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    Importance of Project Management

    Projects represent change and allow organizations toeffectively introduce new products, new

    process, new programs

    Project management offers a means for dealing withdramatically reduced product cycle times

    Projects are becoming globalized making them moredifficult to manage without a formal methodology

    Project management helps cross-functional teams tobe more effective

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    Management of IT Projects

    More than $250 billion is spent in the US each year onapproximately 175,000 information technology projects.

    Only 26 percent of these projects are completed on time andwithin budget.

    The average cost for a development project for a large companyis more than $2 million.

    Project management is an $850 million industry and is expectedto grow by as much as 20 percent per year.

    Bounds, Gene. The Last Word on Project

    ManagementIIE Solutions, November, 1998.

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    What Defines a Project?

    How does a project

    differ from a

    program?

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    Project Management versus Process Management

    Ultimately, the parallels between process and projectmanagement give way to a fundamental difference:process management seeks to eliminate variabilitywhereas project management must accept variability

    because each project is unique.

    Elton, J. & J. Roe. Bringing Discipline to Project

    Management Harvard Business Review, March-April,

    1998.

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    Measures of Project Success

    Was the movie

    Titanic

    a success?

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    Delayed Openings are a Fact of Life in the Foodservice,

    Hospitality Industry

    Disney's shipbuilder was six months late in delivering its new cruise ships,and thousands of customers who had purchased tickets were stranded.

    Even with that experience, their second ship was also delivered well after the

    published schedules. Universal Studios in Orlando, Fla. had been building a

    new restaurant and entertainment complex for more than two years. They

    advertised a December opening, only to announce in late November that it

    would be two or three months late.

    Even when facilities do open close to schedule, they are rarely finished

    completely and are often missing key components. Why do those things

    happen? With all of the sophisticated computers and project management

    software, why aren't projects completed on schedule?

    Frable, F. Nation's Restaurant News (April 12, 1999)

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    IT Project Outcomes

    More than 200%

    late

    Cancelled

    On-Time

    Less than 20%

    late

    21-50% late

    51-100% late

    101-200% late

    26%

    29%

    6%

    16%

    9%

    8%

    6%

    Source: Standish Group Survey, 1999 (from a

    survey of 800 business systems projects)

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    Why do Projects Fail?

    Studies have shown that the following factorscontribute significantly to project failure:

    Improper focus of the project management system

    Fixation on first estimates

    Wrong level of detail

    Lack of understanding about project management tools; too much

    reliance on project management software

    Too many people

    Poor communication

    Rewarding the wrong actions

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    Why do IT Projects Fail?

    Ill-defined or changing requirements

    Poor project planning/management

    Uncontrolled quality problems

    Unrealistic expectations/inaccurate estimates

    Naive adoption of new technology

    Source: S. McConnell, Construx Software Builders, Inc.

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    QuickTime and aPhoto - JPEG decompressor

    are needed to see this picture.

    Have You Ever Lost Sight of theProject Goals?

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    Not all Projects Are Alike

    [in IT projects], if you ask people whats done and what remains to be

    done there is nothing to see. In an IT project, you go from zero to 100

    percent in the last second--unlike building a brick wall where you can see

    when youre halfway done. Weve moved from physical to non-physical

    deliverables.

    J. Vowler (March, 2001)

    Engineering projects = task-centric

    IT projects = resource-centric

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    Shenhars Taxonomy of Project Types

    DegreeofUncertainty/Risk

    SystemComplexity/Scope

    High

    Low-

    Tech

    AssemblyProjects

    ArrayProjects

    SystemProjects

    Medium-Tech

    High-Tech

    Super High-Tech

    Construction

    Newcellphone

    New shrink-wrappedsoftware

    ERPimplementationin multi-national

    firm

    Auto repair

    Advancedradarsystem

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    Project Life Cycle

    TimePhase 1 Phase 2 Phase 3 Phase 4Formation & Planning Scheduling & Evaluation &Selection Control Termination

    RequiredResour

    ces

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    Life Cycle Models: Pure Waterfall

    ConceptDesign

    Requirements

    Analysis

    Architecture

    Design

    Detailed

    Design

    Coding &

    Debugging

    System

    Testing

    Source: S. McConnell

    Rapid Development(Microsoft Press, 1996)

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    Life Cycle Models: Code & Fix

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    Design, Cost, Time Trade-offs

    Target

    COST

    DESIGN

    Due Date

    Budget

    Constraint

    Optimal Time-Cost

    Trade-off

    Required

    Performance

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    Optional Scope Contracts

    Fixed Scope Contract specifies SCHEDULE, COST, SCOPE

    Optional Scope Contract specifies SCHEDULE, COST, QUALITY

    (general design guidelines may be indicated)

    Since it is widely accepted that you can select

    three of the four dimensions (or perhaps only

    two), what to do?

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    Importance of Project Selection

    There are two ways for a business to succeed

    at new products: doing projects right, and

    doing the right projects.

    Cooper, R.G., S. Edgett, & E. Kleinschmidt.

    Research Technology Management, March-April, 2000.

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    Project Initiation & Selection

    Critical factors1) Competitive necessity

    2) Market expansion

    3) Operating requirement

    Numerical Methods1) Payback period

    2) Net present value (NPV) or Discounted Cash Flow (DCF)

    3) Internal rate of return (IRR)

    4) Expected commercial value (ECV)

    Project Portfolio1) Diversify portfolio to minimize risk

    2) Cash flow considerations

    3) Resource constraints

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    Payback Period

    Number of years needed for project to

    repay its initial fixed investment

    Example: Project costs $100,000 and is expected

    to save company $20,000 per year

    Payback Period = $100,000 / $20,000 = 5 years

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    Net Present Value (NPV)

    Discounted Cash Flow (DCF)

    Let Ft = net cash flow in period t (t = 0, 1,..., T)

    F0= ini tial cash investment in time t = 0

    r = discount rate of return (hurdle rate)

    NPV =

    Ft

    1 + rtt = 0

    T

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    Internal Rate of Return (IRR)

    Find value of r such that NPV is equal to 0

    F0 + F1

    1 + r+ F2

    1 + r2= 0

    Example (with T = 2):

    Find r such that

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    DCF Project Example*

    *Hodder, J. and H.E. Riggs. Pitfalls in Evaluating Risky Projects, Harvard

    Business Review, Jan-Feb, 1985, pp. 128-136.

    Product

    Demand Product Life

    Annual Net

    Cash Inflow Probability

    High 20 years $24 million 0.3

    Medium 10 years $12 million 0.5

    Low Abandon Project None 0.2

    Phase I Research and Product De velopment

    $18 million annual research cost for 2 years60% probability of succ ess

    Phase II Market Development

    Undertaken only if product development is succes sful

    $10 million annual expenditure for 2 years to develop marketing and

    distribution c hannels (net of any revenues earned in tes t marketi

    Phase III SalesProceeds only if Phase I and I I verify opportunity.

    Production is subcontracted and all cash flows are after-tax and occu

    at year's end.

    The results of Phase II (available at the end of year 4) identify the

    product's mar ket po tential as indic ated below:

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    DCF Project Example (contd)

    Year Expe cte d Cash Flow (in $ million)

    1 -18

    2 -18

    3 0.6 (-10) = -

    4 0.6 (-10) = -5 - 14 .6 (0.3 x 24 + 0.5 x 12) = 7.92

    15 - 24 .6 (0.3 x 24) = 4.32

    What is the internal rate of return for this project?

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    DCF Example Continued

    What if you can sell the product (assuming that both Research and

    Product Development AND Market Development are successful) to a

    third party? What are the risks AT THAT POINT IN TIME?

    Assume that discount rate r2 is 5%

    Probability

    What is 20 years of cash inflow at $24M/year? $299.09 0.3

    What is 10 years of cash inflow at $12M/year? $92.66 0.5

    Expected value of product at Year 4: $136.06

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    DCF Example Continued

    Expected cash flows (with sale of product at end of year 4) are now:

    Outflow Inflow Net Probability

    Expe cted

    Cash Flow

    Year 1 18.00$ (18.00)$ 1 (18.00)$

    Year 2 18.00$ (18.00)$ 1 (18.00)$Year 3 10.00$ (10.00)$ 0.6 (6.00)$

    Year 4 10.00$ 136.06$ 126.06$ 0.6 75.63$

    What is the internal rate of return for this project?

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    Criticisms of NPV/DCF

    1) Assumes that cash flow forecasts are accurate; ignoresthe human bias effect

    2) Fails to include effects of inflation in long term

    projects

    3) Ignores interaction with other proposed and ongoing

    projects (minimize risk through diversification)

    4) Use of a single discount rate for the entire project (risk

    is typically reduced as the project evolves)

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    Expected Commercial Value (ECV)

    Develop New

    Product

    Technical Failure

    Technical Success

    Probability = pt

    Probability = 1 - pt

    Launch New

    Product

    Commercial

    Failure (with net

    benefit = 0)

    Commercial Success

    (with net benefit =

    NPV)

    Probability = pc

    Probability = 1 - pc

    Risk class 1 Risk class 2

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    DCF Example Revisited

    Discount rate r1 Discount rate r2

    Research &

    Product

    Development

    Development

    Succeeds

    Probability = pt

    Development Fails

    Probability = 1 - pt

    Market

    Development

    Product Demand

    High0.3

    Product Demand

    Medium

    Product Demand

    Low

    0.5

    0.2

    Drop project

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    Ranking/Scoring ModelsProfitability/value

    1) Increase in profitability?2) Increase in market share?3) Will add knowledge to organization that can be leveraged by other projects?4) Estimated NPV, ECV, etc.Organization's Strategy1) Consistent with organization's mission statement?2) Impact on customers?Risk1) Probability of research being successful?2) Probability of development being successful?3) Probability of process success?4) Probability of commercial success?5) Overall r isk of project6) Adequ ate market demand?7) Competitors in marketOrganizat ion Costs

    1)

    Is new facilit y needed?2) Can use current personnel?3) External consultants needed?4) New hires needed?Miscellaneous Factors1) Impact on environmental standards?2) Impact on workforce safety?3) Impact on quality?4) Social/political implications

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    Scoring Attributes

    vi xi =1 - exp L - xi

    1 - exp L - U.

