Chapter 6Scheduling

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Learning Objectives

Estimate the duration for each activity Establish the estimated start time and required

completion time for the overall project Calculate the earliest times at which each activity

can start and finish, based on the project’s estimated start time

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Learning Objectives (Cont.)

Calculate the latest times by which each activity must start and finish in order to complete the project by its required completion time

Determine the amount of positive or negative slack

Identify the critical (longest) path of activities

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Real World Example

• Vignette: R. R. Donnelley & Sons• Project: Convert 18,000 users dispersed across 200

facilities throughout the world from a dozen major e-mail systems into one standardized system.

• The project was completed six months ahead of schedule without any disruption to business processing.

• Lessons Learned: detailed planning and scheduling are essential; resource management is crucial; and you must have great teamwork.

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Real World Example

• Vignette: London Ambulance Service

• Project: After two failed attempts, develp an ambulance dispatching system capable of handling a million calls per year based on 800 vehicles, 7.5 million residents, 2.5 million tourists, dispersed over 640 square miles.

• Results: the number of ambulances on the way within three minutes doubled; the number of ambulances on the scene within 8 minutes tripled. Lives are being saved.

• Lessons Learned: encourage open communications; involve the team in planning; break the project into manageable pieces.

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Activity Duration Estimates

• The first step in scheduling is to estimate how long each activity will take.

• The duration estimate is the total elapsed time for the work to be done PLUS any associated waiting time.

• The person responsible for performing the activity should help make the duration estimate.

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Project Start and Finish Times

• It is necessary to select an estimated start time and a required completion time for the overall project.

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Schedule Calculations

• A project schedule includes:– the earliest times (or dates) at which each

activity can start and finish, based on the project's estimated start time (or date)

– the latest times (or dates) by which each activity must start and finish in order to complete the project by its required completion time (or date)

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Earliest Start and Finish Times

• Earliest start time (ES) is the earliest time at which a particular activity can begin.

• Earliest finish time (EF) is the earliest time by which a particular activity can be completed.

• EF = ES + Duration Estimate

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Earliest Start and Finish Times Rule #1

• The earliest start time for an activity must be the same as or later than the latest of all the earliest finish times of all the activities leading directly into that particular activity.

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Latest Start and Finish Times

• Latest finish time (LF) is the latest time an activity must be finished in order for the entire project to be completed by its completion time.

• Latest start time (LS) is the latest time an activity must be started in order for the entire project to be completed by its completion time.

• LS = LF – Duration Estimate

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Latest Start and Finish Times Rule #2

• The latest finish time for a particular activity must be the same as or earlier than the earliest of all the latest start times of all the activities emerging directly from that particular activity.

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Total Slack, Defined

• Total slack (TS) or float is the difference between the calculated earliest finish time of the very last activity and the project’s required completion time.

• Total Slack = LF - EF or• Total Slack = LS - ES

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Total Slack (Cont.)

• If total slack is positive, it is the maximum time the activities on the path can be delayed.

• If total slack is negative, it is the amount of time the activities on the path must be accelerated.

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Critical Path

• The critical path is the longest path in the diagram.• The activities that make up the critical path have

the least slack.• All activities with this value are on the critical

path.

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Types of Critical Paths

• Noncritical paths have positive values of total slack.

• Critical paths have zero or negative values of total slack.

• The most critical path is the longest critical path.

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Free Slack

• The amount of time an activity can be delayed without delaying the start of other activities.

• It is the relative difference between the amounts of total slack for activities entering into the same activity.

• It is always a positive value.

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Scheduling for Information System Development

• Some common problems that push IS projects past their required completion time: Failure to identify all user requirements Logical design flaws Continuing growth of project scope Underestimating learning curves for new

software packages

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Project Management Software

• Allows one to perform scheduling functions.• Activity durations can be estimated in a variety of

ways.• Project start and finish times can be entered in a

variety of ways.• Can calculate dates, times, total and free slack.

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Probability Considerations Activity Duration Estimates

• Optimistic time: time to complete an activity if everything goes perfectly well.

• Most likely time: time to complete an activity under normal conditions.

• Pessimistic time: time to complete an activity under adverse circumstances.

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Probability Considerations The Beta Probability Distribution

• When using three time estimates, it is assumed that they follow a beta probability distribution.

• The expected duration is calculated using the following formula:

– te = F(to + 4(tm) + tp)/6

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Probability Considerations Probability Fundamentals

• Network planning that uses three time estimates for each activity can be considered a stochastic or probabilistic technique, since it allows for uncertainty.

• Any technique that uses only one time estimate is considered to be a deterministic technique.

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Probability Fundamentals (Cont.)

• The total probability distribution is a normal probability distribution.

• The variance for the beta probability distribution of an activity is:

• Variance = 2 = BBC((F(tp – to,6))2

• The standard deviation, , is another measure of the dispersion of a distribution and is equal to the square root of the variance.

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Probability Fundamentals (Cont.)

• The total probability distribution of the critical path activities is a normal distribution.

• The mean equals the sum of the individual activity expected durations.

• The variance equals the sum of the individual activity variances.

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Calculating Probability

• The probability of completing a project before its required compleiton time:

• Z = F(LF – EF,t) LF = the required completion time (latest

finish). EF = the earliest expected finish time (mean of

the normal distribution). t = the standard deviation of the total

distribution of activities on the longest path.

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Calculating Probability (Cont.)

• Z measures the number of standard deviations between EF and LF on the normal probability curve.