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© 2007 Pearson Education

Project Management

- Used to manage large complex projects
- Has three phases:
- Project planning
- Project scheduling
- Project controlling

Phase 1: Project Planning

- What is the project goal or objective?
- What are the activities (or tasks) involved?
- How are activities linked?
- How much time required for each activity?
- What resources are required for each activity?

Phase 2: Project Scheduling

- When will the entire project be completed?
- What is the scheduled start and end time for each activity?
- Which are the “critical” activities?
- Which are the noncritical activities?

Phase 2: Project Scheduling (cont.)

- How late can noncritical activities be w/o delaying the project?
- After accounting for uncertainty, what is the probability of completing the project by a specific deadline?

Phase 3: Project Controlling

At regular intervals during the project the following questions should be considered:

- Is the project on schedule? Early? Late?
- Are costs equal to the budget? Over budget? Under budget?
- Are there adequate resources?
- What is the best way to reduce project duration at minimum cost?

Identifying Activities

- Subdivides a large project into smaller units
- Each activity should have a clearly defined starting point and ending point
- Each activity is clearly distinguishable from every other activity
- Each activity can be a project in itself

Work Breakdown Structure (WBS)

Divides the project into its various subcomponents and defines hierarchical levels of detail

Level

1 Project

2 Major tasks in project

3 Subtasks in major tasks

4 Activities to be completed

Identify for Each Activity:

- Which other activities must be completed previously (predecessors)
- Time required for completion
- Resources required

This completes the project planning phase.

Project Scheduling Phase

Commonly used techniques:

- Program Evaluation and Review Technique (PERT)
- Critical Path Method (CPM)

Project Management Example:General Foundry Inc.

- Have 16 weeks to install a complex air filter system on its smokestack
- May be forced to close if not completed w/in 16 weeks due to environmental regulations
- Have identified 8 activities

Drawing the Project Network

- AON – Activity on Node networks show each activity as a node and arcs show the immediate predecessor activities
- AOA – Activity on Arc networks show each activity as an arc, and the nodes represent the starting and ending points

We will use the AON method

Determining the Project Schedule

- Some activities can be done simultaneously so project duration should be less than 25 weeks
- Critical path analysis is used to determine project duration
- The critical path is the longest path through the network

Critical Path Analysis

Need to find the following for each activity:

- Earliest Start Time (EST)
- Earliest Finish Time (EFT)
- Latest start time (LST)
- Latest Finish Time (LFT)

Forward Pass

- Identifies earliest times (EST and EFT)
- EST Rule: All immediate predecessors must be done before an activity can begin
- If only 1 immediate predecessor, then

EST = EFT of predecessor

- If >1 immediate predecessors, then

EST = Max {all predecessor EFT’s}

Backward Pass

- Identifies latest times (LST an LFT)
- LFT Rule:
- If activity is the immediate predecessor to only 1 activity, then

LFT = LST of immediate follower

- If activity is the immediate predeccor to multiple activities, then

LFT = Min {LST of all imm. followers}

LST Rule:

LST = LFT – activity time

Slack Time and Critical Path(s)

- Slack is the length of time an activity can be delayed without delaying the project

Slack = LST – EST

- Activities with 0 slack are CriticalActivities
- The Critical Path is a continuous path through the network from start to finish that include only critical activities

Total Slack Time vs. Free Slack Time

- Total slack time is shared by more than 1 activity

Example: A 1 week delay in activity B will leave 0 slack for activity D

- Free slack time is associated with only 1 activity

Example: Activity F has 6 week of free slack time

Variability in Activity Times

- Activity times are usually estimates that are subject to uncertainty
- Approaches to variability:
- Build “buffers” into activity times
- PERT – probability based
- Computer simulation

PERT Analysis

- Uses 3 time estimates for each activity

Optimistic time (a)

Pessimistic time (b)

Most likely time (m)

- These estimates are used to calculate an expected value and variance for each activity (based on the Beta distribution)

Expected activity time (t)

t = (a + 4m + b)

6

- Variance = [ (b – a) / 6 ]2
- Standard deviation = SQRT(variance)

= (b – a)

6

Go to file 7-1.xls

Project Variance and Standard Deviation

- Project variance (σp2)

= ∑ (variances of all critical path activities)

σp2 = 0.11 + 0.11 + 1.0 + 1.78 + 0.11

= 3.11

- Project standard deviation (σp)

= SQRT (Project variance)

σp = SQRT ( 3.11) = 1.76

Probability of Project Completion

- What is the probability of finishing the project within 16 weeks?
- Assumptions:
- Project duration is normally distributed
- Activity times are independent
- Normal distribution parameters:

μp = expected completion time= 15 weeks

σp = proj standard deviation = 1.76 weeks

Normal Probability Calculations

Z = (Target time – expected time)

σp

Z = (16 - 15) = 0.57

1.76

This means 16 weeks is 0.57 standard deviations above the mean of 15 weeks.

Probability Based on Standard Normal Table

Prob (proj completion < 16 weeks) = 0.7158

Project Duration fora Given Probability

- What project duration does General Foundry have a 99% chance of completing the project within?

i.e. Prob (proj duration < ? ) = 0.99

- From Std. Normal Table, this corresponds to Z = 2.33

Scheduling Project Costs

- Estimate total cost for each activity
- Identify when cost will actually be spent

(we will assume costs are spread evenly)

- Use EST and LST for each activity to determine how costs are spread over project

Monitoring and Controlling Project Costs

- While the project is underway, costs are tracked and compared to the budget
- What is the value of work completed?

Value of work completed

= (% of work completed) x (total activity budget)

- Are there any cost overruns?

Cost difference

= (Actual cost) – (Value of work completed)

Project Crashing

- Reducing a project’s duration is called crashing
- Some activities’ times can be shortened (by adding more resources, working overtime, etc.)
- The crash time of an activity is the shortest possible duration, and has an associated crash cost

Steps in Project Crashing

- Compute the crash cost per time period
- Find the current critical path (CP)
- Find the lowest cost way to crash the CP by 1 time period
- Update all activity times. If further crashing is needed, go to step 2.

Crashing UsingLinear Programming

Decision: How many time periods to crash each activity?

Objective: Minimize the total crash cost

Decision Variables

Ti = time at which activity i starts

Ci = number of periods to crash activity i

Constraints

- An activity cannot begin before all immediate predecessors are complete
- There is a maximum amount that each activity can be crashed

Go to file 7-2.xls

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