    To convert various measurement scales to a (0, 1) range.

    LINEAR SCALE: value of attribute i is

    EXPONENTIAL SCALE: value of attribute i is

    vi xi =xi - L

    U - L

    0.00

    0.10

    0.20

    0.30

    0.40

    0.50

    0.60

    0.70

    0.80

    0.90

    1.00

    1 2 3 4 5 6 7

    Res ponse

    Linear Scale

    Exponential Scale

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    Ranking/Scoring Example

    Attribute Measurement ScaleAttribute

    Weight (wi)

    1) Does project increase market share? unlikely likely 30%

    2) Is new facilit y needed? yes no 15%

    3) Are there safety concerns? likely unsure no 10%

    4) Likeli hood o f successful t echnical development? unlikely likely 20%

    5) Likelihood of successful commercial development? unlikely likely 25%

    1 2 3 4 5

    1 2 3 4 5

    1 2 3 4 5

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    Attribute #1 #2 #3 #4 #5

    Project

    Score (Vj)

    Project A 4 yes likely 4 1

    Project B 2 no unsure 3 4

    Linear ScaleProject A 0.75 0.25 0 0.75 0 0.413

    Project B 0.25 0.75 0.5 0.5 0.75 0.525

    Exponential ScaleProject A 0.97 0.64 0.00 0.97 0.00 0.581

    Project B 0.64 0.97 0.88 0.88 0.97 0.845

    Ranking/Scoring Example (contd)

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    Analyzing Project Portfolios: Bubble Diagram

    Expected NPV

    Prob of Commercial Success

    HighZero

    Low

    High

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    Analyzing Project Portfolios: Product vs Process

    Extentof Process Change

    Source: Clark and Wheelwright, 1992

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    Key Elements of Project Portfolio Selection Problem

    1. Multi-period investment problem

    2. Top management typically allocates funds to different

    product lines (e.g., compact cars, high-end sedans)

    3. Product lines sell in separate (but not necessarilyindependent) market segments

    4. Product line allocations are changed frequently

    5. Conditions in each market segment are uncertain from

    period to period due to competition and changing

    customer preferences

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    Stage-Gate Approach

    Installation Plan

    Facility Prep

    Training Plan

    Implementation

    Detail Design

    Schedule & Budget

    Contingency Plan

    Product &

    Performance Reviews

    Initiation Define Design ControlImprove

    Work Statement

    Risk Assessment

    Purchasing Plan

    Change Mgt

    Initiation

    Project Review

    Charter

    Source: PACCAR Information Technology Division

    Renton, WA

    Production close-out

    Lessons learned

    Post-project audit

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    Project Selection Example

    Y e a r (t)

    1 2 3 4

    Project A ($40) $10 $20 $20

    Project B ($65) ($25) $50 $50Budget

    Limit (B t ) $120 $20 $40 $55

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    Phases of Project Management

    n Project formulation and selection

    n Project planningu Summary statement

    u Work breakdown structure

    u Organization plan

    u risk management

    u

    Subcontracting and bidding processn Project scheduling

    u Time and schedule

    u Project budget

    u Resource allocation

    u Equipment and material purchases

    n Monitoring and controlu Cost control metrics

    u Change orders

    u Milestone reports

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    Project Planning

    n

    Summary Statementu Executive summary: mission and goals, constraintsu Description and specifications of deliverables

    u Quality standards used (e.g., ISO)

    u Role of main contractor and subcontractors

    u Composition and responsibilities of project team

    n Organization Planu Managerial responsibilities assigned; signature authority

    u Cross impact matrix (who works on what)

    u Relationship with functional departments

    u Project administration

    u Role of consultants

    u Communication procedures with organization, client, etc.

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    Importance of Project Planning

    The 6P Rule of Project Management:

    PriorPlanning Prevents PoorProject

    Performance

    If you fail to plan, you will plan to fail

    Anonymous

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    Work Breakdown Structure (WBS)

    1) Specify the end-item deliverables

    2) Subdivide the work, reducing the dollars and

    complexity with each additional subdivision

    3) Stop dividing when the tasks are manageable workpackages based on the following:

    Skill group(s) involved

    Managerial responsibility

    Length of time

    Value of task

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    Work Packages/Task Definition

    The work packages (tasks or activities) that are defined

    by the WBS must be:

    Manageable

    Independent

    Integratable

    Measurable

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    Design of a WBS

    The usual mistake PMs make is to lay out too many tasks;subdividing the major achievements into smaller and

    smaller subtasks until the work breakdown structure

    (WBS) is a to do list of one-hour chores. Its easy to get

    caught up in the idea that a project plan should detaileverything everybody is going to do on the project. This

    springs from the screwy logic that a project managers job

    is to walk around with a checklist of 17,432 items and tick

    each item off as people complete them.

    The Hampton Group (1996)

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    Two-Level WBS

    1. Charity Auction

    1.1 Event

    Planning

    1.2 Item

    Procurement

    1.3 Marketing 1.4. Corporate

    Sponsorships

    WBS level 1

    WBS level 2

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    Three-Level WBS

    1.1 Event

    Planning

    1.2 Item

    Procurement

    1.3 Marketing

    1. Charity Auction

    1.4 Corporate

    Sponsorships

    1.1.1 Hire Auctioneer

    1.1.2. Rent space

    1.1.3 Arrange fordecorations

    1.2.1 Silent

    auction items

    1.2.2 Live auction

    items

    1.2.3 Raffle items

    1.3.1 Individual

    ticket sales

    1.3.2 Advertising

    1.1.4 Print catalog

    WBS level 1

    WBS level 2

    WBS level 3

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    Estimating Task Durations (contd)

    Benchmarking

    Modular approach

    Parametric techniques

    Learning effects

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    Beta Distribution

    Completion time of task j

    Optimistic Timetjo

    Pessimistic Time tjp

    Time

    Probability density

    function

    Expected duration =Most Likely Time = tm

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    Beta Distribution

    For each task j, we must make three estimates:

    most optimistic time

    most pessimistic time

    most likely time

    tjo

    tjp

    tjm

    Expected duration j =tjo + tj

    p + 4tjm

    6

    Variance of task j = j2 = tj

    p

    - tjo 2

    36

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    Estimating Task Durations: Painting a Room

    Task: Paint 4 rooms, each is approximately 10 x 20. Use flat paint on walls,

    semi-gloss paint on trim and woodwork. Each room has two doors and four

    windows. You must apply masking tape before painting woodwork around thedoors and windows. Preparation consists of washing all walls and woodwork

    (some sanding and other prep work will be needed). Only one coat of paint is

    necessary to cover existing paint. All supplies will be provided at the start of the

    task. Previous times on similar painting jobs are indicated in the table below.

    hours min hours min

    27 25 31 52

    38 25 19 1533 12 26 27

    17 44 30 27

    26 7 25 21

    22 1 24 28

    14 2 32 58

    30 27 32 1

    28 30 13 43

    21 13 42 45

    23 59 22 57

    27 44 32 1523 15 32 31

    37 6 27 15

    17 54 26 11

    17 13 21 52

    What is your estimate of the average time you will

    need? What is your estimate of the variance?

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    Estimating Task Durations with Incentives

    Task: Consider the painting job that you havejust estimated. Now, however, there are

    explicit incentives for meeting your estimated

    times. If you finish painting the room before

    your specified time, you will receive a $10

    bonus payment. HOWEVER, if you finish

    the painting job after your specified time, you

    will be fined $1000.Revised estimated time =

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    Estimating Task Durations with Incentives

    Task: Consider the painting job that you havejust estimated. Now, however, there are

    explicit incentives for meeting your estimated

    times. If you finish painting the room before

    your specified time, you will receive a $10

    bonus payment. If you finish the painting job

    after your specified time, there is no penalty.

    Revised estimated time =

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    Role of Project Manager/Team

    Project Manager

    Client

    Subcontractors

    Regulating

    Organizations

    Project Team

    Functional

    Managers

    Top

    Management

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    Responsibilities of a Project Manager

    To the organization and top management

    Meet budget and resource constraints

    Engage functional managers

    To the project team Provide timely and accurate feedback

    Keep focus on project goals Manage personnel changes

    To the client Communicate in timely and accurate manner

    Provide information and control on changes/modifications

    Maintain quality standards

    To the subcontractors Provide information on overall project status

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    Project Team

    What is a project team?

    A group of people committed to achieve a

    common set of goals for which they hold

    themselves mutually accountable

    Characteristics of a project team

    Diverse backgrounds/skills

    Able to work together effectively/develop synergy

    Usually small number of people Have sense of accountability as a unit

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    I design user interfaces to please an audience of one.

    I write them for me. If Im happy, I know some cool

    people will like it. Designing user interfaces by

    committee does not work very well; they need to becoherent. As for schedule, Im not interested in

    schedules; did anyone care when War and Peace came

    out?

