OPSM 301 Operations Management

1. Koç University OPSM 301 Operations Management Class 9: Project Management: PERT and project crashing Zeynep Aksin zaksin@ku.edu.tr

2. Announcements • Change in syllabus plan as follows: • Will swap last session on project management with decision trees • Last session of project management will be after the bayram on 8/11 • Class will be held in the lab (TBA) • Second group assignment will be due • We will have quiz 2 on Project Management • Decision Trees will be on 1/11 • Quiz 3 on 10/11 Thursday

3. Example Suppose you are an advertising manager responsible for the launch of a new media advertising campaign. The campaign (project) has the following activities: Activity Predecessors Time A. Media bids none 2 wks B. Ad concept none 6 C. Pilot layouts B 3 D. Select media A 8 E. Client approvalA,C 6 F. Pre-production B 8 G. Final production E,F 5 H. Launch campaign D,G 0

4. CPM with Three Activity Time Estimates

5. Some CPM/PERT Assumptions • Project control should focus on the critical path • The activity times in PERT follow the beta distribution, with the variance of the project assumed to equal the sum of the variances along the critical path

6. Beta Distribution Assumption Assume a “Beta” distribution density activity duration

7. Beta Distribution Assumption density activity duration a m b

8. Expected Time and Variance a + 4m + b 6 Expected Time = (b - a)2 36 Variance =

9. Expected Times

10. ES EF LS LF 21 32 7 21 C, 14 E, 11 0 7 32 36 7 21 21 32 H, 4 A, 7 0 7 7 12 32 36 12 19 36 54 0 0 D, 5 F, 7 Start 0 I, 18 20 25 25 32 0 0 36 54 0 5.33 5.33 16.33 B 5.33 G, 11 19.67 25 25 36

11. Expected Completion Time = 54 Days C, 14 E, 11 H, 4 A, 7 D, 5 F, 7 Start 0 I, 18 B 5.33 G, 11

12. Pr(t < D) t TE = 54 What is the probability of finishing this project in less than 53 days? We need the variance also! D=53

13. Sum the variance along the critical path =

14. Pr(t < D) t D=53 TE = 54 p(z < -.156) =.436, or 43.6% There is a 43.6% probability that this project will be completed in less than 53 weeks.

15. © 1995 Corel Corp. PERT Probability Example You’re a project planner for General Dynamics. A submarine project has an expected completion time of 40 weeks, with a standard deviation of 5 weeks. What is the probability of finishing the sub in 50 weeks or less?

16. Converting to Standardized Variable - - X T 50 40 = = = Z 2 . 0 s 5 Normal Distribution Standardized Normal Distribution s = 1 s = 5 Z m = 40 50 X T Z = 0 2.0 z

17. Obtaining the Probability Standardized Normal Probability Table (Portion) Z .00 .01 .02 s = 1 .50000 .50399 .50798 0.0 Z : : : : .97725 .97725 .97784 .97831 2.0 m Z = 0 2.0 .98214 .98257 .98300 2.1 z Probabilities in body

18. Variability of Completion Time for Noncritical Paths • Variability of times for activities on noncritical paths must be considered when finding the probability of finishing in a specified time. • Variation in noncritical activity may cause change in critical path.

19. Time-Cost Models • Basic Assumption: Relationship between activity completion time and project cost • Time Cost Models: Determine the optimum point in time-cost tradeoffs • Activity direct costs • Project indirect costs • Activity completion times

20. Project Costs vs. Project Duration

21. Cost Analysis • We assume a linear relation between activity duration and activity cost • Regulate activity durations to minimize the total project cost

22. Cost Analysis • We require two time estimates and two associated cost estimates: • Normal Time: Time required if a usual amount of resources are applied to the activity. • Normal Cost: Cost of completing an activity in normal time. • Crash Time: Least time that an activity can be performed in if all available resources are applied to it. • Crash Cost: Cost of completing an activity in crash time. • Incremental Cost: • I = (Crash Cost - Normal Cost)/(Normal Time - Crash Time) • I=Cost of reducing duration of an acitivity by 1 unit of time

23. Crash and Normal Times and Costs for Activity B

24. Steps for Solution 1. Perform PERT analysis using normal times and calculate I for all critical activities 2. Pick the activity (critical) with the smallest I and shorten its duration as much as possible. That is, until • a. Duration reaches crash time • b. Another path becomes critical 3. If duration of the project cannot be reduced any more, then stop; otherwise return to the second step The above process results in the modified crash program.

25. A ES EF LS LF NT,CT Example NT 4,2 CC,NC B (normal time, crash time) 4 8 4 5 4,2 9 2,1 D 0 4 11 50,30 9 4 2 0 4 9 5, 2 11 C 4 9 70,10 100,10 4 5 9 (crash cost, normal cost) 65,50

26. Solution Procedure • Crash the activity with smallest I (least cost) • Check if critical path changed at each step • Continue crashing until satisfied or not possible • Total Cost = Indirect cost + direct cost, • Minimum Cost schedule is the one that has minimum total cost

27. Advantages of PERT/CPM • Especially useful when scheduling and controlling large projects. • Straightforward concept and not mathematically complex. • Graphical networks aid perception of relationships among project activities. • Critical path & slack time analyses help pinpoint activities that need to be closely watched. • Project documentation and graphics point out who is responsible for various activities. • Applicable to a wide variety of projects. • Useful in monitoring schedules and costs.

28. Limitations of PERT/CPM • Assumes clearly defined, independent, & stable activities • Specified precedence relationships • Activity times (PERT) follow beta distribution • Subjective time estimates • Over-emphasis on critical path