Chapter 9 Project Scheduling

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Chapter 9Project Scheduling
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What is Project?

• Company introduces new product(s)
• Moving operations from one plant to new plant
• Building an apartment complex
• Paving a street
• Launching a space shuttle
• Planning a political campaign
• Writing a textbook
• Define a project as a set of partially ordered,
  interrelated activities that must be completed to
  achieve a goal.

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The Elements of Project Scheduling

• Project Definition
• Statement of project objectives, goals, and
  resources required
• Activity Definitions
• Content and requirements of each activity (time
  and resources)
• Activity Relationships
• Defining the precedence constraints between all
  activities
• Project Scheduling
• Specification of starting and ending times of
  all activities identifies critical activities
• Project Monitoring
• Keeping track of the progress of the project and
  revises the plan accordingly

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Steps for a project planning, scheduling, and
control study
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Benefits of Project Planning, Scheduling and
Control

• In-depth consideration of the project is to be
  completed before any work on the project has been
  started
• Clear statement of project objectives is
  necessary
• Determine all activities that make up the project
• Determine start and finish times of each activity
• Determine most critical activities for the
  project
• Determine overall resource requirements
• Include what if planning
• Keep realistic expectations about deadlines and
  budgets
• Promotes a spirit of camaraderie among the
  participants of the project

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Organizing the Project

• Choose a project manager
• goal oriented, good communication and
  interpersonal skills, good organizational skills
• vision, ability to foresee potential problems,
  flexibility and creativity in solving problems
• responsible and accountable for the entire
  project
• Project manager assembles a project team
• members are experts in their respective areas
• team members work on the project part-time
• project manager has authority to pick all team
  members
• regularly scheduled meetings are held at
  specified times or at milestones, plus at any
  time when problem arise
• formal reports maybe necessary

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Defining Activities and the Network

• List all activities that make up the project
• each activity should have a definite beginning
  and ending point
• subactivities (at the correct level of details)
• details should be no more than needed to assign
  resources and manage the activity
• get an accurate estimate of the duration of each
  activity
• Network
• activity arc, events (beginning, end) nodes,
• precedence, predecessor, successor, burst event,
  merge event
• A project is represented by a collection of nodes
  and arcs
• This graphical representation is called a network

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Network Diagrams

• Two classic formats
• AOA Activity on Arrow
• AON Activity on Node
• Each task labeled with
• Identifier
• (usually a letter/code)
• Duration
• (in std. unit like days)

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Network Representation
Gantt chart?
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Critical Path Method

• An analytical tool that provides a schedule that
  completes the project in minimum time subject to
  the precedence constraints.
• In addition, CPM provides
• Starting and ending times for each activity
• Identification of the critical activities
  
• (i.e., the ones whose delay necessarily delays
  the project)
• Identification of the non-critical activities,
  and the amount of slack time available when
  scheduling these activities

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Critical Path Method

• CPM contains forward and backward passes
• forward pass is used to compute the earliest
  start and earliest finish time for each activity
  in the project
• EFi ESiti

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Critical Path Method

• CPM contains forward and backward passes
• backward pass is used to calculate the latest
  allowable start and finish times for each
  activity in the project
• LSi LFi-ti

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Critical Path Method

• After completing calculation on forward and
  backward passes, determine the critical pass and
  critical activities by calculating slack of each
  activity Si LSi - ESi

ES?
LS?
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Critical Path Method

• The critical path and critical activities by
  calculating slack of each activity Si LSi -
  ESi. Critical pass is assigned through all arcs
  that have zero slack

Slack?
After the critical path is determined, we may
wish to obtain more accurate estimates of the
duration of critical and near-critical
activities.
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Critical Path Method Schedule

• There are two schedules that are often discussed
  in project management
• early start schedule, which has all activities
  starting as soon as possible
• late start schedule, which assigns the latest
  possible start to all activities

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PERT Project Evaluation and Review Technique

• PERT is a generalization of Critical Path Method
  to allow for uncertain activity times.
• For each activity the user must specify
• a minimum completion time
• b maximum completion time
• m most likely completion time
• The method assumes each activity
• time follows a beta distribution,
• which can be fit precisely with
• specification of a, b, and m
• Example a 5, b 20 and m 17

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PERT Project Evaluation Review Technique