    Developer, Microsoft CorporationAs reported by MacCormack and Herman, HBR Case 9-600-097:

    Microsoft Office 2000

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    Intra-team Communication

    M = Number of project team membersL = Number of links between pairs of team members

    If M =2, then L = 1

    If M =3, then L = 3

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    Number of Intra-team Links

    L = Number of Intra-team Links = N

    2=

    N(N-1)

    2

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    Importance of Communication

    On the occasion of a migration from the east, men discovered aplain in the land of Shinar, and said to one another, Come, let

    us build ourselves a city with a tower whose top shall reach the

    heavens. The Lord said, Come, let us go down, and there

    make such a babble of their language that they will not

    understand one anothers speech. Thus, the Lord dispersedthem from there all over the earth, so that they had to stop

    building the city.

    Genesis 11: 1-8

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    Project Performance and Group Harmony

    Two schools of thought:

    1) Humanistic school -- groups that have positivecharacteristics will perform well

    2) Task oriented school -- positive group

    characteristics detract from group performance

    What is the relationship between the design ofmultidisciplinary project teams and project success?

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    Project Performance and Group Harmony (contd)

    Experiment conducted using MBA students at UW and

    Seattle U using computer based simulation of pre-operationaltesting phase of nuclear power plant*

    Total of 14 project teams (2 - 4 person project teams) with atotal of 44 team members; compared high performance (low

    cost) teams vs low performance (high cost) teams

    Measured: Group Harmony

    Group Decision Making Effectiveness

    Extent of Individuals Contributions to Group

    Individual Attributes

    *Brown, K., T.D. Klastorin, & J. Valluzzi. Project Management

    Performance: A Comparison of Team Characteristics,IEEE Transactions on

    Engineering Management, Vol 37, No. 2 (May, 1990), pp. 117-125.

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    Group Harmony: High vs Low Performing Groups

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    Extent of Individual Contribution: High vs LowPerforming Groups

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    Decision Making Effectiveness: High vs LowPerforming Groups

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    Project Organization Types

    Functional: Project is divided and assigned to appropriate functionalentities with the coordination of the project being carried out by

    functional and high-level managers

    Functional matrix: Person is designated to oversee the projectacross different functional areas

    Balanced matrix: Person is assigned to oversee the project andinteracts on equal basis with functional managers

    Project matrix: A manager is assigned to oversee the project and isresponsible for the completion of the project

    Project team: A manager is put in charge of a core group ofpersonnel from several functional areas who are assigned to the

    project on a full-time basis

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    Project Organization Continuum

    Project Team

    Organization

    Project Matrix

    Project fully managed

    by functional managers Project fully managed by

    project team manager

    FunctionalOrganization

    Functional Matrix

    Balanced Matrix

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    A Business School as a Matrix Organization

    Dean

    Associate Dean for

    Undergraduate

    Program

    Associate Dean for

    MBA Programs

    Director of

    Doctoral Program

    Accounting

    Department Chair

    Marketing

    Department Chair

    Finance Department

    Chair

    Gloria

    Diane

    Bob

    ZeldaLarry

    Curly

    Moe

    Barby

    Leslie

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    Matrix Organizations & Project Success

    Matrix organizations emerged in 1960s as analternative to traditional means of project

    teams

    Became popular in 1970s and early 1980s

    Still in use but have evolved into many different

    forms

    Basic question: Does organizational structure

    impact probability of project success?

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    Organizational Structure & Project Success Studies by Larson and Gobeli (1988, 1989)

    Sent questionnaires to 855 randomly selected PMI members

    Asked about organizational structure (which one best describes the primary

    structure used to complete the project)

    Perceptual measures of project success: successful, marginal, unsuccessful

    with respect to :

    1) Meeting schedule2) Controlling cost

    3) Technical performance

    4) Overall performance

    Respondents were asked to indicate the extent to which they agreed with

    each of the following statements:1) Project objectives were clearly defined

    2) Project was complex

    3) Project required no new technologies

    4) Project had high priority within organization

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    Classification of 547 respondents (64% response rate)

    30% project managers or directors of project mgt programs16% top management (president, vice president, etc.)

    26% managers in functional areas (e.g., marketing)

    18% specialists working on projects

    Industries included in studies

    14% pharmaceutical products10% aerospace

    10% computer and data processing products

    others: telecommunications, medical instruments, glass products,software development, petrochemical products, houseware goods

    Organizational structures:

    13% (71): Functional organizations

    26% (142): Functional matrix

    16.5% (90): Balanced matrix

    28.5% (156): Project matrix

    16% (87): Project team

    Study Data

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    ANOVA Results by Organizational Structure

    Controlling

    Cost

    Meeting

    Schedule

    Technical

    Performance

    Overall

    Results

    Organizational Structure N Ave (SD) Ave (SD) Ave (SD) Ave (SD)

    A

    Functional

    Organization 71 1.76 (.83) 1.77 (.83) 2.30 (.77) 1.96 (.84)

    B Functional Matrix 142 1.91 (.77) 2.00 (.85) 2.37 (.73) 2.21 (.75)

    C Balanced Matrix 90 2.39 (.73) 2.15 (.82) 2.64 (.61) 2.52 (.61)

    D Project Matrix 156 2.64 (.76) 2.30 (.79) 2.67 (.57) 2.54 (.66)

    E Project Team 87 2.22 (.82) 2.32 (.80) 2.64 (.61) 2.52 (.70)

    Total Sample 546 2.12 (.79) 2.14 (.83) 2.53 (.66) 2.38 (.70)

    F-statistic 10.38* 6.94* 7.42* 11.45*

    Scheffe Results

    A,B < C,D,E

    E < D A, B < C < D,E A, B < C,D, E A, B < C,D, E

    *Statisticall y signif icant at a p

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    Summary of Results

    Project structure significantly related to project success

    New development projects that used traditional functional organization

    had lowest level of success in controlling cost, meeting schedule,

    achieving technical performance, and overall results

    Projects using either a functional organization or a functional matrix had

    a significantly lower success rate than the other three structures

    Projects using either a project matrix or a project team were more

    successful in meeting their schedules than the balanced matrix

    Project matrix was better able to control costs than project team

    Overall, the most successful projects used a balanced matrix, project

    team, or--especially--project matrix

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    Subcontracting = Business Alliance

    n When you subcontract part (or all) of a

    project, you are forming a business

    alliance....

    Intelligent Business Alliances: A business relationship for

    mutual benefit between two or more parties with compatible

    or complementary business interests and/or goals

    Larraine Segil, Lared Presentations

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    Communication and Subcontractors

    How is knowledge

    transferred?

    What types of communication mechanism(s) will be

    used between company and subcontractor(s)?

    WHAT a companycommunicates.....

    HOW a companycommunicates.....

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    Personality Compatibility

    Corporate

    Personality

    Subcontractor

    Personality

    Individual

    Personality

    Project

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    Subcontracting Issues

    n What part of project will be subcontracted?n What type of bidding process will be used? What type of

    contract?

    n Should you use a separate RFB (Request for Bids) for

    each task or use one RFB for all tasks?n What is the impact on expected duration of project?

    n Use a pre-qualification list?

    n Incentives? Bonus for finishing early? Penalties for

    finishing after stated due date?

    What is impact of risk on expected project cost?

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    Basic Contract Types

    n Fixed Price Contractu Client pays a fixed price to the contractor irrespective of actual audited

    cost of project

    n Cost Plus Contract

    u Client reimburses contractor for all audited costs of project (labor, plant,& materials) plus additional fee (that may be fixed sum or percent of costs

    incurred)

    n Units Contract

    u Client commits to a fixed price for a pre-specified unit of work; final

    payment is based on number of units produced

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    Incentive (Risk Sharing) Contracts

    General Form:Payment to Subcontractor = Fixed Fee + (1 - B) (Project Cost)

    where B = cost sharing rate

    Cost Plus Contract

    B = 0 B = 1

    Fixed Price Contract

    Linear & Signalling

    Contracts

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    Why Use Incentive Contracts?

    Expected Cost of Project = $100MTwo firms bid on subcontract

    Firm 1 Firm 2

    Fixed Fee (bid) $5 M $7 M

    Project Cost $105 M $95 M

    (inefficient producer)

    What is result if Cost Plus Contract (B = 0) used?

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    Washington State Bid Code (WAC 236-48-093)

    n WAC 236-48-093: A contract shall be awarded to the lowest responsible and responsive

    bidder based upon, but not limited to, the following criteria where applicable and onlythat which can be reasonably determined:

    n 1) The price and effect of term discounts...price may be determined by life cycle costing

    if so indicated in the invitation to bid

    n 2) The conformity of the goods and/or services bid with invitation for bid or request for

    quotation specifications depicting the quality and the purposes for which they are

    required.n 3) The ability, capacity, and skill of the bidder to perform the contract or provide the

    services required.

    n 4) The character, integrity, reputation, judgement, experience, and efficiency of the

    bidder.

    n 5) Whether the bidder can perform the contract with the time specified.

    n 6) The quality of performance on previous contracts for purchased goods or services.n 7) The previous and existing compliance by the bidder with the laws relating to the

    contract for goods and services.

    n 8) Servicing resources, capability, and capacity.

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    Competitive Bidding: Low-Bid System

    n In the low-bid system, the owner wants the mostbuilding for the least money, while the contractorwants the least building for the most money. Thetwo sides are in basic conflict.

