Project Scheduling Tools

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Project Scheduling Tools
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1. Sequencing

• There are four possible sequencing modes in MS
  Project. Suppose B follows A.
• FS Finish Start Start B after A is completed
• SS Start Start Start A and B at same time
• FF Finish Finish Finish A and B at same time
• SF Start Finish Start A after B is completed
• Lags are delays between work on activities

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FS Sequence - Traditional
A

• B

E.g. Sand and Paint
A
B
Lag
E.g. Sprinklers and Landscape
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SS Sequence
A
E.g. Plant Lawn and Flowers

• B

A
E.g. Drywall Hang and Tape
B
Lag
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FF Sequence
A
E.g. Olympics

• B

A
Lag
E.g. Olympics
B
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SF Sequence
A
E.g. Not Practical

• B

A
B
E.g. Ocean Cruise
Lag
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2. Activity Uncertainty

• PERT assumptions (Richard Schonberger and Ken Mac
  Crimmon
• Beta distribution assumption
• PERT approximation formula for mean and variance
• Estimates of a, m, and b
• Errors of above up to 30, but tend to cancel
• Worse problem is merge event bias (probability
  near-critical path becomes critical) estimates
  consistently optimistic

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Example 2.1
B,2
A,1
D,1
C,3
Critical path is ACD but ABD is near critical.
Criticality index probability path critical.
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Use Simulation or Monte Carlo Analysis

• Generate random numbers (electronic, formulas,
  tables, books) i.e. 28
• Convert to random probabilities i.e. .28 What
  is probability of probability?
• Convert random probability to random variate.
  Follows distribution of say actual activity time.

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Finding Random Variates, Problem 2.1

• B C PMF CDF
• Mean 1 1 2 .3 .3
• Mean 2 3 .4 .7
• Mean 1 3 4 .2 .9
• Mean 2 4 5 .1 1.0
• Random probability of .28 gives B random variate
  of 1 .46 gives C value of 3.

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Simulation of Problem 2.1

• RN B(2) RN C(3) Length Path
• .28 1 .46 3 5 ACD
• .97 4 .09 2 6 ABD
• .63 2 .33 3 5 ACD
• .53 2 .76 4 6 ACD
• .73 3 .00 5 7 ACD
• Expected length 5.8 gt 5 (merge event bias)
• Criticality index of ACD 0.8 or 80

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Project Simulation

• Simulation includes
• GERT Graphical Evaluation and Review Technique
• Crystal Ball Copy comes with text
• Simulation includes
• Probabilistic branching from node B may follow
  A
• Probabilistic times for activities various
  distributions
• Flexibility in node realization activity time
  can 0
• Looping permitted rework
• Critique of Simulation R. Schonberger
  recommends intensive critical path scrutiny

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3. Limited Resource Scheduling

• Resources include labor, material, equipment,
  space, and money
• Money versus time tradeoffs
• Methods
• Crashing How to shorten activities cost
  penalties
• Resource loading amount of resource needed per
  period.
• Resource leveling or balancing evening out
  resource use, reacting to limited resources
• Simulation programs can help level

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