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Project Management

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Work Breakdown Structure

Relocation of St. John’s Hospital Organizing and Site Preparation Level 0 Physical Facilities and Infrastructure Level 1 Select administration staff Purchase and deliver equipment Site selection and survey Select medical equipment Construct hospital Develop information system Level 2 Prepare final construction plans Bring utilities to site Interview applicants for nursing and support staff

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Install medical equipment Train nurses and support staff Figure 2.1

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Diagramming the Network AON approach (Activity On Node)

S AON T U Activity Relationships S precedes T, which precedes U.

S T U S and T must be completed before U can be started. Figure 2.2

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Diagramming the Network

S T S AON T U U V Figure 2.2

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Activity Relationships T and U cannot begin until S has been completed.

U and V can’t begin until both S and T have been completed. 2 – 4

Diagramming the Network

AON S T U V S T U Figure 2.2

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

V Activity Relationships U cannot begin until both S and T have been completed; V cannot begin until T has been completed.

T and U cannot begin until S has been completed and V cannot begin until both T and U have been completed.

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Network Diagram

S = 36 A 0 12 S = 2 S = 41 S = 0 Start S = 2 S = 2 S = 0 S = 0 S = 0 S = 0 Figure 2.4

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S = 26 Finish 2 – 6

Project Schedule

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The earliest start time (ES) for an activity is the latest earliest finish time of any preceding activities



The earliest finish time (EF) is the earliest start time plus its estimated duration



The latest finish time (LF) for an activity is the latest start time of any preceding activities



The latest start time (LS) is the latest finish time minus its estimated duration



For simplicity, all projects start at time zero.

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Activity Slack

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Activity slack is the maximum length of time an activity can be delayed without delaying the entire project

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Activities on the critical path have zero slack

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Activity slack can be calculated in two ways S = LS – ES or S = LF – EF

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Calculation of Slack Time

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Slack Time = LF – EF EF = summing Expected Time from left to right

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If two or more activities precede an activity, choose the largest EF of these activities LF = summing Expected Time from right to left

 

Set LF equals to EF for the last activity If two or more activities precede an activity, choose the smallest LF of these activities

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Refers to the time in which an activity can be completed without delaying the project

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Tasks on the critical path has Slack Time = 0 LS = LF - t; ES = EF - t 2 – 9

Gantt Chart

Figure 2.5

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Comparison of Gantt Charts and Network Diagrams

 Gantt Charts  Visually shows duration of tasks  Visually shows time overlap between tasks  Visually shows slack time  Network Diagrams  Visually shows dependencies between tasks  Visually shows which tasks can be done in parallel  Shows slack time by data in rectangles

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Cost-Time Relationships

8000 — 7000 — 6000 — 5200 5000 — 4000 — Crash cost (CC) Linear cost assumption Estimated costs for a 2-week reduction, from 10 weeks to 8 weeks 3000 — Normal cost (NC) 0 — | 5 | 6 | 7 8 | 9 | 10 | 11 (Crash time) (Normal time) Time (weeks) Figure 2.6

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Statistical Analysis

Area under curve between a and b is 99.74%

a m

Mean Time Beta distribution

b

Figure 2.7

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a

3 σ 3 σ

m

Mean Time Normal distribution

b

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Statistical Analysis



The mean of the beta distribution can be estimated by

t e

= a + 4m + b 6

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The variance of the beta distribution for each activity is 2 σ 2 =

b

– a 6

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Analyzing Probabilities:



Because the central limit theorem can be applied, the mean of the distribution is the earliest expected finish time for the project

T E



Expected activity times = = Mean of normal distribution

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Because the activity times are independent σ 2 =



(Variances of activities on the critical path)

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Using the z-transformation z =

T

– T

E



σ 2 where T = due date for the project

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