    Steven Goldblatt

    Department of Building Construction

    University of Washington

    The Seattle Times, Nov 1, 1987

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    Precedence Networks

    Networks represent immediate precedence relationshipsamong tasks (also known as work packages or activities)

    and milestones identified by the WBS

    Milestones (tasks that take no time and cost $0 but indicate

    significant events in the life of the project)Two types of networks: Activity-on-Node (AON)

    Activity-on-Arc (AOA)

    All networks: must have only one (1) starting and one (1)ending point

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    Precedence Networks: Activity-on-Node (AON)

    A

    B

    C

    D

    Start End

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    Precedence Diagramming

    Standard precedence network (either AOA or AON) assumes that a successor

    task cannot start until the predecessor(s) task(s) have been completed.Alternative relationships can be specified in many software packages:

    Finish-to-start (FS = a): Job B cannot start until a days after Job A isfinished

    Start-to-start (SS = a): Job B cannot start until a days after Job A hasstarted

    Finish-to-finish (FF = a): Job B cannot finish until a days after Job Ais finished

    Start-to-finish (SF = a): Job B cannot finish until a days after Job Ahas started

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    Critical Path Method (CPM): Basic Concepts

    Task A

    7 months

    Task B

    3 months

    End

    Task C

    11 months

    Start

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    Critical Path Method (CPM): Basic Concepts

    Start

    Task A

    7 months

    Task B

    3 months

    Task C

    11 months

    End

    ESStart = 0

    LFStart = 0

    ESA = 0

    LFA = 8

    ESB = 7

    LFB = 11

    ESC = 0

    LFC = 11

    ESEnd = 11

    LFEnd = 11

    ESj = Earliest starting time for task (milestone) j

    LFj = Latest finish time for task (milestone) j

    AON P d N t k Mi ft P j t

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    AON Precedence Network: Microsoft Project

    Start

    1 0d

    Wed 12/20/00 Wed 12/20/00

    Ta sk A

    2 7d

    Wed 12/20/00 Thu 12/28/00

    Task C

    4 11d

    Wed 12/20/00 Wed 1/3/01

    End

    5 0d

    Wed 1/3 /0 1 Wed 1/3 /0 1

    Ta sk B

    3 3d

    Fri 12/29 /00 Tue 1 /2 /01

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    Critical Path Method (CPM): Example 2

    TaskA14 wks

    TaskD

    12 wks

    TaskE6 wks

    TaskB9 wks

    TaskC20 wks

    TaskF9 wks

    START END

    ESF=LFF=

    ESD=LFD=

    ES ST ART = 0LFST ART = 0

    ESA=LFA=

    ESB=LFB=

    ESEND=LFEND=

    ESC=LFC=

    ESE=LFE=

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    Example 2: Network Paths

    Path Tasks

    Expected

    Duration (wks)

    1 START-A-D-F-END 35

    2 START-A-D-E-END 323 START-B-D-F-END 30

    4 START-B-D-E-END 27

    5 START-C-E-END 26

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    Example 2: CPM Calculations

    E A R L I E S T L A T E S T

    Task or

    Milestone

    Duration

    ( )

    Start Time

    (ESi) Finish Time Start Time

    Finish Time

    (LFi)

    ST ART 0 0 0 0 0

    A 14 0 14 0 14

    B 9 0 9 5 14C 20 0 20 9 29

    D 12 14 26 14 26

    E 6 26 32 29 35

    F 9 26 35 26 35

    END 0 35 35 35 35

    ti

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    Example 2: Calculating Total Slack (TSi)

    Task or

    Milestone

    Duration

    ( )

    Earliest

    Start Time

    (ESi)

    Lastest

    Finish Time

    (LFi)

    Total Slack

    (TSi)

    Critical

    Task?

    ST ART 0 0 0 0 YesA 14 0 14 0 Yes

    B 9 0 14 5 No

    C 20 0 29 9 No

    D 12 14 26 0 Yes

    E 6 26 35 3 No

    F 9 26 35 0 Yes

    END 0 35 35 0 Yes

    ti

    Total Slack for task i = TSi = LFi - ESi - ti

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    Slack (Float) Definitions (for task i)

    Total Slack (TSi) = LF

    i

    - ESi

    - ti

    Free Slack (FSi) = ESi,min - ESi - ti

    where ESi,min = minimum early start time of all tasks that

    immediately follow task i

    = min (ESj for all task j Si)

    Safety Slack (SSi) = LFi - LFi,max - ti

    where LFi,max = maximum late finish time of all tasks that

    immediately precede task i

    = min (LFj for all task j Pi)

    Independent Slack (ISi) = max (0, ESi,min - LFi,max - ti)

    E l #2 LP M d l

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    Example #2: LP Model

    Decision variables: STARTj = start time for task j

    END = ending time of project (END milestone)

    Minimize END

    subject to

    STARTj FINISHi for all tasks i that immediately precede task j

    STARTj 0 for all tasks j in project

    where FINISHi = STARTi + ti = STARTi + duration of task i

    E l #2 E l S l M d l

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    Example #2: Excel Solver Model

    Gantt Chart

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    Gantt Chart

    Microsoft Project 4.0

    P j t B d ti

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    Project Budgeting The budget is the link between the functional units and the project

    Should be presented in terms of measurable outputs

    Budgeted tasks should relate to work packages in WBS and

    organizational units responsible for their execution

    Should clearly indicate project milestones

    Establishes goals, schedules, and assigns resources (workers,

    organizational units, etc.)

    Should be viewed as a communication device

    Serves as a baseline for progress monitoring & control

    Update on rolling horizon basis

    May be prepared for different levels of aggregation (strategic,

    tactical, short-range)

    P j t B d ti ( td)

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    Project Budgeting (contd)

    Top-down Budgeting: Aggregate measures (cost,

    time) given by top management based on

    strategic goals and constraints

    Bottom-up Budgeting: Specific measures aggregated

    up from WBS tasks/costs and subcontractors

    I i P j t B d t

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    Issues in Project Budgets

    How to include risk and uncertainty factors?

    How to measure the quality of a project budget?

    How often to update budget?

    Other issues?

    C iti l P th M th d (CPM) E l 2

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    Critical Path Method (CPM): Example 2

    TaskA14 wks

    TaskD

    12 wks

    TaskE6 wks

    TaskB9 wks

    TaskC20 wks

    TaskF9 wks

    START END

    ESF= 26LFF= 35

    ESD= 14LFD= 26

    ES ST ART = 0LFST ART = 0

    ESA= 0

    LFA= 14

    ESB= 0LFB= 14

    ESEND= 35LFEND= 35

    ESC= 0LFC= 29

    ESE= 26LFE= 35

    P j t B d t E l

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    Project Budget Example

    Task or

    Milestone

    Duration

    (tj)

    Early Start

    Time (ESj)

    Latest Start

    Time (LSj)

    No. of

    Resource A

    workers

    No. of

    Resource B

    workers

    Material

    Costs

    Direct Labor

    Cost/wk

    Labor +

    Materials

    ST ART 0 0 0 - - - - -

    A 14 0 0 2 0 340$ 800$ 1,140$

    B 9 0 5 4 12 125$ 8,800$ 8,925$

    C 20 0 9 3 14 -$ 9,600$ 9,600$

    D 1214 14 0 8 200$ 4,800$ 5,000$

    E 6 26 29 1 0 560$ 400$ 960$

    F 9 26 26 4 10 90$ 7,600$ 7,690$

    END 0 35 35 - - - - -

    Cost for Resource A worker = $400/week

    Cost for Resource B worker = $600/week

    P j t B d t E l ( td)

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    Project Budget Example (contd)Early Start Times

    Task1 2 3 4 5 6 7 8 9 10 11 12

    A 1140 800 800 800 800 800 800 800 800 800 800 800

    B 8925 8800 8800 8800 8800 8800 8800 8800 8800

    C 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600

    D

    E

    F

    Weekly Subtotals 19665 19200 19200 19200 19200 19200 19200 19200 19200 10400 10400 10400

    Cumulative 19665 38865 58065 77265 96465 115665 134865 154065 173265 183665 194065 204465

    Late Start Times

    Task 1 2 3 4 5 6 7 8 9 10 11 12

    A 1140 800 800 800 800 800 800 800 800 800 800 800

    B 8925 8800 8800 8800 8800 8800 8800 8800

    C 9600 9600 9600 9600

    D

    E

    F

    Weekly Subtotals 1140 800 800 800 9725 9600 9600 9600 19200 19200 19200 19200

    Cumulative 1140 1940 2740 3540 13265 22865 32465 42065 61265 80465 99665 118865

    W e e k

    W e e k

    C l ti C t

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    Cumulative Costs

    Range of

    feasible budgets

    Weekly Costs (Cash Flows)

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    Weekly Costs (Cash Flows)

    M i C h Fl

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    Managing Cash Flows

    Want to manage payments and receipts

    Must deal with budget constraints on

    project and organization requirements (e.g.,

    payback period) Organization profitability

    C h Fl E l

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    Cash Flow Example

    M1

    END

    START

    Task B

    8 mos

    Receive payment

    of $3000

    Receive payment

    of $3000

    Make paymentof $5000

    Task C

    4 mos

    Task A

    2 mos

    M2

    Task D8 mos

    Task E

    3 mos

    C h Fl E l S l M d l

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    Cash Flow Example: Solver Model

    Material Management Issues

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    Material Management Issues

    When to order materials? How much to order?

