1. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 1 Chapter 13. Project Management Time in Weeks Activities481216202428323640444852566064 A B C D E F G H

2. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 2 Outline   The Characteristics of Projects   The Project Manager   Managing Teams and Relationships on Projects   Planning and Scheduling with Gantt Charts   The Gantt Chart   Pert & CPM   The Network   Deterministic Approach- Critical Path Method   Probabilistic Approach   Project Compression (Crashing or time reduction in project length)

3. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 3 The Characteristics of Projects  Projects are unique and non-routine endeavors, designed to accomplish a specified set of objectives (to create new products and services) in a limited time.  Typical examples of such non-routine projects are moving a hospital to a new location by a certain date, or renovating an outpatient facility to meet changing demand patterns.  Projects like those have considerable costs. They involve a large number of activities that must be carefully planned and coordinated to achieve the desired results, and may take a long time to complete.

4. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 4 The Characteristics of Projects Life-cycle concept -- projects go through a series of stages including, formulation and analysis, planning, implementation, and termination. Projects bring together personnel with diverse knowledge and skills, as their contributions are necessitated by the projects

5. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 5 The Project Manager...... Bears the ultimate responsibility for completion of the project. The pros and cons of working on projects include: The effect of expert full-time employees assigned to a project Working for two bosses Dynamic environment, thriving factor Working with new people, team spirit

6. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 6 ActivityTime A. Land acquisition 4 weeks B. Hire a radiation oncologist 16 weeks C. Select contractor and develop a construction plan 8 weeks D. Build the facility 24 weeks E. Acquire equipment 28 weeks F. Hire technical staff 4 weeks G. Purchase and set up information systems and software 8 weeks H. Testing of equipment 4 weeks Time in Weeks Activities481216202428323640444852566064 A B C D E F G H Exhibit 13.1 Gantt Chart for Launching a New Radiation Oncology Service

7. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 7 PERT/CPMPERT/CPM  Program Evaluation and Review Technique (PERT) and the Critical Path Method (CPM) are tools for planning and coordinating large projects  Using PERT/CPM managers can obtain: A graphical display of project activities An estimate of how long the project will take An indication of which activities are the most critical to timely project completion An indication of how long any activity can be delayed without lengthening the project.

8. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 8 Activity Precedence Relationships ActivityPredecessor A B CA,B DC EC FD,E G HF,G

9. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 9 ARROW NODE The Network (precedence) Diagram The network diagram is a diagram of project activities that shows the sequential relationships by use of arrows and nodes.

10. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 10 Activity A Activity B Activity C Activity A Activity B Dummy Activity Activity C Activity on Arc Activity on Node A B C Figure 13.1 Network Representations a) b) c)

11. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 11 Activity-on-Arrow (A-O-A). Network convention in which arrows designate activities. Activity-on-Node (A-O-N). Network convention in which nodes designate activities. Activities. Project steps that consume resources and/or time Events. The starting and finishing of activities, designated by nodes in the A-O-A convention. Path. A sequence of activities that leads from the starting node to the finishing node. The Network Diagram, cont. A glossary of terms

12. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 12 Critical Path. The longest path equaling the expected project duration. Critical Activities. All the activities on the critical path. Slack. Allowable slippage (time) for a path; the difference between the length of a path and the length of the critical path. ES, EF, LS, LF. E (earliest); L (latest); S (start); F (finish) times of each activity. The Network Diagram, cont. A glossary of terms

13. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 13 ESLS EF LF Activity Name Figure 13.3 Activity Start and Finish Times

14. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 14 Figure 13.2 AON Network Diagram for Radiation Oncology Start A B C D E F G HEnd Critical Path Method (CPM)

15. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 15 Critical Path Method (CPM) Paths and activitiesPath time length 1) A-C-D-F-H 4 + 8 + 24 + 4 + 4 = 44 weeks 2) A-C-D-G-H 4 + 8 + 24 + 8 + 4 = 48 weeks 3) A-C-E-F-H 4 + 8 + 28 + 4 + 4 = 48 weeks 4) A-C-E-G-H 4 + 8 + 28 + 8 + 4 = 52 weeks 5) B-C-D-F-H16 + 8 + 24 + 4 + 4 = 56 weeks 6) B-C-D-G-H16 + 8 + 24 + 8 + 4 = 60 weeks 7) B-C-E-F-H16 + 8 + 28 + 4 + 4 = 60 weeks 8) B-C-E-G-H16 + 8 + 28 + 8 + 4 = 64 weeks Path Lengths for the Radiation Oncology Project

16. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 16 Deterministic Time Estimates-- estimates for each activity are fairly certain. Probabilistic Time Estimates-- estimates for each activity are subject to variation. Optimistic Estimate-- Length of time required under optimum conditions (o). Pessimistic Estimate-- length of time required under worst conditions (p). Most likely time estimate-- the most probable length of time required (m). Beta Distribution-- A distribution which describes the inherent variability in the time estimates. Time Estimates

17. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 17 Beta Distribution MeanVariance Assumption: path duration times are independent of each other; requiring that activity times be independent, and that each activity is on only one path. Invoke Central Limit Theorem to use normal distribution. t path = Σt e Path Mean Standard Deviation  path =

18. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 18 The Normal Distribution:. Probabilistic Time Estimates, cont.

19. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 19 Example 13.1 In planning for a new radiation oncology clinic, project managers determined that due to the nature of some of the activities, time estimates vary. After consulting with experts in each of the activity areas, they have calculated the optimistic, pessimistic and most likely time estimates, in weeks, as shown in Table below: ActivityOptimistic (o) Most Likely (m) Pessimistic (p) A248 B81624 C4816 D122436 E162836 F2412 G48 H246

20. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 20 Table 13.4 Calculation of Expected Time and Standard Deviations on Each Path for the Radiation Oncology Project Table 13.4 Calculation of Expected Time and Standard Deviations on Each Path for the Radiation Oncology Project Paths Activitiesomp t path = Σt e Σσ 2 σ pat h 1 A248 4.33 1.00 C4816 8.674.00 D122436 24.0046.0016.00 24.224.92 F2412 5.002.78 H246 4.000.44 2 A248 4.33 1.00 C4816 8.674.00 D122436 24.0049.0016.00 23.224.82 G4812 8.001.78 H246 4.000.44

21. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 21 Path t path σ path 1) ACDFH46.004.923.86 2) ACDGH49.004.823.32 3) ACEFH49.334.403.56 4) ACEGH52.334.282.96 5) BCDFH57.675.511.33 6) BCDGH60.675.420.80 7) BCEFH61.005.040.79 8) BCEGH64.004.940.20 Table 13.5 Path Completion Probabilities

22. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 22 tete tsts 50% 84% 64 69 Weeks (1σ = 5) Figure 13.6 Project Completion Probabilities by the Specified Time z 0122.5

23. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 23 Completion time in weeks 5) BCDFH 8) BCEGH 7) BCEFH 6) BCDGH p=.9082 p=.7881 p=.7852 p=.5793 Figure 13.5 Completion Probabilities for 65 Weeks 57.7 60.7 61 64 58 60 61 64 65

24. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 24 Path Completion Probabilities The last step in the analysis is the computation of joint probability, that is, we are interested in the joint effect of all the paths on the completion of the project. This is a simple multiplication of the completion probabilities of the significant paths (paths 5 through 8). The probability of completion of this project within 65 weeks is: P (completion by 65th week) =.9082 *.7881 *.7852 *.5793 =.3255 or 32.5%. Similarly, one can compute the probability of completion for other target days such as 66, 67 and 70 weeks. P (completion by 66th week) =.9345 *.8365 *.8389 *.6700 =.4394 or 43.9%. P (completion by 67th week) =.9545 *.8770 *.8830 *.7486 =.5533 or 55.3%. P (completion by 70th week) =.9871 *.9573 *.9625 *.8869 =.8066 or 80.7%.

25. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 25 Table 13.6 Path Completion Probabilities Desired completion time in weeksCritical PathProbability 64B-C-E-G-H0.5000 65B-C-E-G-H0.5801 66B-C-E-G-H0.6571 67B-C-E-G-H0.7280 68B-C-E-G-H0.7908 69B-C-E-G-H0.8441 70B-C-E-G-H0.8876 71B-C-E-G-H0.9216 72B-C-E-G-H0.9472 73B-C-E-G-H0.9656 74B-C-E-G-H0.9784 75B-C-E-G-H0.9869 76B-C-E-G-H0.9924

26. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 26 Crash only those activities that are on the critical path to obtain reduction on project completion time. In order to crash, need information on:  Regular time and crash time estimates for each activity.  Regular costs and crash cost estimates for each activity.  A list of activities that are on the critical path. Project Compression: Trade-Offs Between Reduced Project Time and Cost

27. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 27 Overhead and indirect costs Total cost (TC) Cumulative (direct) cost of compression Cost Minimum TC Minimum compression or normal finish time Optimal solution Figure 13.10 Project Duration and Compression (Crashing) Costs Compression of time (crashing) Maximum compression time

28. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 28 Example 13.2: The indirect costs for design and implementation of a new health information system project are $8,000 per week. The project activities (A through I), their normal durations and compressed durations, and also the direct compression, or crashing, costs are shown in Figure 13.7. Find optimal earlier project completion time.

29. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 29 A B C D E F G H Figure 13.11 Project Compression I Star t Finis h NormalCompressed Direct compression costs Activitytimetime per week (in 000) A201911 B75748 C42406 D454410 E28267 F211820 G40400 H201918 I201920

30. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 30 Solution We apply the algorithm shown earlier to this example in successive iterations to find the solution for the optimal earlier project completion time. Iteration 1 Step 1: There are three paths. Adding the times of the activities, we obtain the path times. Since ABEGHI is the longest time path, with 203 days, it is the critical path. PathsPath time ABCFHI198 ABDFHI201 ABEGHI203* Since activity G is not available for compression, it is not shown in the rankings. Among the remaining activities on the critical path, activity E has the lowest compression cost, and thus it is selected for time reduction.

31. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 31 Iteration 1 Step 2: Rank critical activities according to their costs. Critical activities Compression costRank A113 B82 E71 Gn/a H184 I205 Solution Step 3: Since we can reduce this activity by two days, the new completion time considered for the project becomes (203-2 = 201) 201 days. Step 4: The cost of compression for two days for activity E is 2 * $7,000 = $14,000. The indirect project cost for 201 days @ $8,000 per day amounts to $1,608,000 (201*8,000 = $1,608,000). The total cost for 201 days then is equivalent to $1,622,000 (14,000 + 1,608,000). Step 5: Without compressing the project, we would incur only the indirect costs, which would be for 203 days without the time reduction. The total cost for 203 days then would be $1,624,000 (203 * $8,000). Comparing that to the total cost for 201 days (see step 4): $1,624,000 to $1,622,000, we observe a decrease. Thus we can continue compressing the project.

32. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 32 Solution Iteration 2 Step 1: After compression of two days in iteration 1, among the three paths we now have two paths with equivalent path times. Both ABDFHI and ABEGHI are the longest paths, with 201 days; thus both are critical paths. PathsPath time ABCFHI198 ABDFHI201* ABEGHI201* Step 2: Rank critical activities according to their costs. Critical activities Compression CostRank Critical activities Compression cost Rank A112A 3 B81B8 1 E7n/aD10 2 Gn/a F20 5 H183H 4 I204I 5

33. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 33 Iteration 2 Now we are considering critical activities from both paths simultaneously. In the ABEGHI path, we have exhausted compression time for activity E; hence it is no longer available for compression and is not shown in the rankings. Among the remaining activities on both critical paths, the activity B has the lowest compression cost, so it is selected for time reduction. Step 3: Since we can reduce activity B by only one day, the new completion time to consider for the project becomes 200 (201-1) days. Step 4: The cost of compression for activity B for one day is 1 * $8,000 = $8,000. The indirect cost for the project for 200 days @ $8,000 per day amounts to $1,600,000 (200*8,000 = $1,600,000). The total cost for 200 days, then, is equivalent to $1,622,000 (14,000 + 8,000+ 1,600,000). Please note that the direct compression costs should be added in cumulatively; that is, for all 3 days of compression the project incurred $22,000 (14,000 + 8,000). Step 5: From iteration 1, the total cost for 201 days was $1,622,000. Comparing that to the total cost for 200 days (see step 4): $1,622,000 to $1,622,000, we observe no change. Thus we can still continue compressing the project.

34. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 34 Solution Iteration 3 Step 1: After compression by one day in iteration 2, of the three paths we still have two paths, ABDFHI and ABEGHI, with 200 days each; both are critical paths. Step 1: After compression by one day in iteration 2, of the three paths we still have two paths, ABDFHI and ABEGHI, with 200 days each; both are critical paths. Step 2: Rank critical activities according to their costs. PathsPath time ABCFHI198 ABDFHI200* ABEGHI200* Critical Activitie s Compression costRank Critical Activities Compression costRank A111A 2 B8n/aB8 E7 D101 Gn/a F204 H182H 3 I203I 4 Step 5: cost is $1,625,000; hence stop compression.

35. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 35 Figure 13.12 Total Cost of Compression

36. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 36 Project management Software CA Super Project Harvard Total Manager MS Project Sure Track Project Manager Time Line

37. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 37 Advantages of PM Software  Imposes a methodology  Provides logical planning structure  Enhances team communication  Flag constraint violations  Automatic report formats  Multiple levels of reports  Enables what-if scenarios  Generates various chart types

38. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 38 Clinical Health Applications (Clinical Paths) Clinical Health Applications (Clinical Paths) Administrative Applications Administrative Applications Applications

39. Chapter 13: Quantitatve Methods in Health Care Management Yasar A. Ozcan 39 The End