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**Chapter 7 Project Management**

© 2007 Pearson Education

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**Project Management Used to manage large complex projects**

Has three phases: Project planning Project scheduling Project controlling

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**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?

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**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?

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**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?

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**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?

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**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

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**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 Activities to be completed

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**Example Work Breakdown Structure**

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**Identify for Each Activity:**

Which other activities must be completed previously (predecessors) Time required for completion Resources required This completes the project planning phase.

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**Project Scheduling Phase**

Commonly used techniques: Program Evaluation and Review Technique (PERT) Critical Path Method (CPM)

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**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

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**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

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**AON Network for General Foundry**

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**Activity Time Estimates**

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**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

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**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)

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**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}

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EFT Rule: EFT = EST + activity time Node Notation:

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**Forward Pass: Earliest Start and Finish Times**

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**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}

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LST Rule: LST = LFT – activity time

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**Backward Pass: Latest Start and Finish Times**

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**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 Critical Activities The Critical Path is a continuous path through the network from start to finish that include only critical activities

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**Project Schedule and Slack Times**

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**Critical Path and Slack Times**

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**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

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**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

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**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)

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**Expected activity time (t) t = (a + 4m + b) 6 **

Variance = [ (b – a) / 6 ]2 Standard deviation = SQRT(variance) = (b – a) Go to file 7-1.xls

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**Project Variance and Standard Deviation**

Project variance (σp2) = ∑ (variances of all critical path activities) σp2 = = 3.11 Project standard deviation (σp) = SQRT (Project variance) σp = SQRT ( 3.11) = 1.76

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**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

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**Normal Probability Calculations**

Z = (Target time – expected time) σp Z = ( ) = 0.57 1.76 This means 16 weeks is 0.57 standard deviations above the mean of 15 weeks.

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**Probability Based on Standard Normal Table**

Prob (proj completion < 16 weeks) =

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**Project Duration for a 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

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Z = (? ) = 2.33 1.76 So ? = x 1.76 = 19.1 weeks

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**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

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**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)

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**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

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**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.

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**Crashing Using Linear 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

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**There is a maximum amount that each activity can be crashed**

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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