    Example:

    Single material needed for Task B (2 units) and Task E (30 units)

    Fixed cost to place order = S

    Cost of holding raw materials proportional to number of unit-weeks in

    stock

    Cost of holding finished product greater than the cost of holding raw

    materials

    Project can be delayed (beyond 17 weeks) at cost of $P per week

    Material Management Example

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    Material Management Example

    Task A

    4 wksTask B

    8 wksTask C

    5 wks

    Task D

    6 wksTask E

    2 wksTask F

    3 wks

    EndStart2 units

    30 units

    LSA = 0 LSB = 4 LSC = 12

    LSD = 6 LSE = 12 LSF = 14

    Lot-Sizing Decisions in Projects

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    Lot Sizing Decisions in Projects

    To minimize holding costs, only place orders at Late Starting Times

    Can never reduce holding costs by delaying project

    Time

    1 2 3 4 5 6 7 8 9 10 11 12

    Demand: 2 30

    Order option #1: 32

    Order option #2: 2 30

    Choose the option that minimizes inventory cost = order cost + holding

    cost of raw materials

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    Time-Cost Tradeoffs

    Ti C t T d ff E l

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    Time-Cost Tradeoff Example

    Task

    Normal

    Duration Normal Cost

    Marginal Cost

    to Crash One

    WeekA 7 $60 $8

    B 6 $85 $5

    C 15 $55 $10

    D 10 $120 $4

    A

    B

    C

    D

    Start End

    Ti C t T d ff E l ( td)

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    Time-Cost Tradeoff Example (contd)

    Project

    Duration

    (weeks) Critical Path(s) Task(s) Reduced

    Total Direct

    Cost

    22 Start-A-C-End - $320

    21 Start-A-C-End A $328Start-A-B-End

    20 Start-A-C-End C $338Start-A-B-End

    19 Start-A-C-End C $348Start-A-B-End

    18 Start-A-C-End A, B $361Start-A-B-End

    Linear Time-Cost Tradeoff

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    Linear Time-Cost TradeoffIn theory, the normal or expected duration of a task can be reduced by

    assigning additional resources to the task

    Time

    Cost

    Crash

    Point

    Normal

    Point

    Slope (bj) = Increase in cost by

    reducing task by one time unit

    Normal time =Crash time =

    Normal

    cost =

    Crash

    cost =

    tjNtj

    c

    Cjc

    CjN

    Balancing Overhead & Direct Costs

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    Balancing Overhead & Direct Costs

    Project

    Duration

    Cost

    Indirect

    (overhead)

    Costs

    Direct

    Costs

    Total Cost

    Crash

    Time

    Normal TimeMinimum Cost

    Solution

    Time-Cost Tradeoff (Direct Costs Only)

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    ( y)

    Given Normal point with cost and time

    and Crash point with cost and time

    Assume constant marginal cost of crashing task j =

    Decision Variables: Sj = Starting time of task j

    END = End time of project

    tj = Duration of task j

    Minimize Total Direct Cost =

    Sj Si + ti for all tasks i Pj

    for all tasks in project

    END = Tmax

    tj, Sj 0

    CjN

    Cjc

    tjc

    tjN

    bj =Cj

    c - CjN

    tjc - tj

    N

    bj tjj

    tjc tj tj

    N

    General Time-Cost Tradeoffs

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    where

    I = indirect (overhead) cost/time period

    P = penalty cost/time period if END is delayed beyond

    deadline Tmax

    L = number of time periods project is delayed beyond

    deadline Tmax

    Minimize Total Costs = + I (END) + P Lbj tjj

    QUESTION: HOW TO DEFINE L?

    Software Project Schedules

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    j

    Observe that for the programmer, as for the chef, the urgency ofthe patron may govern the scheduled completion of the task, but itcannot govern the actual completion. An omelet, promised in tenminutes, may appear to be progressing nicely. But when it has notset in ten minutes, the customer has two choices--wait or eat itraw. Software customers have the same choices.

    The cook has another choice; he can turn up the heat. Theresult is often an omelet nothing can save--burned in one part, rawin another.

    F.P. Brooks, The Mythical Man-Month,Datamation, Vol 20, No 12 (Dec, 1974), pp.44-52.

    Coordination Costs (Software Development Project)

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    Coordination Costs (Software Development Project)

    n Assume you want to develop program that will require (approximately) 50,000 lines of

    PERL code

    n A typical programmer can write approximately 1500 lines of code per week

    n Coordination time is M (M-1)/2 weeks

    No. ofProgrammers

    No. of

    WeeksCoding

    No. of

    CoordinationWeeks

    Total

    Number ofWeeks

    1 33.33 0 33.33

    2 16.67 1 17.67

    3 11.11 3 14.11

    4 8.33 6 14.33

    5 6.67 10 16.67

    6 5.56 15 20.56

    7 4.76 21 25.76

    8 4.17 28 32.17

    9 3.70 36 39.7010 3.33 45 48.33

    11 3.03 55 58.03

    Brooks Law

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    Brook s Law

    Adding manpower to a latesoftware project makes it later.

    n F.P. Brooks, The Mythical Man-Month,Datamation, Vol 20, No 12 (Dec, 1974),pp. 44-52.

    Compressing New Product Development

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    p g pProjects

    Traditional Method

    Design follows a sequential pattern where

    information about the new product is slowly

    accumulated in consecutive stages

    Stage 0 Stage 1 Stage N

    New Product Development Process

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    New Product Development Process

    Overlapped Product Design

    Allows downstream design stages to start before

    preceding upstream stages have finalized theirspecifications.

    Stage 0

    Stage 1

    Stage N

    Issues and Tradeoffs

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    Issues and Tradeoffs

    What are the tradeoffs when moving from a

    traditional sequential product design process

    to an overlapped product design process?

    Increased uncertainty (that leads to additional

    work)

    Can add additional resources to tasks to reduce

    duration--but costs are increased

    Classic PERT Model Defined

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    Since task durations are now random variables, time of any

    milestone (e.g., end of project) is now RV

    Assume all tasks are statistically independent

    Use values ofj to identify expected critical path

    Since time of event (e.g., ESk) is now sum of independent RVs,

    central limit theorem specifies that ESk is approximatelynormally distributed with mean E[ESk] and variance Var[ESk]

    where there exists s paths to task k

    Expected early start time of task k = E ESk =max

    sj

    tasks j on path s

    Classic PERT Model (contd)

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    Expect Project Duration = E[E SEND] = jtasks j on CP

    Variance of Project Duration = Var[E SEND] = j2

    tasks j on CP

    Thus, expected project duration is defined as:

    Using central limit theorem and standard normal distribution:

    P ESEND Tmax = P z Tmax - E ESEND

    Var ESEND

    PERT Example #1

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    Duration Estimates Expected

    Task Description Predecessors Optimistic Pessimistic Likely Duration Variance

    A Requi rements Analysis none 2 14 6 6.67 4.00

    B Programming A 4 12 7 7.33 1.78

    C Hardware acquisi tion A 2 13 8 7.83 3.36D User training A 12 18 14 14.33 1.00

    E Implementation B, C 3 7 5 5.00 0.44

    F Testing E 3 7 4 4.33 0.44

    END End of project D, F 0 0 0 0.00 0.00

    StartTask A

    RequirementsAnalysis

    Task CHardware

    Acquisition

    Task BProgramming

    Task FTesting

    Task DUser

    Training

    Task EImplementation

    End

    PERT Example #1 (contd)

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    Expected

    Task Path Early Start Variance Due Date Zi Pr(zi)

    B,C,D Start-A 6.67 4.00 6 -0.33 0.37

    E Start-A-C 14.50 7.36 15 0.18 0.57

    F Start-A-C-E 19.50 7.81 20 0.18 0.57

    End Start-A-C-E-F-End 23.83 8.25 25 0.41 0.66

    PERT Expe cted Dur at i on = 23 .8 3 Ex pected CP = {Star t , A, C , E, F , En d}

    PERT Var ia nce = 8.25 0

    StartTask A

    RequirementsAnalysis

    Task CHardware

    Acquisition

    Task BProgramming

    Task FTesting

    Task DUser

    Training

    Task EImplementation

    End

    PERT Example #2

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    Task B

    B= 12

    B2 = 4

    Task D

    D= 3

    D2 = 1

    Task A

    A= 4

    A2 = 2

    Task C

    C= 10

    C2 = 5

    ENDSTART

    Example #3: Discrete Probabilities

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    Task A Task B Task C Task D

    Value Prob Value Prob Value Prob Value Prob

    7 0.333 2 0.2 5 0.2 3 0.3

    8 0.333 12 0.8 15 0.2 12 0.7

    9 0.333 25 0.6

    START END

    Task A

    (8.0)

    Task B

    (10.0)

    Task C

    (19.0)

    Task D

    (9.3)

    Example #3 (contd)

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    Task A Task B Task C Task D Critical Pr ob of Len gth PATHS