• Steps in the PERT planning process
• Identify the specific activities and milestones
• The activities are the tasks required to
  complete the project. The milestones are the
  events marking the beginning and end of one or
  more activities. It is helpful to list the tasks
  in a table that in later steps can be expanded to
  include information on sequence and duration
• Determine the proper sequence of the activities
• Construct a network diagram
• Estimate the time required for each activity
• Optimistic time - generally the shortest time in
  which the activity can be completed a
• Most likely time - the completion time having
  the highest probability m Note that this time
  is different from the expected time of the
  completion
• Pessimistic time - the longest time that an
  activity might require b
• Determine the critical path
• Update the PERT chart as the project progresses

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PERT (continued)

• The mean and standard deviation of activity
  times are estimated from the following formulas
  (based on the beta distribution)
• The beta shape parameters are calculated using
  estimates of a, b, m
• In PERT one assumes that the path the with
  longest expected completion time is the true
  critical path (this is only an approximation,
  since true critical path is a random variable)

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PERT Example

• To determine the mean and variance of 1-2, use

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Benefits of PERT

• Produce expected project completion time
• Produce probability of completion before a
  specified date
• Identify the critical path activities that
  directly impact the completion time
• Identify the activities that have slack time and
  that can lend resources to critical path
  activities
• Determine activity start and end dates

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Limitations of PERT (1)

• The activity time estimates are somewhat
  subjective and depend on judgment.
• In cases where there is little experience in
  performing an activity, the numbers may be only a
  guess.
• In other cases, if the person or group performing
  the activity estimates the time there may be bias
  in the estimate

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Limitations of PERT (2)

• Even if the activity times are well-estimated,
  PERT assumes a beta distribution for these time
  estimates, but the actual distribution may be
  different
• Even if the beta distribution assumption holds,
  PERT assumes that the probability distribution of
  the project completion time is the same as the
  that of the critical path.
• Because other paths can become the critical path
  if their associated activities are delayed, PERT
  consistently underestimates the expected project
  completion time

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Time Costing Methods

• Suppose that projects can be expedited by
  reducing the time required for critical
  activities.
• Doing so results in an increase in some costs and
  a decrease in others.
• The goal is to determine the optimal number of
  days to schedule the project to minimize total
  cost

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Time Costing Methods

• Assume that there is a linear time/cost
  relationship for each activity
• Since direct costs decline with the project time
  and indirect costs increase with the project
  time, the total cost curve is a convex function
  whose minimum corresponds to the optimal solution

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Resource Considerations

• When multiple projects compete for resources
  (such as materials and worker time), projects
  schedules may be impacted due to insufficient
  resources
• Renewable resource people
• Nonrenewable resource material
• Adding resources into considerations created
  problems
• Complexity in planning, scheduling and control of
  the project
• With limited resources the CPM schedule may no
  longer be feasible

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Resource Considerations

• Resource-constrained problem finish the project
  as quickly as possible while never using more of
  the resources that available
• Resource leveling problem using unlimited
  resources, arrange for the use of the same amount
  all the time (40 workers every day)
• Both problems are NP-hard and the best solution
  can be guarantied only by enumeration of all
  possible solutions ? use some heuristic

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Resource Considerations Graphic Approaches

• For rough planning, graphic approaches are all
  that are needed. The most widely used tool for
  resource consideration is the resource profile,
  sometimes called a load profile or skyline graph
• Back to our example
• Table contains electronic engineers needed,
• and illustrates the resource profile.

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Resource Considerations Graphic Approaches

Early Start Schedule
Cumulative Number of Engineers
Late Start Schedule
Time
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Resource Considerations Graphic Approaches
Number of Engineers
Early Start Schedule
5-8
4
7-8
3-6
3-5
4-7
3
6-8
4-6
2-3
3-5
2
1-2
2-4
1
Time
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Recommended Problems

• Read Ch. 9 (9.1 9.7)
• 9.3, 9.10, 9.16, 9.20, 9.23, 9.25

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References

• Presentation by McGraw-Hill/Irwin
• Production Operations Analysis by S.Nahmias
• Production Planning, Control, and Integration
  by Sipper and Bulfin Jr.
• http//www.snc.edu/socsci/chair/333/stones/page4.h
  tml
• http//www.netmba.com/operations/project/pert/
• http//www.pcworld.com/downloads/file_download.asp
  ?fid6311fileidx1 Microsoft project
• http//www.geocities.com/qtsplus/DownloadInstructi
  ons.htmDOWNLOAD_INSTRUCTIONS QTS analysis for
  Excel