward Pass - Intuition • It’s 8am. Suppose you want to know the earliest time you can arrange to meet a friend after performing some tasks • Wash hair (5 min) • Boil water for tea (10 min) • Eat breakfast (10 min) • Walk to campus (5 min) • What is the earliest time you could meet your friend?

27. CPM Calculations • Backward Pass • Late Start Times (LS) • Latest time an activity can start without delaying the completion of the project • Late Finish Times (LF) • Latest time an activity can finish without delaying the completion of the project Source: Hegazy, 2002 Hendrickson and Au, 1989/2003

28. Backward Pass - Intuition • Your friend will arrive at 9am. You want to know by what time you need to start all things • Wash hair (5 min) • Boil water for tea (10 min) • Eat breakfast (10 min) • Walk to campus (5 min) • What is the latest time you should start?

29. Slack or Float • It’s 8am, and you know that your friend will arrive at 9am. How much do you have as free time? • Wash hair (5 min) • Boil water for tea (10 min) • Eat breakfast (10 min) • Walk to campus (5 min)

30. CPM Example Draw AON network Source: Badiru & Pulat, 1995

31. Forward Pass F 4 A 2 End D 3 ES EF 0 0 G 2 B 6 Start E 5 C 4 Source: Badiru & Pulat, 1995

32. Forward Pass 2 6 F 4 0 2 11 11 A 2 2 5 End D 3 9 11 0 6 0 0 G 2 B 6 Start 0 4 4 9 E 5 C 4 Source: Badiru & Pulat, 1995

33. Backward Pass 2 6 F 4 0 2 11 11 A 2 2 5 End D 3 11 11 9 11 0 6 LS LF 0 0 G 2 B 6 Start 0 4 4 9 E 5 C 4 • LF(k) = Min{LS(j)} j S(k) • LS(k) = LF(k) – D(k)  Source: Badiru & Pulat, 1995

34. Backward Pass 2 6 F 4 0 2 11 11 7 11 A 2 2 5 End D 3 4 6 11 11 6 9 9 11 0 6 0 0 G 2 B 6 Start 9 11 0 0 3 9 0 4 4 9 E 5 C 4 0 4 4 9 Source: Badiru & Pulat, 1995

35. Slack or Float • The amount of flexibility an activity possesses • Degree of freedom in timing for performing task 2 6 4 F 4 0 2 11 11 7 11 A 2 End 2 5 D 3 4 6 11 11 6 9 9 11 0 0 G 2 B 6 0 6 Start 9 11 0 0 3 9 0 4 4 9 E 5 C 4 0 4 4 9 Source: Hendrickson and Au, 1989/2003

36. Total Slack or Float • Total Slack or Float (TS or TF) • Max time can delay w/o delaying the project • TS(k) = {LF(k) - EF(k)} or {LS(k) - ES(k)} 2 6 TS = 4 F 4 0 2 11 11 7 11 A 2 End 2 5 D 3 4 6 11 11 6 9 9 11 0 0 G 2 B 6 0 6 Start 9 11 0 0 3 9 0 4 4 9 E 5 C 4 0 4 4 9

37. Free Slack or Float • Free Slack or Float (FS or FF) • Max time can delay w/o delaying successors • FS(k) = Min{ES(j)} - EF(k) j S(k)  2 6 F 4 0 2 11 11 7 11 A 2 End 2 5 D 3 4 6 11 11 FS = 3 6 9 9 11 0 0 G 2 B 6 0 6 Start 9 11 0 0 3 9 0 4 4 9 E 5 C 4 0 4 4 9

38. Independent Slack or Float • Independent Slack or Float (IF) • Like Free float but assuming worst-case finish of predecessors • IF(k) = Max { 0, ( Min(ES(j)) - Max(LF(i)) – D(k) ) } j S(k), i P(k)   IF = 1 2 6 F 4 0 2 11 11 7 11 A 2 End 2 5 D 3 4 6 11 11 6 9 9 11 0 0 G 2 B 6 0 6 Start 9 11 0 0 3 9 0 4 4 9 E 5 C 4 0 4 4 9

39. CPM Analysis Activity Duration ES EF LS LF TS FS IF Critical A 2 0 2 4 6 4 0 0 B 6 0 6 3 9 3 3 3 C 4 0 4 0 4 0 0 0 Yes D 3 2 5 6 9 4 4 0 E 5 4 9 4 9 0 0 0 Yes F 4 2 6 7 11 5 5 1 G 2 9 11 9 11 0 0 0 Yes Adapted from: Badiru & Pulat, 1995

40. Critical Path • The path with the least slack or float in the network • Activities in that path: critical activities • For algorithm as described, at least one such path • Must be completed on time or entire project delayed • Determines minimum time required for project • Consider near-critical activities as well!

41. Critical Path If EFi = ESj, then activity i is a critical activity (here, activity i is an immediate predecessor of activity j 2 6 F 4 0 2 11 11 7 11 A 2 End 2 5 D 3 4 6 11 11 6 9 9 11 0 0 G 2 B 6 0 6 Start 9 11 0 0 3 9 0 4 4 9 E 5 C 4 0 4 4 9 Source: Badiru & Pulat, 1995

42. Path Criticality • Rank paths from more critical to less critical = minimum total float = maximum total float = total float or slack in current path

43. Path Criticality - Example • Calculate Path Criticality • αmin = 0, αmax = 5 • Path 1: [(5-0)/(5-0)](100 %) = 100 % • Path 2: [(5-3)/(5-0)](100 %) = 40 % • Path 3: [(5-4)/(5-0)](100 %) = 20 % • Path 4: [(5-5)/(5-0)](100 %) = 0 % Source: Badiru & Pulat, 1995