    Combination Value Prob Value Prob Value Prob Value Prob Path CP of CP A,D B, D C

    1 7 0.333 2 0.2 5 0.2 3 0.3 A, D 0.004 10 0.004 0.000 0.000

    2 7 0.333 2 0.2 5 0.2 12 0.7 A, D 0.009 19 0.009 0.000 0.0003 7 0.333 2 0.2 15 0.2 3 0.3 C 0.004 15 0.000 0.000 0.004

    4 7 0.333 2 0.2 15 0.2 12 0.7 A, D 0.009 19 0.009 0.000 0.000

    5 7 0.333 2 0.2 25 0.6 3 0.3 C 0.012 25 0.000 0.000 0.012

    6 7 0.333 2 0.2 25 0.6 12 0.7 C 0.028 25 0.000 0.000 0.028

    7 7 0.333 12 0.8 5 0.2 3 0.3 B, D 0.016 15 0.000 0.016 0.000

    8 7 0.333 12 0.8 5 0.2 12 0.7 B, D 0.037 24 0.000 0.037 0.000

    9 7 0.333 12 0.8 15 0.2 3 0.3 B, D 0.016 15 0.000 0.016 0.000

    10 7 0.333 12 0.8 15 0.2 12 0.7 B, D 0.037 24 0.000 0.037 0.000

    11 7 0.333 12 0.8 25 0.6 3 0.3 C 0.048 25 0.000 0.000 0.048

    12 7 0.333 12 0.8 25 0.6 12 0.7 C 0.112 25 0.000 0.000 0.112

    13 8 0.333 2 0.2 5 0.2 3 0.3 A, D 0.004 11 0.004 0.000 0.000

    14 8 0.333 2 0.2 5 0.2 12 0.7 A, D 0.009 20 0.009 0.000 0.00015 8 0.333 2 0.2 15 0.2 3 0.3 C 0.004 15 0.000 0.000 0.004

    16 8 0.333 2 0.2 15 0.2 12 0.7 A, D 0.009 20 0.009 0.000 0.000

    17 8 0.333 2 0.2 25 0.6 3 0.3 C 0.012 25 0.000 0.000 0.012

    18 8 0.333 2 0.2 25 0.6 12 0.7 C 0.028 25 0.000 0.000 0.028

    19 8 0.333 12 0.8 5 0.2 3 0.3 B, D 0.016 15 0.000 0.016 0.000

    20 8 0.333 12 0.8 5 0.2 12 0.7 B, D 0.037 24 0.000 0.037 0.000

    21 8 0.333 12 0.8 15 0.2 3 0.3 B, D 0.016 15 0.000 0.016 0.000

    22 8 0.333 12 0.8 15 0.2 12 0.7 B, D 0.037 24 0.000 0.037 0.000

    23 8 0.333 12 0.8 25 0.6 3 0.3 C 0.048 25 0.000 0.000 0.048

    24 8 0.333 12 0.8 25 0.6 12 0.7 C 0.112 25 0.000 0.000 0.112

    25 9 0.333 2 0.2 5 0.2 3 0.3 A, D 0.004 12 0.004 0.000 0.000

    26 9 0.333 2 0.2 5 0.2 12 0.7 A, D 0.009 21 0.009 0.000 0.00027 9 0.333 2 0.2 15 0.2 3 0.3 C 0.004 15 0.000 0.000 0.004

    28 9 0.333 2 0.2 15 0.2 12 0.7 A, D 0.009 21 0.009 0.000 0.000

    29 9 0.333 2 0.2 25 0.6 3 0.3 C 0.012 25 0.000 0.000 0.012

    30 9 0.333 2 0.2 25 0.6 12 0.7 C 0.028 25 0.000 0.000 0.028

    31 9 0.333 12 0.8 5 0.2 3 0.3 B, D 0.016 15 0.000 0.016 0.000

    32 9 0.333 12 0.8 5 0.2 12 0.7 B, D 0.037 24 0.000 0.037 0.000

    33 9 0.333 12 0.8 15 0.2 3 0.3 B, D 0.016 15 0.000 0.016 0.000

    34 9 0.333 12 0.8 15 0.2 12 0.7 B, D 0.037 24 0.000 0.037 0.000

    35 9 0.333 12 0.8 25 0.6 3 0.3 C 0.048 25 0.000 0.000 0.048

    36 9 0.333 12 0.8 25 0.6 12 0.7 C 0.112 25 0.000 0.000 0.112

    6.8% 32.0% 61.1%

    Example #3 (contd)

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    Length of Cumulative

    CP's Prob Prob

    10 0.004 0.00

    11 0.004 0.01

    12 0.004 0.01

    15 0.108 0.12

    19 0.019 0.14

    20 0.019 0.16

    21 0.019 0.18

    24 0.224 0.4025 0.599 1.00

    Task A Task B Task C Task D

    6.8% 32.0% 61.1% 38.8%

    Criticality Indices

    Expected Project Duration = 23.22

    Monte-Carlo Simulation (PERT Example 1)

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    Task Duration Early Latest Total Expected

    Task (Uniform Dist) Start Finish Slack Duration Variance

    A 4.99 0 4.99 0.00 6.67 4.00

    B 4.75 4.99 9.74 0.00 7.33 1.78C 3.38 4.99 9.74 1.36 7.83 3.36

    D 12.20 4.99 21.02 3.83 14.33 1.00

    E 5.94 9.74 15.68 0.00 5.00 0.44

    F 5.34 15.68 21.02 0.00 4.33 0.44

    END 0.00 21.02 21.02 0.00 0.00 0.00

    Run Proj ect Duration t(B) t(C) t(D) t(E) t(F)

    1 31.07 1 0 0 1 1

    2 27.41 0 1 0 1 1

    3 23.97 1 0 0 1 1

    4 28.93 0 1 0 1 1

    5 26.85 1 0 0 1 1

    6 28.82 0 0 1 0 0

    7 28.77 0 1 0 1 1

    197 30.37 0 1 0 1 1

    198 29.78 1 0 0 1 1

    199 25.33 1 0 0 1 1200 29.70 0 1 0 1 1

    Ave 27.13 48.5% 42.0% 9.5% 90.5% 90.5%

    Var 16.777

    Project Makespan Lower Limit Upper Limit

    95% Confidence interval 26.56 27.72

    99% Confidence interval 26.37 27.90

    Calculating Confidence Intervals

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    For a confidence interval, we can use the sample meanand the estimated standard error of the mean

    where s is the sample standard deviation and n is the

    number of trials

    Using a normal approximation, a (1- a) two-

    sided confidence interval is given by

    sX =snX

    X -+ za/2 s

    New Product Development Projects

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    START

    Lease

    Mfg/Office

    Space

    Identify/hirestaff

    Design of

    physical unit

    Electronics

    design Software

    Assemble prototype Beta test

    prototype

    END

    Beta test fails (with

    probability of 0.25)

    and rework is needed

    Beta test fails (withprobability of 0.25)

    and rework is needed

    New Product Development Projects (contd)

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    START

    Lease

    Mfg/Office

    Space

    Identify/hire

    staff

    Design of

    physical unit

    Electronics

    design Software

    Assemble prototype Beta test

    prototype

    END

    Beta test fails andrework is needed

    Prob = .25

    Prob = .75

    Critical Chain and the Theory of Constraints (TOC)

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    Use deterministic CPM model with buffers to deal with any

    uncertainties,

    Place project buffer after last task to protect the customers

    completion schedule,

    Exploit constraining resources (make certain that resources are

    fully utilized),

    Avoid wasting time slack time by encouraging early task

    completions,

    Carefully monitor the status of the buffer(s) and communicate

    this status to other project team members on a regular

    basis, and Make certain that the project team is 100 percent focused on

    critical chain tasks

    Project Goal (according to Goldratt): Meet Project Due Date

    Project Buffer Defined

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    Project Buffer is placed at the end of the project to protect the

    customers promised due date

    PERT Example #1 Revisited with Project Buffer

    Start

    Task B

    Programming

    UserTask DUsertraining

    Task E

    Implementation

    EndProject

    Buffer

    Task Arequirements

    analysis

    Task CHardwareacquisition

    Task F

    Testing

    Calculating Project Buffer Size

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    For tasks k on critical chain, we can calculate project buffer

    using following formula that project will be completed

    within worst-case duration estimates around 90 percent of

    the time:

    For those who want a scientific approach to sizingbuffers....

    Buffer = tasks k on cr itic al chain

    tkp - k

    2

    Implications of Project Uncertainty

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    Assume that the duration of both tasks A and B are described by a

    normal distribution with a mean of 30 days

    START END

    Task A

    Task B

    What is the probability that the project will be completed within 30

    days?

    Uncertainty and Worker Behavior

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    Consider a project with two tasks that must be completed serially

    The duration of each task is described by a RV with values Ti (i = 1, 2)

    Values of T1 Prob Values of T2 Prob

    7 0.3 14 0.5

    8 0.4 18 0.5

    9 0.38.0 16

    Start Task 1 Task 2 End

    Parkinsons Law (Expanding Work)

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    Work expands so as to fill the time available for its

    completion

    Professor C.N. Parkinson (1957)

    Set a deadline D = 24 days

    So T(D) = project makespan (function of D) where

    E[T(D)] = E(T1) + E(T2) + E[max(0, D - T1 - T2)]

    Values of T1 Prob Values of T2 Prob

    Project

    Makespan Prob

    7 0.3 14 0.5 24 0.15

    7 0.3 18 0.5 25 0.158 0.4 14 0.5 24 0.2

    8 0.4 18 0.5 26 0.2

    9 0.3 14 0.5 24 0.15

    9 0.3 18 0.5 27 0.15

    E[T(D)] = 25 days

    Procrastinating Worker

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    Set a deadline D = 24 daysE[T(D)] = E(T1) + E(T2) + E{max[0, D - T1 - E(T2)]}

    Can show that E[T(D)] E[T(D)] D

    What are the implications for project managers?

    Values of T1 Prob

    E[De lay] =

    max[0, D - T1 - E(T2)] E[Makespan]

    7 0.3 1 24

    8 0.4 0 24

    9 0.3 0 25

    8 0.3 24.30

    Schoenbergers Hypothesis

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    An increase in the variability of task durations willincrease the expected project duration.

