1. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Planning and Managing Projects Chapter 8

2. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,IJohnson

3. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital AON Network FinishStart A B C D E F G H I J K Figure 8.4

4. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital Completion Time FinishStart K6K6 I 15 F 10 C 10 D 10 E 24 G 35 H 40 J4J4 A 12 B9B9

5. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital Completion Time FinishStart K6K6 I 15 F 10 C 10 D 10 E 24 G 35 H 40 J4J4 A 12 B9B9 Path Expected Time (wks) A-F-K28 A-I-K33 A-C-G-J61 B-D-H-J63 B-E-J37

6. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.Immediate ActivityDescriptionPredecessor(s)Responsibility ASelect administrative and medical staff.—Johnson BSelect site and do site survey.—Taylor CSelect equipment.AAdams DPrepare final construction plans and layout.BTaylor EBring utilities to the site.BBurton FInterview applicants and fill positions inAJohnson nursing, support staff, maintenance, nursing, support staff, maintenance, and security. and security. GPurchase and take delivery of equipment.CAdams HConstruct the hospital.DTaylor IDevelop an information system.ASimmons JInstall the equipment.E,G,HAdams KTrain nurses and support staff.F,I,JJohnson St. Adolf’s Hospital Completion Time FinishStart K6K6 I 15 F 10 C 10 D 10 E 24 G 35 H 40 J4J4 A 12 B9B9 Path Expected Time (wks) A-F-K28 A-I-K33 A-C-G-J61 B-D-H-J63 B-E-J37

7. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Earliest Start and Earliest Finish Times A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 I 15 F 10 Finish Start

8. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Earliest Start and Earliest Finish Times Finish Earliest start time Earliest finish time A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 27 33 22 57 59 6319 59 9 33 0 9 9 19 12 22 Critical path Start

9. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 27 33 22 57 59 6319 59 9 33 0 9 9 19 12 22 Latest Start and Latest Finish Times Finish Start Project finish Time = 63

10. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Latest Start and Latest Finish Times A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 27 33 22 57 59 6319 59 9 33 0 9 9 19 12 22 63 Latest finish time Finish Start Latest finish time 63

11. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Latest Start and Latest Finish Times A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 27 33 22 57 59 6319 59 9 33 0 9 9 19 12 22 Latest start time Latest finish time Finish Start 57 63 59 63 Latest start time

12. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Latest Start and Latest Finish Times A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 22 57 59 6319 59 9 33 0 9 9 19 12 22 2 14 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Earliest start time Earliest finish time Latest start time Latest finish time Critical path Finish Start 27 33 57 63 42 57 47 57

13. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Activity Slack Analysis A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 22 57 59 6319 59 9 33 0 9 9 19 12 22 2 14 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Finish Start 27 33 57 63 42 57 47 57

14. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Start A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 22 57 59 6319 59 9 33 0 9 9 19 12 22 2 14 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Finish Activity Slack Analysis Activity Slack Slack = LS – ES or Slack = LF – EF 27 33 57 63 42 57 47 57

15. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Start A 12 K6K6 C 10 G 35 J4J4 H 40 B9B9 D 10 E 24 0 12 I 15 F 10 12 27 12 22 22 57 59 6319 59 9 33 0 9 9 19 12 22 2 14 14 24 24 59 0 9 9 19 19 59 35 59 59 63 Finish Activity Slack Analysis Activity Slack Slack K = 57 – 27 = 30 or Slack K = 63 – 33 = 30 27 33 57 63 42 57 47 57

16. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital C 10 G 35 E 24 I 15 F 10 12 27 12 22 22 57 9 33 12 22 14 24 24 59 35 59 B9B9 0 9 D 10 9 19 H 40 19 59 J4J4 59 63 K6K6 Finish Critical Path 27 33 57 63 42 57 47 57 Node DurationESLS Slack A12022 B9000 C1012142 D10990 E2493526 F10124735 G3522242 H4019190 I15124230 J459590 K6275730

17. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Linear cost assumption St. Adolf’s Hospital 8000 — 7000 — 6000 — 5000 — 4000 — 3000 — 0 — Direct cost (dollars) |||||| 567891011 Time (weeks) Figure 8.11 Cost-Time Relationships in Cost Analysis Crash cost (CC) Normal cost (NC) (Crash time) (Normal time) Estimated costs for a 2-week reduction, from 10 weeks to 8 weeks 5200

18. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital TABLE 8.1DIRECT COST AND TIME DATA FOR THE ST. ADOLF’S HOSPITAL PROJECT A12$ 12,00011$ 13,0001$ 1,000 B950,000764,00027,000 C104,00057,0005600 D1016,000820,00022,000 E24120,00014200,000108,000 F1010,000616,00041,500 G35500,00025530,000103,000 H401,200,000351,260,000512,000 I1540,0001052,50052,500 J410,000113,00021,000 K630,000534,00014,000 Totals$1,992,000$2,209,000 Maximum NormalNormalCrashCrashTimeCost of TimeCostTimeCostReductionCrashing per Activity(NT)(NC)(CT)(CC)(wk)Week

19. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Modeling project schedule in Excel Forward schedule (Earliest time) ES = EF of predecessor, if only one predecessor ES = Max(EF of predecessors), if more than one EF = ES + Activity duration Backward schedule (Latest time) LF = LS of successor, if only one successor ES = Min(LS of successors), if more than one LS = LF - Activity duration

20. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Optimal crashing using Excel Solver Target cell = Cost or project completion time Changing cells = Crashing time Constraints = Crashing time <= MTR Options: Non-negativeNon-negative ToleranceTolerance Estimates, derivative, searchEstimates, derivative, search

21. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Pert = Project Evaluation Review Technique Finding probability for project completion time

22. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Probabilistic Time Estimates Figure 8.12 (a) Beta Distribution Mean mab Time Probability

23. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Probabilistic Time Estimates AF I CG Finish D E HBJ K Start te =te =te =te = a + 4m + b 6Mean 2 =2 =2 =2 = ( ) b – ab – a66b – ab – a666 2Variance

24. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Activity B Most OptimisticLikelyPessimistic (a)(m)(b) 7815 Probabilistic Time Estimates AF I CG Finish D E HBJ K Start Example 8.6

25. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Activity B Most OptimisticLikelyPessimistic (a)(m)(b) 7815 Probabilistic Time Estimates t e = = 9 weeks 7 + 4(8) + 15 6  2 = = 1.78 ( ) 15 - 7 6 2 AF I CG Finish D E HBJ K Start Example 8.6

26. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Example 8.6 St. Adolf’s Hospital OptimisticLikelyPessimisticExpectedVariance Activity(a)(m)(b)Time (t e )(  2 ) Time Estimates (wk)Activity Statistics A111213120.11 B781591.78 C51015102.78 D8916101.78 E142530247.11 F6918104.00 G253641357.11 H354045402.78 I101328159.00 J121545.44 K56760.11

27. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital  2 =  (variances of critical path activities)  2 = 1.78 + 1.78 + 2.78 + 5.44 = 11.78 What is the probability the project will be completed in 65 days? Critical Path = B - D - H - J T E = 9 + 10 + 40 + 4 = 63 days Example 8.7  = 11.78 = 3.432

28. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Probabilities Critical Path = B - D - H - J T = 65 days T E = 63 days  = 3.432 Example 8.7 z = T – T E  = 65 – 63 3.432 = 0.58 From Normal table in page 807, for z = 0.58, the table area = 0.7190 The probability that the project will be Completed within 65 days is 71.9%

29. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Project duration (weeks) Probability of meeting the schedule is 0.7190 Length of critical path Normal distribution: Mean = 63 weeks;  = 3.432 weeks Probability of exceeding 65 weeks is 0.2810 6365

30. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital Normal table for 98%, z = 2.055  = 63 + 2.055 (3.432) = 70.05 weeks Critical Path = B - D - H - J Expected project completion time with 98% probability T = T E + z 

31. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. St. Adolf’s Hospital  2 =  (variances of activities)  2 = 0.11 + 2.78 + 7.11 + 5.44 = 15.44 z = = 1.02 65 – 61 15.44 Probabilities Path = A - C - G – J Find probability for T = 65 days T E = 12 + 10 + 35 + 4 = 61 days From Appendix 2 P z =.8461 Example 8.7 z = T – T E  2