1. © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project management; Chapter 5 MGMT 405, POM, 2012/13. Lec Notes Chapter 5: Project Management Department of Business Administration FALL 20 12 - 2013

2. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 2 Outline: What You Will Learn... Discuss the behavioral aspects of projects in terms of project personnel and the project manager. Discuss the nature and importance of a work breakdown structure in project management. Give a general description of PERT/CPM techniques. Construct simple network diagrams. List the kinds of information that a PERT or CPM analysis can provide. Analyze networks with deterministic times. Analyze networks with probabilistic times. Describe activity “crashing” and solve typical problems.

3. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 3 Project: Unique, one-time operations designed to accomplish a specific set of objectives in a limited time frame. Build A A Done Build B B Done Build C C Done Build D Ship JANFEBMARAPRMAYJUN On time! Projects

4. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 4 Project Management How is it different?  Limited time frame  Narrow focus, specific objectives  Less bureaucratic Why is it used?  Special needs  Pressures for new or improves products or services What are the Key Metrics  Time  Cost  Performance objectives What are the Key Success Factors?  Top-down commitment  Having a capable project manager  Having time to plan  Careful tracking and control  Good communication

5. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 5 Project Management What are the Major Administrative Issues?  Executive responsibilities  Project selection  Project manager selection  Organizational structure  Organizational alternatives  Manage within functional unit  Assign a coordinator  Use a matrix organization with a project leader What are the tools?  Work breakdown structure  Network diagram  Gantt charts  Risk management

6. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 6 Deciding which projects to implement  Criteria-attractive-cost and benefit-available fund Selecting a project manager  Central person Selecting a project team  Person’s knowledge and skills-relationship with others Planning and designing the project  Goals-timetable-budget-resources Managing and controlling project resources  Personnel-equipment-budget Deciding if and when a project should be terminated  Likelihood of success-costs-resources Key Decisions

7. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 7 Project Manager Responsible for: WorkQuality Human ResourcesTime CommunicationsCosts

8. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 8 Temptation to understate costs Withhold information Misleading status reports Falsifying records Comprising workers’ safety Approving substandard work Ethical Issues

9. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 9 Project Life Cycle Concept Feasibility Planning Execution Termination Management Concept: A proposal needed Feasibility: Cost, benefit and risk analyses Planning: find out the necessary human resources, time and cost Execution: control for time, available resource and cost Termination: It should be reevaluated for the sake of project’s safety

10. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 10 Work Breakdown Structure Project X Level 1 Level 2 Level 3 Level 4

11. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 11 Planning and Scheduling MARAPRMAYJUNJULAUGSEPOCTNOVDEC Locate new facilities Interview staff Hire and train staff Select and order furniture Remodel and install phones Move in/startup Gantt Chart

12. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 12 PERT and CPM PERT: Program Evaluation and Review Technique CPM: Critical Path Method  Both techniques are widely used for planning and coordinating large-scale projects.  Using the two techniques, manager are able to obtain: Graphically displays project activities Estimates how long the project will take Indicates most critical activities Show where delays will not affect project

13. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 13 The Network Diagram Network (precedence) diagram – diagram of project activities that shows sequential relationships by the use of arrows and nodes. Activity-on-arrow (AOA) – a network diagram convention in which arrows designate activities. Activity-on-node (AON) – a network diagram convention in which nodes designate activities. Activities – steps in the project that consume resources and/or time. Events – the starting and finishing of activities, designated by nodes in the AOA convention.

14. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 14 The Network Diagram Path  Sequence of activities that leads from the starting node to the finishing node Critical path  The longest path; determines expected project duration Critical activities  Activities on the critical path Slack  Allowable slippage for path; the difference the length of path and the length of critical path  Slack is the length of the time where an activity can be delayed without interfering with the project completion. Dummy  Using this variable does not cost any burden for the company. This exists solely for the purpose of establishing precedence relationships for the sake of simplicity and is not asssigned any time.

15. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 15 Project Network – Activity on Arrow 1 2 3 4 56 Locate facilities Order furniture Furniture setup Interview Hire and train Remodel Move in AOA

16. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 16 Project Network – Activity on Node 1 2 3 5 6 Locate facilities Order furniture Furniture setup Interview Remodel Move in 4 Hire and train 7S AON

17. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 17 Network Conventions a b ca b c a b c d a b c Dummy activity a and b must be completed before c can start a must be completed before b or c can start a and b must be completed before b or c can start a must be completed before c can start// b and dummy must be completed before c can start

18. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 18 Network activities  ES: early start  EF: early finish-EF=ES+t  LS: late start-LS=LF-t  LF: late finish Used to determine  Expected project duration  Slack time-LS-ES or LF-EF  Critical path Computing Algorithm ES t EF LSLF ES t EF

19. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 19 Example 1-Bank Network convention The following table contains information related to the major activities of a research project. Use the information to do the following: (a) Draw a precedence diagram using AOA and AON (b) Find the critical path based AOA. (c) Determine the expected length of the project. (d)The amount of slack time for each path ActivityImmediate PredecessorExpected Time (days) a-5 ca8 dc2 ba7 e-3 fe6 ib, d10 mf,i8 g-1 hg2 kh17 endk,m

20. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 20 Answer-Bank Network convention c a f g h d Activities with no predecessors are at the beginning (life side) of the network. Activities with multiple predecessors are located at path intersections. (a) Use first AOA ; the precedence diagram using AOA is constructed as follows: 5 8 2 b 7 e 3 6 i 10 m 8 1 2 k 17 S End

21. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 21 Example-Bank Network convention (b)Find the critical path based AOA. a-c-d-i-m * =5+8+2+10+8=33 # a-b-i-m=5+7+10+8=30 e-f-m= 3+6+8=17 g-h-k=1+2+17=20 a-c-d-i-m*- Critical path (c) Determine the expected length of the project. 33 # - Expected project duration

22. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 22 Answer-Bank Network convention c a f g h d (d) calculate the amount of slack time for each path 5 8 2 b 7 e 3 6 i 10 m 8 1 2 k 17 S End 5 0 13 5 5 15 12 15 25 33 25 0 3 3 9 0 1 1 3 3 20 33 25 33 16 14 13 25 19 16 15 13 5 15 8 5 0 25 LSLF ES t EF

23. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 23 Example 2-Bank Network convention The following table contains information related to the major activities of a research project. Use the information to do the following: (a) Draw a precedence diagram using AOA (b) Find the critical path based AOA. (c) Determine the expected length of the project. (d)The amount of slack time for each path ActivityImmediate PredecessorExpected Time (days) a-8 ba6 db3 ca11 e-4 fe9 gc, d, f1 endc, d, f

24. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 24 Example 2-Bank Network Figure 1 2 3 4 56 8 weeks 6 weeks 3 weeks 4 weeks 9 weeks 11 weeks 1 week Locate facilities Order furniture Furniture setup Interview Hire and train Remodel Move in (a) Bank Network question

25. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 25 Answer-Bank Network Figure (b) and (c) Critical Path  Knowledge of slack times provides managers with information for planning allocation of scarce resources and for directing control efforts toward those activities that may be most susceptible to delaying the project.

26. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 26 Example-ES-EF-LS-LF-slack 1 2 3 4 56 0 8 8 8 6 14 14 3 17 0 4 4 4 9 13 8 11 19 19 1 20 LSLF ES t EF EF: early finish-EF=ES+t LS: late start-LS=LF-t Slack time-LS-ES or LF-EF (d) Required: Compute slack time, ES, EF, LS and LF Forward pass Backward pass

27. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 27 Answer (d- cont...) -ES-EF-LS-LF-slack 1 2 3 4 56 0 8 8 8 6 14 14 3 17 0 4 4 4 9 13 8 11 19 19 1 20 LSLF ES t EF 19 1 20 1920 0 EF: early finish-EF=ES+t LS: late start-LS=LF-t Slack time-LS-ES or LF-EF 10 9 19 4 13 6 6 4 10 0 4 6 811 19 8 19 0 16 3 19 14 17 2 10 6 16 8 14 2 0 8 8 0 8 0 Forward pass Backward pass

28. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 28 PERT model-Time Estimates  The main determinant of the way PERT and CPM networks are analysed and interpreted is whether activity time estimates are probabilistic or deterministic. Deterministic  Time estimates that are fairly certain Probabilistic  Estimates of times that allow for variation

29. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 29 Probabilistic Time Estimates Optimistic time  Time required under optimal conditions Pessimistic time  Time required under worst conditions Most likely time  Most probable length of time that will be required

30. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 30 Probabilistic Estimates Activity start Optimistic time Most likely time (mode) Pessimistic time toto tptp tmtm tete Beta Distribution is generally used to describe the inherent variability in time Estimates. Although there is no real theoretical justification for using the Beta Distribution, it has certain features that make it attractive in practice.

31. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 31 Expected Time tete = t o + 4t m +t p 6 t e = expected time t o = optimistic time t m = most likely time t p = pessimistic time The knowledge of the expected path times and their std. Deviation enables a manager to compute probabilistic estimates of the project completion time as such specific time and scheduled time

32. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 32 Variance    (t p – t o ) 2 36    = variance t o = optimistic time t p = pessimistic time The size of Variance reflects the degree of uncertainty associated with an activity’s time: The large the variance, the greater the uncertainty.

33. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 33 Advantages of PERT Forces managers to organize Provides graphic display of activities Identifies  Critical activities  Slack activities 1 2 3 4 56

34. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 34 Limitations of PERT Important activities may be omitted Precedence relationships may not be correct Estimates may include a fudge factor May focus solely on critical path 1 2 3 4 56 142 weeks

35. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 35 Example-Probabilistic Time Estimates 1-3-4 a 3-4-5 d 3-5-7 e 5-7-9 f 2-4-6 b 4-6-8 h 2-3-6 g 3-4-6 i 2-3-5 c Optimistic time Most likely time Pessimistic time Given the following diagram: Compute The expected time The expected duration Identify the critical path The variance The std. deviation

36. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 36 Probabilistic Time Estimates Answer-Probabilistic Time Estimates

37. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 37 Probabilistic Time Estimates Answer-Probabilistic Time Estimates 2.83 a 4.00 d 5.0 e 7.0 f 4.00 b 6.0 h 3.33 g 4.17 i 3.17 c T abc = 10.0 T def = 16.0 T ghi = 13.50

38. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 38 Path Probabilities Z = Specified time – Path mean Path standard deviation Z indicates how many standard deviations of the path distribution the specified time is beyond the expected path duration. The more positive the value, the better. A negative value of z indicates that the specified time is earlier than the expected path duration. Z=+3.00-probability 100%- From the relevant table +3.00 is almost equal to 0.9987.

39. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 39 Example-The Path probability example of probabilistic time estimates (the previous example): Given the information on the example of probabilistic time estimates (the previous example): Determine  The probability that the project can be completed within 17 weeks of its start.  The probability that the project will be completed within 15 weeks of its start.  The probability that the project will not be completed within 15 weeks of its start.

40. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 40 Answer-The Path probability Determine  The probability that the project can be completed within 17 weeks of its start. Path: a-b-c Z = 17 – 10 0.97 =7.22 Determine  The probability that the project will be completed within 17 weeks of its start. Path: d-e-f Z = 17 – 16 1 =1=1 Prob.comp in 17 week = 1.00 Appendix B, Table B, p.p 884/5 Prob.comp in 17 week = 0.8413 Appendix B, Table B, p.p 885

41. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 41 Answer-The Path probability Determine  The probability that the project will be completed within 17 weeks of its start. Path: g-h-i Z = 17 – 13.5 1.07 =3.27 Prob.comp in 17 week = 1.00 Appendix B, Table B, p.p 884/5 Prob finish in 17 week = 1.00 X 0.8413 X 1.00= 0.8413

42. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 42 Answer-The Path probability Determine  The probability that the project can be completed within 15 weeks of its start. Path: a-b-c Z = 15 – 10 0.97 =5.15 Determine  The probability that the project will be completed within 15 weeks of its start. Path: d-e-f Z = 15 – 16 1 =-1.00 Prob.comp in 15 week = 1.00 Appendix B, Table B, p.p 884/5 Prob.comp in 15 week = 0.1587 Appendix B, Table B, p.p 885

43. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 43 Answer-The Path probability Determine  The probability that the project will be completed within 15 weeks of its start. Path: g-h-i Z = 15 – 13.5 1.07 =1.40 Prob.comp in 15 week = 0.9192 Appendix B, Table B, p.p 884/5 The probability that the project will not be completed within 15 weeks of its start: 1- 0.1459=0.8541 Prob finish in 15 week = 1.00 X 0.1587 X 0.9192= 0.1459

44. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 44 17 Weeks 10.0 16.0 13.5 1.00 a-b-c d-e-f g-h-i Answer-The Path probability-Graphically 0.8413

45. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 45 15 Weeks 10.0 16.0 13.5 1.00 0.9192 a-b-c d-e-f g-h-i Answer-The Path probability-Graphically 0.1587

46. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 46 Table 12.3, page 569

47. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 47 Time-cost Trade-offs: Crashing Exluded from the exam topics  In many projects, it is possible to reduce the length of a project by injecting additional resources. The impetus to shorten projects may reflect efforts to avoid late penalties, or/ to take advantage of monetary incentives for timely completion of a project, or/ to free resources for use on other projects. This is called crashing. Crash – briefly, shortening activity duration Procedure for crashing  Crash the project one period at a time  Only an activity on the critical path  Crash the least expensive activity  Multiple critical paths: find the sum of crashing the least expensive activity on each critical path

48. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 48 Time-Cost Trade-Offs: Crashing Total cost Shorten Cumulative (direct) cost of crashing Expected indirect costs Optimum CRASH

49. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 49 Example-Crashing Using the following information, develop the optimal time cost solution. Indirect costs are $ 1000 per day. (a)Determine which activities are on the critical path, its length, and the length of the other path (b)Rank the critical activities in order of lowest crashing cost, and determine the number of days each can be crashed. (c)Determine the critical path after each reduction by shortening the project. ActivityNormal timeCrash timeCost per day to crash a66 c108$500 d54300 b41700 e97600 f21800

50. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 50 6a6a 4d4d 5c5c 10 b 9e9e 2f2f Determine the expected length of the project.

51. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 51 Answer-Crashing (a) Determine which activities are on the critical path, its length, and the length of the other path Path length a-b-f 18 c-d-e-f 20 (critical path) (b) Rank the critical activities in order of lowest crashing cost, and datermine the number of days each can be crashed. ActivityCost per day to crashAvailable days c$ 3001 e 6002 d 7003 f 8001

52. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 52 Answer-Crashing (c) Determine the critical path after each reduction by shortening the project. (1) Shorten activity c one day at a cost of $ 300. The length of the critical path becomes 19 days. (2) Activity c cannot be shorten any more. Shorten activity e one day at cost of $ 600. The length of the critical path c-d-e-f becomes 18 days which is the same as length of path a-b-f. (3) The path are now both critical, further improvement will necesitate shortening both paths. Path Activity Cost per day to crash a-b-f ano reduction possible b $ 500 f 800 c-d-e-f c no further reduction possible d $ 700 e 600 f 800

53. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 53 Answer-Crashing At the first glance, it would seem that crashing f would not be advantageous, because it has the highest crashing cost. However, f is on both paths, so shortening f by one day would shorten both paths by one day for a cost of $ 800. The option of shortening the least expensive activity on each path would cost $ 500 for b and $ 600 for e or $ 1100. Thus shorten f by one day. The project duration is now 17 days. (4) At this point, no additional improvement is feasible. The cost to crash b is $ 500 and the cost to crash e is $ 600, for a total of $ 1100 and that would exceed the indirect costs of $ 100 per day. (5) The crashing sequence is summarized below: Length after crashing n days Path n=0 1 2 3 a-b-f 18 18 1817 c-d-e-f 20 19 1817 activity crashed c e f cost $300 600 800

54. MGMT 405, POM, 2012/13. Lec Notes © Stevenson, McGraw Hill, 2010- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Project Management; Chapter 5 54 Thanks