    Schoenbergers Hypothesis Illustrated

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    START END

    Task A

    Task B

    Duration of

    Task A Probability

    Duration of

    Task B Probability

    12 0.1 10 0.5

    14 0.8 15 0.5

    16 0.1

    14.0 12.5

    Schoenbergers Hypothesis Illustrated

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    Realization

    Task A

    Duration

    Task B

    Duration Probability Max (A, B)

    1 12 10 0.05 12

    2 14 10 0.4 14

    3 16 10 0.05 16

    4 12 15 0.05 15

    5 14 15 0.4 15

    6 16 15 0.05 16

    Duration of

    Task A Probability

    Duration of

    Task B Probability

    12 0.3 10 0.5

    14 0.4 15 0.5

    16 0.314.0 12.5

    Increasing the variance of Task A:

    Results in an increased expected duration = 14.65 days

    Expected duration equals 14.55 days

    Risk Management

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    All projects involve some degree of risk

    Need to identify all possible risks and outcomes

    Need to identify person(s) responsible for managing

    project risks

    Identify actions to reduce likelihood that adverse

    events will occur

    Risk Analysis

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    Risk Exposure (RE) or Risk Impact =

    (Probability of unexpected loss) x (size of loss)

    Example: Additional features required by client

    Loss: 3 weeksProbability: 20 percent

    Risk Exposure = (.20) (3 weeks) = .6 week

    How to Manage Project Risks?

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    Preventive Actions

    Actions taken in anticipation of adverse events

    May require action before project actually begins

    Examples?

    Contingency Planning What will you do if an adverse event does occur?

    Trigger point invokes contingency plan

    Frequently requires additional costs

    Risk and Contracts

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    H igh Low Low H igh

    Degree of Risk

    Contractor Client

    Fixed Price Contract Cost Plus Contract

    Firm price

    Elements

    can be

    renegotiated Incentives

    T&M

    with limits

    Cost Plus

    with

    Incentives

    Time &

    materials

    Tornado Diagram

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    Wage Rate

    Direct Labor Hours

    Material Units Needed

    Early Completion Bonus

    Material Unit Cost

    Interest rates

    Energy costs

    Overhead

    Project Cost ($000's)

    $1290

    $1265

    $1260

    $1310

    $1350

    $1350

    $1380

    $1400

    $1700

    $1720

    $1680

    $1690

    $1640

    $1620

    $1625

    $1760

    $1500 $1600 $1800$1700$1400$1300$1200

    Sensitivity Chart

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    Wage Rate 0.85

    Direct Labor Hours 0.73

    Material Units Needed 0.62

    Early Completion Bonus -0.45

    Material Un it Cos t 0.42

    Inter es t rates 0.28

    Energy cos ts 0.19

    Overhead 0.10

    0 0.5 1.0-0.5

    Rank Order Correlation with Total Project Cost

    Van Allen Company

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    Strike Expected

    (wks) Prob Duration

    3 0.45 1.354 0.3 1.20

    5 0.25 1.25

    E[Strike Duration] 3.80

    Resource Allocation & Leveling

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    Resource Leveling: Reschedule the noncriticaltasks to smooth resource requirements

    Resource Allocation: Minimize project

    duration to meet resource availability constraints

    Resource Allocation & Leveling

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    Three types of resources:1) Renewable resources: renew themselves

    at the beginning of each time period (e.g.,

    workers)

    2) Non-Renewable resources: can be used at

    any rate but constraint on total number

    available

    3) Doubly constrained resources: bothrenewable and non-renewable

    Resource Leveling

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    Task B

    2 wks

    Task E

    3 wks

    Task C

    9 wks

    Task D

    5 wks

    Task F

    2 wks

    Task A

    3 wks

    START Task G

    5 wksEND

    Task Workers Duration ( tj) Early Start Late Start

    A 7 3 0 0

    B 3 2 0 3C 2 9 3 4

    D 10 5 3 3

    E 4 3 2 5

    F 5 2 2 11

    G 6 5 8 8

    Resource Leveling: Early Start Schedule

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    Resource Leveling: Late Start Schedule

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    Resource Leveling: Microsoft Project

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    5

    10

    15

    20

    25

    Workers Ov era ll ocat ed: Al loca te d:

    T W T F S S M T W T F S S M T W T F S S M T W T F S

    Dec 17, '00 Dec 24, '00 Dec 31, '00 Jan 7, '01

    10 10 10 10 10 10 10 10 10 10 16 16 16 16 16 21 21 21

    Renewable Resource Allocation Example(Single Resource Type)

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    TaskB3 wks

    TaskD5 wks

    TaskA4 wks

    TaskE

    4 wks

    START

    END

    TaskC1 wk

    3 workers

    5 workers

    6 workers

    8 workers

    7 workers

    Maximum number of workers available = R = 9 workers

    Resource Allocation Example: Early Start Schedule

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    Maximum number of workers available = R = 9 workers

    Start

    End

    Week 1 2 3 4 5 6 7 8 9 10 11 12

    No. of Worke rs/wk 8 8 8 11 14 8 8 8 7 7 7 7

    Cumulative Workers 8 16 24 35 49 57 65 73 80 87 94 101

    "Waste d" worker-wks 1 1 1 - - - - - - - - -

    Task B:

    5 workers

    Task A:

    3 workers

    Task C:

    6 workers

    Task E:

    7 workersTask D:

    8 workers

    Resource Allocation Example: Late Start Schedule

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    Maximum number of workers available = R = 9 workers

    Start

    End

    Week 1 2 3 4 5 6 7 8 9 10 11 12

    No. of Workers/wk 5 5 5 11 11 11 11 14 7 7 7 7

    Cumulative Workers 5 10 15 26 37 48 59 73 80 87 94 101

    "Waste d" worker-wks - - - - - - - - 2 2 2 2

    Task B:

    5 workers

    Task A:

    3 workers

    Task C:

    6 workers

    Task E:

    7 workersTask D:

    8 workers

    Resource Allocation HeuristicsRk

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    n Some heuristics for assigning priorities to available tasks j, where denotes the

    number of units of resource k used by task j

    n 1) FCFS: Choose first available task

    n 2) GRU: (Greatest) resource utilization =

    n 3) GRD: (Greatest) resource utilization x task duration =

    n 4) ROT: (Greatest) resource utilization/task duration =

    n 5) MTS: (Greatest) number of total successors

    n 6) SPT: Shortest processing time = min {tj}

    n 7) MINSLK: Minimum (total) slack

    n 8) LFS: Minimum (total) slack per successor

    n 9) ACTIMj: (Greatest) time from start of task j to end of project = CP - LSj

    n 10) ACTRESj: (max) (ACTIMj)

    n 11) GENRESj: w ACTIMj + (1-w) ACTRESj where 0 w 1

    Rjk

    Rjk

    k

    Rjk/ tj

    k

    Rjk

    k

    tj

    Resource Allocation Problem #2

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    Task A1

    6 da sTask A2

    4 da s

    EndStartTask B1

    3 da s

    Task C1

    2 da s

    Task B2

    5 da s

    Task C2

    5 da s

    Purple CrewGold Crew

    How to schedule tasks to minimize project makespan?

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    Priority scheme: schedule tasks using total slack (i.e., tasks with

    smaller total slack have higher priority)

    Task A1 Task B1 Task C1

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

    Task A2 Task B2 Task C2

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

    Gold Crew

    Purple

    Resource Allocation Example (contd)

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    But, can we do better? Is there a better priority scheme?

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

    Gold Crew

    Purple

    Microsoft Project Solution (Resource Leveling Option)

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    Soluti on by: M icrosoft Project 2000

    Critical Chain Project Management

    Id if h i i l h i f k h d i h ll

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    Identify the critical chain: set of tasks that determine the overall

    duration of the project

    Use deterministic CPM model with buffers to deal with uncertainty

    Remove padding from activity estimates (otherwise, slack will be

    wasted). Estimate task durations at median.

    Place project buffer after last task to protect customers completion

    schedule

    Exploit constraining resource(s)

    Avoid wasting slack times by encouraging early task completions

    Have project team focus 100% effort on critical tasks Work to your plan and avoid tampering

    Carefully monitor and communicate buffer status

    Critical Chain Buffers

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    Project Buffer: placed after last task in project to protect schedule

    Feeding Buffers: placed between a noncritical task and a critical taskwhen the noncritical task is an immediate predecessor of the critical task

    Resource Buffers: placed just before a critical task that uses a new

    resource type

    Critical Chain Illustrated

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    Task A1

    6 da s

    Task A2

    4 da s

    EndStart

    Task B1

    3 da s

    Task C1

    2 da s

    Task B2

    5 da s

    Task C2

    5 da s

    Resource Buffers

    Feeding Buffers

    Non-Renewable Resources

    12 units

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    Task B5 wks

    Task D2 wks

    Task C3 wks

    Task A6 wksST ART END

    6 units

    10 units

    8 units

    Task Duration

    No. of Nonrene wable

    Resource s Units

    Needed Early Start Late Start

    A 6 6 0 0

    B 5 12 6 6

    C 3 10 6 8

    D 2 8 11 11

    Non-Renewable Resources: Graphical Solution

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    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

    40

    36

    32

    28

    24

    20

    16

    12

    8

    4

    Cumulative ResourcesSupplied

    CumulativeResources

    Cumulative Resources

    Required

    Resource Allocation Problem #3

    Issue: When is it better to team two or more

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    Issue: When is it better to team two or more

    workers versus letting them work separately?

    Have 2 workers, Bob and Barb, and 4 tasks: A, B, C, D

    Bob and Barb can work as a team, or they can work separately

    When should workers be assigned to tasks? Which configurationdo you prefer?

    How to Assign Project Teams?

