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Introduction to Management Science 8th Edition by Bernard W. Taylor III. Chapter 8 Project Management. Chapter Topics. The Elements of Project Management The Project Network Probabilistic Activity Times Activity-on-Node Networks and Microsoft Project

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slide1

Introduction to Management Science

8th Edition

by

Bernard W. Taylor III

Chapter 8

Project Management

Chapter 8 - Project Management

slide2

Chapter Topics

  • The Elements of Project Management
  • The Project Network
  • Probabilistic Activity Times
  • Activity-on-Node Networks and Microsoft Project
  • Project Crashing and Time-Cost Trade-Off
  • Formulating the CPM/PERT Network as a Linear Programming Model

Chapter 8 - Project Management

slide3

Overview

  • Uses networks for project analysis.
  • Networks show how projects are organized and are used to determine time duration for completion.
  • Network techniques used are:
    • CPM (Critical Path Method)
    • PERT (Project Evaluation and Review Technique)
  • Developed during late 1950’s.

Chapter 8 - Project Management

slide4

Elements of Project Management

  • Management is generally perceived as concerned with planning, organizing, and control of an ongoing process or activity.
  • Project Management is concerned with control of an activity for a relatively short period of time after which management effort ends.
  • Primary elements of Project Management to be discussed:
    • Project Team
    • Project Planning
    • Project Control

Chapter 8 - Project Management

slide5

The Elements of Project Management

The Project Team

  • Project team typically consists of a group of individuals from various areas in an organization and often includes outside consultants.
  • Members of engineering staff often assigned to project work.
  • Most important member of project team is the project manager.
  • Project manager is often under great pressure because of uncertainty inherent in project activities and possibility of failure.
  • Project manager must be able to coordinate various skills of team members into a single focused effort.

Chapter 8 - Project Management

slide6

The Elements of Project Management

The Project Network

  • A branch reflects an activity of a project.
  • A node represents the beginning and end of activities, referred to as events.
  • Branches in the network indicate precedence relationships.
  • When an activity is completed at a node, it has been realized.

Figure 8.2

Network for Building a House

Chapter 8 - Project Management

slide7

The Project Network

Planning and Scheduling

  • Network aids in planning and scheduling.
  • Time duration of activities shown on branches:

Figure 8.3

Network for Building a House with Activity Times

Chapter 8 - Project Management

slide8

The Project Network

Concurrent Activities

  • Activities can occur at the same time (concurrently).
  • A dummy activity shows a precedence relationship but reflects no passage of time.
  • Two or more activities cannot share the same start and end nodes.

Figure 8.4

Expanded Network for Building a House Showing Concurrent Activities

Chapter 8 - Project Management

slide9

The Project Network

Paths Through a Network

Table 8.1

Paths Through the House-Building Network

Chapter 8 - Project Management

slide10

The Project Network

The Critical Path (1 of 2)

  • The critical path is the longest path through the network; the minimum time the network can be completed. In Figure 8.5:
    • Path A: 1  2  3  4  6  7, 3 + 2 + 0 + 3 + 1 = 9 months
    • Path B: 1  2  3  4  5  6  7, 3 + 2 + 0 + 1 + 1 + 1 = 8 months
    • Path C: 1  2  4  6  7, 3 + 1 + 3 + 1 = 8 months
    • Path D: 1  2  4  5  6  7, 3 + 1 + 1 + 1 + 1 = 7 months

Chapter 8 - Project Management

slide11

The Project Network

The Critical Path (2 of 2)

Figure 8.6

Alternative Paths in the Network

Chapter 8 - Project Management

slide12

The Project Network

Activity Scheduling – Earliest Times

  • ES is the earliest time an activity can start. ESij = Maximum (EFi)
  • EF is the earliest start time plus the activity time. EFij = ESij + tij

Figure 8.7

Earliest Activity Start and Finish Times

Chapter 8 - Project Management

slide13

The Project Network

Activity Scheduling – Earliest Times

  • LS is the latest time an activity can start without delaying critical path time. LSij = LFij - tij
  • LF is the latest finish time. LFij = Minimum (LSj)

Figure 8.8

Latest Activity Start and Finish Times

Chapter 8 - Project Management

slide14

The Project Network

Activity Slack

  • Slack is the amount of time an activity can be delayed without delaying the project.
  • Slack Time exists for those activities not on the critical path for which the earliest and latest start times are not equal.
  • Shared Slack is slack available for a sequence of activities.

