Project Sceduling

1
Project Management CPM/PERT
Professor Ahmadi

2
Learning Objectives

• Understand how to plan, monitor, and control
  projects using PERT/CPM.
• Determine earliest start, earliest finish, latest
  start, latest finish, and slack times for each
  activity.
• Understand the impact of variability in activity
  times.
• Understand important role of software such as
  Microsoft Project in project management.

3
Project Planning

• Specific questions that are considered
• What is goal or objective of project?
• What are various activities (or tasks) that
  constitute project?
• How are these activities linked?
• What are precedence relationships between
  activities?
• What is time required for each activity?
• What other resources (such as labor, raw
  materials, and machinery) are required for each
  activity?

4
Project Scheduling

• Questions to be answered
• When will project be completed?
• What is schedule for each activity?
• What are critical activities in project?
• What are non-critical activities in project?
• By how much can a non-critical activity be
  delayed without affecting completion time of
  entire project?
• If variability in activity times is considered,
  what is probability project will be completed by
  a specific deadline?

5
Project Controlling

• Control of large projects involves close
  monitoring of schedules, resources, and budgets.
• Questions to be answered
• At any particular date or time, is project on
  schedule, behind schedule, or ahead of schedule?
• At any particular date or time, is money spent on
  project equal to, less than, or greater than
  budgeted amount?
• Are there enough resources available to finish
  project on time?
• If project is to be finished in shorter amount of
  time, what is best way to accomplish this at
  least cost?

6
Gantt Chart for a New Voice Recognition System
Apr.
May
June
July
Aug.
Project Activities

• a. Design System
• b. Build Prototype
• c. Test Prototype
• d. Estimate Material Costs
• e. Estimate Labor Costs
• f. Refine Design
• g. Build the final Product
• h. Demonstrate the product
• i. Market the Product

7
Drawing Project Network

• There are two major approaches for drawing a
  project network -- Activity on Node (AON), and
  Activity on Arc (AOA).
• Although both approaches are popular in practice,
  many project management software packages,
  including Microsoft Project 2000, use AON
  networks.
• Focus is on AON networks.

8
CPM and PERT

• Network techniques
• Developed in 1950s
• CPM by DuPont for chemical plants (1957)
• PERT by Booz, Allen Hamilton with the U.S.
  Navy, for Polaris missile (1958)
• Consider precedence relationships and
  interdependencies
• Each uses a different estimate of activity times

9
CPM/PERT

• CPM stands for Critical Path Method. It is
  Project Scheduling with Known Activity Times
  (CPM)
• PERT stands for Program Evaluation Review
  Technique. It is Project Scheduling with
  Uncertain Activity Times (PERT)
• PERT/CPM is used to plan the scheduling of
  individual activities that make up a project.
• PERT/CPM can be used to determine the
  earliest/latest start and finish times for each
  activity, the entire project completion time and
  the slack time for each activity.

10
Project Network

• A project network can be constructed to model the
  precedence of the activities.
• The nodes of the network represent the
  activities.
• The arcs of the network reflect the precedence
  relationships of the activities.
• A critical path for the network is a path
  consisting of activities with zero slack.

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Determining the Critical Path

• Step 1 Make a forward pass through the network
  as follows For each activity i beginning at the
  Start node, compute
• Earliest Start Time the maximum of the earliest
  finish times of all activities immediately
  preceding activity i. (This is 0 for an activity
  with no predecessors.)
• Earliest Finish Time (Earliest Start Time)
  (Time to complete activity i.
• The project completion time is the maximum of
  the Earliest Finish Times at the Finish node.

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Determining the Critical Path

• Step 2 Make a backwards pass through the
  network as follows Move sequentially backwards
  from the Finish node to the Start node. At a
  given node, j, consider all activities ending at
  node j. For each of these activities, (i,j),
  compute
• Latest Finish Time the minimum of the latest
  start times beginning at node j. (For node N,
  this is the project completion time.)
• Latest Start Time (Latest Finish Time) - (Time
  to complete activity (i,j)).

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Determining the Critical Path

• Step 3 Calculate the slack time for each
  activity by
• Slack (Latest Start) - (Earliest Start),
  or
• (Latest Finish) - (Earliest
  Finish).
• A critical path is a path of activities, from
  the Start node to the Finish node, with 0 slack
  times.

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Uncertain Activity Times

• In the three-time estimate approach, the time to
  complete an activity is assumed to follow a Beta
  distribution.
• An activitys mean completion time is
• t (a 4m b)/6
• Each activitys completion time variance is
• S2 ((b-a)/6)2
• a the optimistic completion time estimate
• b the pessimistic completion time estimate
• m the most likely completion time estimate
• The variance of the critical path is ?2 ? S2

15
Uncertain Activity Times

• In the three-time estimate approach, the critical
  path is determined as if the mean times for the
  activities were fixed times.
• The overall project completion time is assumed to
  have a normal distribution with mean equal to the
  sum of the means along the critical path and
  variance equal to the sum of the variances along
  the critical path.

16
Network for construction of a new
buildingExample 1

• A project comprises of the following activities
  and their predecessors.
• Activity Description Predecessor
• A Survey site --
• B Initial design --
• C Obtain approval A,B
• D Select architect C
• E Establish budget C
• F Finalize design D,E
• G Obtain financing E
• H Hire contractor F,G
• Draw a network for this project.

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Critical Path Method (CPM) Example 2

• A project comprises of the following activities
  and their predecessors.
• Immediate Expected
• Activity Predecessor time (days)
• A - 2
• B - 6
• C A 4
• D B 3
• E C, D 1
• a. Draw a network and determine the critical
  path. How long will it take to complete the
  project? 
• b. Provide a detailed activity schedule for the
  project.

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Program Evaluation and Review Technique (PERT)
Example 3

• For the following activities and their
  predecessors and the three time estimates (days)
• Activity Predecessor Optimistic (a) Most
  Probable (m) Pessimistic (b)
• A - 4 7.5 8
• B - 1 2 3
• C A 4 5 6
• D B 7 8 9
• E C, D 6 7 14 
• a. Compute the expected completion time for each
  activity. 
• b. Draw a network and determine the critical path
  based on the expected completion times.
• c. What is the probability of finishing the
  project in less than 19 days?
• d. What is the probability of finishing the
  project in less than 23 days?

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Network for construction of a new buildingRefer
to Example 1-Your turn

• A project comprises of the following activities
  and their predecessors.
• Activity Description Predecessor Time (Days)
• A Survey site -- 12
• B Initial design -- 16
• C Obtain approval A,B 24
• D Select architect C 8
• E Establish budget C 12
• F Finalize design D,E 30
• G Obtain financing E 24
• H Hire contractor F,G 16
• Draw a network for this project and determine the
  critical path. How long would it take to finish
  this project?