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    Configuration #1

    Bob and Barb work jointly on all four tasks; assume that they can complete each

    task in one-half the time needed if either did the tasks individually

    A C

    B D

    Start End

    Configuration #2Bob and Barb work independently. Bob is assigned to tasks A and C; Barb is

    assigned to tasks B and D

    Bob and Barb: Configuration #1

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    TASK A TASK B TASK C TASK D

    Duration Prob Duration Prob Duration Prob Duration Prob

    6 0.33 9 0.667 12 0.6 10 0.255 0.33 6 0.333 7 0.4 6 0.75

    4 0.33

    Expected

    duration 5.0 8.0 10.0 7.0

    Configuration #1

    Bob and Barb work jointly on all four tasks.

    What is the expected project makespan?

    Bob and Barb: Configuration #2

    Bob and Barb work independently. Bob is assigned to tasks A and C; Barb is

    assigned to tasks B and D

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    assigned to tasks B and D

    Realization # A B C D

    Bob

    A + C

    Barb

    B + D

    max

    (A+C,

    B+D) Prob

    1 6 9 12 10 18 19 19 0.03

    2 6 9 12 6 18 15 18 0.10

    3 6 9 7 10 13 19 19 0.02

    4 6 9 7 6 13 15 15 0.07

    5 6 6 12 10 18 16 18 0.02

    6 6 6 12 6 18 12 18 0.05

    7 6 6 7 10 13 16 16 0.01

    8 6 6 7 6 13 12 13 0.039 5 9 12 10 17 19 19 0.03

    10 5 9 12 6 17 15 17 0.10

    11 5 9 7 10 12 19 19 0.02

    12 5 9 7 6 12 15 15 0.07

    13 5 6 12 10 17 16 17 0.02

    14 5 6 12 6 17 12 17 0.05

    15 5 6 7 10 12 16 16 0.01

    16 5 6 7 6 12 12 12 0.03

    17 4 9 12 10 16 19 19 0.03

    18 4 9 12 6 16 15 16 0.10

    19 4 9 7 10 11 19 19 0.02

    20 4 9 7 6 11 15 15 0.07

    21 4 6 12 10 16 16 16 0.02

    22 4 6 12 6 16 12 16 0.05

    23 4 6 7 10 11 16 16 0.01

    24 4 6 7 6 11 12 12 0.03

    Bob and Barb: Configuration #2

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    Bob and Barb work independently. Bob is assigned to tasks A and C; Barb is

    assigned to tasks B and D

    max (A+C,

    B+D) Prob

    Cumulative

    Prob

    12 0.07 0.07

    13 0.03 0.10

    15 0.20 0.30

    16 0.20 0.5017 0.17 0.67

    18 0.17 0.83

    19 0.17 1.00

    Expected Project Makespan: 16.42

    Parallel Tasks with Random Durations

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    STARTEND

    Task B

    Task A

    Assume that both Tasks A and B have possible durations:

    8 days with probability = 0.5

    10 days with probability = 0.5

    What is expected duration of project? (Is it 9 days?)

    Project Monitoring and Control

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    n It is of the highest importance inthe art of detection to be able to

    recognize, out of a number of acts,

    which are incidental and which are

    vital. Otherwise your energy and

    attention must be dissipated instead

    of being concentrated.

    Sherlock Holmes

    Status Reporting?

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    One day my Boss asked me to submit a statusreport to him concerning a project I was working

    on. I asked him if tomorrow would be soon enough.

    He said, "If I wanted it tomorrow, I would have

    waited until tomorrow to ask for it!"

    New business manager, Hallmark Greeting Cards

    Control System Issues

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    n What are appropriate performance metrics?

    n What data should be used to estimate the value of each

    performance metric?

    n

    How should data be collected? From which sources? Atwhat frequency?

    n How should data be analyzed to detect current and future

    deviations?

    n How should results of the analysis be reported? To whom?

    How often?

    Controlling Project Risks

    K i t t l i k d i j t

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    Key issues to control risk during projecct:

    (1) what is optimal review frequency, and

    (2) what are appropriate review acceptance levels

    at each stage?

    Both over-managed and under-managed

    development processes result in lengthy design

    lead time and high development costs.

    Ahmadi & Wang. Managing Development Risk in

    Product Design Processes, 1999

    Project Control & System Variation

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    Common cause variation: in-control or normal

    variation

    Special cause variation: variation caused by forces

    that are outside of the system

    According to Deming:

    Treating common cause variation as if it were special cause variation

    is called tampering

    Tampering always degrades the performance of a system

    Control System Example #1

    Project plan: We estimate that a task

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    n Project plan: We estimate that a task

    will take 4 weeks and require

    n 1600 worker-hours

    At the end of Week 1, 420 worker-hours

    have been used

    Is the task out of control?

    Control System Example (contd)

    Week 2: Task expenses = 460 worker-hours

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    Week 2: Task expenses 460 worker hours

    Is the task out of control?

    370380

    390

    400

    410

    420

    430

    440

    450

    460

    470

    1 2 3 4

    Week

    Week

    Planned Cost

    (BCWS) Actual Cost

    CumulativeActual Cost

    (ACWP)

    1 400 420 420

    2 400 460 880

    Control System Example (contd)

    Week 3: Task expenses = 500 worker-hrs

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    Is the task out of control?

    Week

    Planned cost

    (worker-hours)

    Actual cost

    (worker-hours)

    Cumulative cost

    (worker-hours)

    1 400 420 420

    2 400 460 880

    3 400 500 1380

    0

    100

    200

    300

    400

    500

    600

    1 2 3 4

    Week

    Earned Value Analysis

    I t t t h d l d k f d

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    Integrates cost, schedule, and work performed

    Based on three metrics that are used as the basic

    building blocks:

    BCWS: Budgeted cost of work scheduled

    ACWP: Actual cost of work performed

    BCWP: Budgeted cost of work performed

    Schedule Variance (SV)

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    Schedule Variance (SV) = difference between value of

    work completedand value of scheduled work

    Schedule Variance (SV) = Earned Value - Planned Value

    = BCWP - BCWS

    Cost Variance (CV)

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    Cost Variance (CV) = difference between value ofwork completedand actual

    expenditures

    Cost Variance (CV) = Earned Value - Actual Cost

    = BCWP - ACWP

    Earned Values Metrics Illustrated

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    Worker-Hours

    Week 1 Week 2 Week 3 Week 4 Week 5 Week 6

    Present timeBAC

    Actual Cost(ACWP)

    Earned Value

    (BCWP)

    Planned Value

    (BCWS)

    Schedule Variance

    (SV)

    Cost Variance

    (CV)

    Relative Measure: Schedule Index

    C

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    Schedule Index (SI)=

    BCWP

    BCWS

    If SI = 1, then task is on schedule

    If SI > 1, then task is ahead of schedule

    If SI < 1, then task is behind schedule

    Relative Measure: Cost Index

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    Cost Index (CI)= BCWPACWP

    If CI = 1, then work completed equals

    payments (actual expenditures)

    If CI > 1, then work completed is ahead

    of payments

    If CI < 1, then work completed is behindpayments (cost overrun)

    Example #2

    W E E K1 2 3 4 5 6 7 8 9 10

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    1 2 3 4 5 6 7 8 9 10

    6 6 6 8 10

    12 12 12

    10 10 12 12 12

    Scheduled

    Worker-Hrs 6 6 6 20 22 22 10 12 12 12

    Scheduled

    Worker-Hrs

    (BCWS) 6 12 18 38 60 82 92 104 116 128

    Task A (36 worke r-hrs)

    Task B (36 worker-hrs)

    Task C (56 worker-hr

    Example #2 (contd)

    Progress report at the end of week #5:

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    Week 1 2 3 4 5

    Task A 15% 30% 40% 60% 80%

    Task B 25% 65%

    Task C Not started yet

    Cumulative Percent of Work Completed:

    Worker-Hours Charged to Project:

    Week 1 2 3 4 5

    Task A 5 6 8 10 10

    Task B 15 10

    Task C Not started yet

    Example #2 (contd)

    Progress report at the end of week #5:

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    W E E K1 2 3 4 5 6 7 8 9 10

    Cumulative

    Scheduled

    Worker-Hrs

    (BCWS) 6 12 18 38 60 82 92 104 116 128Actual Worker-

    Hrs Used

    (ACWP) 5 11 19 44 64

    Earned Value

    (BCWP) 5.4 10.8 14.4 30.6 52.2

    Schedule

    Variance (SV) -0.6 -1.2 -3.6 -7.4 -7.8

    Cost Variance

    (CV) 0.4 -0.2 -4.6 -13.4 -11.8

    Example #2 (contd)

    140

    BAC

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    0

    20

    40

    60

    80

    100

    120

    1 2 3 4 5 6 7 8 9 10

    Week

    ACWP

    BCWP

    BCWS

    Schedule

    Variance

    Cost

    Variance

    Using a Fixed 20/80 Rule

    Cumulative Percent of Work Completed:

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    W E E K1 2 3 4 5 6 7 8 9 10

    Cumulative

    Scheduled

    Worker-Hrs

    (BCWS) 6 12 18 38 60 82 92 104 116 128Actual Worker-

    Hrs Used

    (ACWP) 5 11 19 44 64

    Earned Value(BCWP) 7.2 7.2 7.2 14.4 14.4Schedule

    Variance ( SV) 1.2 -4.8 -10.8 -23.6 -45.6Cost Variance

    (CV) 2.2 -3.8 -11.8 -29.6 -49.6

    Week 1 2 3 4 5Task A 20% 20% 20% 20% 20%

    Task B 20% 20%

    Task C Not s tar ted yet

    Using a Fixed 20/80 Rule

    140

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    0

    20

    40

    60

    80

    100

    120

    140

    1 2 3 4