Figure 8.9

Earliest and Latest Activity Start and Finish Times

Chapter 8 - Project Management

slide15

The Project Network

Calculating Activity Slack Time (1 of 2)

  • Slack, Sij, computed as follows: Sij = LSij - ESij or Sij = LFij - EFij

Figure 8.10

Activity Slack

Chapter 8 - Project Management

slide16

The Project Network

Calculating Activity Slack Time (2 of 2)

Table 8.2

Activity Slack

Chapter 8 - Project Management

slide17

Probabilistic Activity Times

  • Activity time estimates usually can not be made with certainty.
  • PERT used for probabilistic activity times.
  • In PERT, three time estimates are used: most likely time (m), the optimistic time (a) , and the pessimistic time (b).
  • These provide an estimate of the mean and variance of a beta distribution:
    • mean (expected time):
    • variance:

Chapter 8 - Project Management

slide18

Probabilistic Activity Times

Example (1 of 3)

Figure 8.11

Network for Installation Order Processing System

Chapter 8 - Project Management

slide19

Probabilistic Activity Times

Example (2 of 3)

Table 8.3

Activity Time Estimates for Figure 8.11

Chapter 8 - Project Management

slide20

Probabilistic Activity Times

Example (3 of 3)

Figure 8.12

Network with Mean Activity Times and Variances

Chapter 8 - Project Management

slide21

Probabilistic Activity Times

Earliest and Latest Activity Times and Slack

Figure 8.13

Earliest and Latest Activity Times

Chapter 8 - Project Management

slide22

Probabilistic Activity Times

Earliest and Latest Activity Times and Slack

Table 8.4

Activity Earliest and Latest Times and Slack

Chapter 8 - Project Management

slide23

Probabilistic Activity Times

Expected Project Time and Variance

  • The expected project time is the sum of the expected times of the critical path activities.
  • The project variance is the sum of the variances of the critical path activities.
  • The expected project time is assumed to be normally distributed (based on central limit theorem).
  • In example, expected project time (tp) and variance (vp) interpreted as the mean () and variance (2) of a normal distribution:
  • = 25 weeks
  • 2 = 6.9 weeks

Chapter 8 - Project Management

slide24

Probability Analysis of a Project Network (1 of 2)

  • Using normal distribution, probabilities are determined by computing number of standard deviations (Z) a value is from the mean.
  • Value is used to find corresponding probability in Table A.1, Appendix A.

Chapter 8 - Project Management

slide25

Probability Analysis of a Project Network (2 of 2)

Figure 8.14

Normal Distribution of Network Duration

Chapter 8 - Project Management

slide26

Probability Analysis of a Project Network

Example 1 (1 of 2)

  • Z value of 1.90 corresponds to probability of .4713 in Table A.1, Appendix A. Probability of completing project in 30 weeks or less: (.5000 + .4713) = .9713.
  • 2 = 6.9  = 2.63
  • Z = (x-)/  = (30 -25)/2.63 = 1.90

Chapter 8 - Project Management

slide27

Probability Analysis of a Project Network

Example 1 (2 of 2)

Figure 8.15

Probability the Network Will Be Completed in 30 Weeks or Less

Chapter 8 - Project Management

slide28

Probability Analysis of a Project Network

Example 2 (1 of 2)

  • Z = (22 - 25)/2.63 = -1.14
  • Z value of 1.14 (ignore negative) corresponds to probability of .3729 in Table A.1, appendix A.
  • Probability that customer will be retained is .1271

Chapter 8 - Project Management

slide29

Probability Analysis of a Project Network

Example 2 (2 of 2)

Figure 8.16

Probability the Network Will Be Completed in 22 Weeks or Less

Chapter 8 - Project Management

slide30

Probability Analysis of a Project Network

CPM/PERT Analysis with QM for Windows

Exhibit 8.1

Chapter 8 - Project Management

slide31

Activity-on-Node Networks and Microsoft Project

  • The project networks developed so far have used the “activity-on-arrow” (AOA) convention.
  • “Activity-on-node” (AON) is another method of creating a network diagram.
  • The two different conventions accomplish the same thing, but there are a few differences.
  • An AON diagram will often require more nodes than an AOA diagram.
  • An AON diagram does not require dummy activities because two “activities” will never have the same start and end nodes.
  • Microsoft Project handles only AON networks.

Chapter 8 - Project Management

slide32

Activity-on-Node Networks and Microsoft Project

Node Structure

This node includes the activity number in the upper left-hand corner, the activity duration in the lower left-hand corner, and the earliest start and finish times, and latest start and finish times in the four boxes on the right side of the node.

Figure 8.17

Activity-on-Node Configuration

Chapter 8 - Project Management

slide33

Activity-on-Node Networks and Microsoft Project

AON Network Diagram

Figure 8.18

House-Building Network with AON

Chapter 8 - Project Management

slide34

Activity-on-Node Networks and Microsoft Project

Microsoft Project (1 of 4)

Exhibit 8.2

Chapter 8 - Project Management

slide35

Activity-on-Node Networks and Microsoft Project

Microsoft Project (2 of 4)

Exhibit 8.3

Chapter 8 - Project Management

slide36

Activity-on-Node Networks and Microsoft Project

Microsoft Project (3 of 4)

Exhibit 8.4

Chapter 8 - Project Management

slide37

Activity-on-Node Networks and Microsoft Project

Microsoft Project (4 of 4)

Exhibit 8.5

Chapter 8 - Project Management

slide38

Project Crashing and Time-Cost Trade-Off

Definition

  • Project duration can be reduced by assigning more resources to project activities.
  • Doing this however increases project cost.
  • Decision is based on analysis of trade-off between time and cost.
  • Project crashing is a method for shortening project duration by reducing one or more critical activities to a time less than normal activity time.
  • Crashing achieved by devoting more resources to crashed activities.

Chapter 8 - Project Management

slide39

Project Crashing and Time-Cost Trade-Off

Example Problem (1 of 5)

Figure 8.19

Network for Constructing a House

Chapter 8 - Project Management

slide40

Project Crashing and Time-Cost Trade-Off

Example Problem (2 of 5)

Crash cost and crash time have linear relationship: total crash cost/total crash time = $2000/5 = $400/wk

Figure 8.20

Time-Cost Relationship for Crashing Activity 12

Chapter 8 - Project Management

slide41

Project Crashing and Time-Cost Trade-Off

Example Problem (3 of 5)

Table 8.5

Normal Activity and Crash Data for the Network in Figure 8.19

Chapter 8 - Project Management

slide42

Project Crashing and Time-Cost Trade-Off

Example Problem (4 of 5)

Figure 8.21

Network with Normal Activity Times and Weekly Activity Crashing Costs

Chapter 8 - Project Management

slide43

Project Crashing and Time-Cost Trade-Off

Example Problem (5 of 5)

  • As activities are crashed, the critical path may change and several paths may become critical.

Figure 8.22

Revised Network with Activity 12 Crashed

Chapter 8 - Project Management

slide44

Project Crashing and Time-Cost Trade-Off

Project Crashing with QM for Windows

Exhibit 8.6

Chapter 8 - Project Management

slide45

Project Crashing and Time-Cost Trade-Off

General Relationship of Time and Cost (1 of 2)

  • Project crashing costs and indirect costs have an inverse relationship.
  • Crashing costs are highest when the project is shortened.
  • Indirect costs increase as the project duration increases.
  • Optimal project time is at minimum point on the total cost curve.

Chapter 8 - Project Management

slide46

Project Crashing and Time-Cost Trade-Off

General Relationship of Time and Cost (2 of 2)

Figure 8.23

A Time-Cost Trade-Off

Chapter 8 - Project Management

slide47

The CPM/PERT Network

Formulating as a Linear Programming Model

  • The objective is to determine the earliest time the project can be completed (i.e., the critical path time).

General linear programming model:

Minimize Z = xi

subject to:

xj - xi tij for all activities i  j

xi, xj 0

Where:

xi = earliest event time of node i

xj = earliest event time of node j

tij = time of activity i  j

Chapter 8 - Project Management

slide48

The CPM/PERT Network

Example Problem Formulation and Data (1 of 2)

Minimize Z = x1 + x2 + x3 + x4 + x5 + x6 + x7

subject to:

x2 - x1 12

x3 - x2  8

x4 - x2  4

x4 - x3 0

x5 - x4 4

x6 - x4 12

x6 - x5  4

x7 - x6 4

xi, xj 0

Chapter 8 - Project Management

slide49

The CPM/PERT Network

Example Problem Formulation and Data (2 of 2)

Figure 8.24

CPM/PERT Network for the House-Building Project with Earliest Event Times

Chapter 8 - Project Management

slide50

The CPM/PERT Network

Example Problem Solution with Excel (1 of 4)

Exhibit 8.7

Chapter 8 - Project Management

slide51

The CPM/PERT Network

Example Problem Solution with Excel (2 of 4)

Exhibit 8.8

Chapter 8 - Project Management

slide52

The CPM/PERT Network

Example Problem Solution with Excel (3 of 4)

Exhibit 8.9

Chapter 8 - Project Management

slide53

The CPM/PERT Network

Example Problem Solution with Excel (4 of 4)

Exhibit 8.10

Chapter 8 - Project Management

slide54

Probability Analysis of a Project Network

Example Problem – Model Formulation

xi = earliest event time of node I

xj = earliest event time of node j

yij = amount of time by which activity i  j is crashed

Minimize Z = $400y12 + 500y23 + 3000y24 + 200y45 + 7000y46 + 200y56 + 7000y67

subject to:

y12 5 y12 + x2 - x1 12 x7 30

y23 3 y23 + x3 - x2 8 y67  1

y24 1 y24 + x4 - x2 4 x67 + x7 - x6 4

y34 0 y34 + x4 - x3 0 xj, yij 0

y45 3 y45 + x5 - x4 4

y46 3 y46 + x6 - x4 12

y56  3 y56 + x6 - x5 4

Chapter 8 - Project Management

slide55

Probability Analysis of a Project Network

Example Problem – Excel Solution (1 of 3)

Exhibit 8.11

Chapter 8 - Project Management

slide56

Probability Analysis of a Project Network

Example Problem – Excel Solution (2 of 3)

Exhibit 8.12

Chapter 8 - Project Management

slide57

Probability Analysis of a Project Network

Example Problem – Excel Solution (3 of 3)

Exhibit 8.13

Chapter 8 - Project Management

slide58

PERT Project Management Example Problem

Problem Statement and Data (1 of 2)

  • Given the following data determine the expected project completion time and variance, and the probability that the project will be completed in 28 days or less.

Chapter 8 - Project Management

slide59

PERT Project Management Example Problem

Problem Statement and Data (2 of 2)

Chapter 8 - Project Management

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PERT Project Management Example Problem

Solution (1 of 4)

Step 1: Compute the expected activity times and variances.

Chapter 8 - Project Management

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PERT Project Management Example Problem

Solution (2 of 4)

Step 2: Determine the earliest and latest times at each node.

Chapter 8 - Project Management

slide62

PERT Project Management Example Problem

Solution (3 of 4)

Step 3: Identify the critical path and compute expected completion time and variance.

Critical path (activities with no slack): 1  2  3  4  5

Expected project completion time (tp): 24 days

Variance: v = 4 + 4/9 + 4/9 + 1/9 = 5 days

Chapter 8 - Project Management

slide63

PERT Project Management Example Problem

Solution (4 of 4)

Step 4: Determine the Probability That the Project Will be Completed in 28 days or less.

Z = (x - )/ = (28 -24)/5 = 1.79

Corresponding probability from Table A.1, Appendix A, is .4633 and P(x  28) = .9633.

Chapter 8 - Project Management