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    Dec is ion Making

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    Overview

    Break-Even Analysis

    Preference Matrices

    Payoff Tables (Decision Tables)

    Decision Trees

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    Break-Even Analys is

    Break-even analysisis used to compare processesby finding the volume at which two differentprocesses have equal total costs.

    Break-even pointis the volume at which totalrevenues equal total costs.

    Variable costs (c)are costs that vary directly withthe volume of output. (EG: material costs, labor, etc.)

    Fixed costs (F)are those costs that remain constantwith changes in output level. (EG: Insurance, rent,property taxes, etc.)

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    Break-Even Analys is

    Gives you a comparison of Revenues andTotal Costs over a range of operations/output.

    Assumes all changes are linear

    Fixed Costs(F) are assumed to be level andconstant as output changes.

    Variable Costs(c) are assumed to change linearlywith output.

    Revenuesare assumed to change linearly withoutput.

    In reality, no changes are linear, but thetechnique can still be helpful.

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    Break-Even Graph

    Dollars

    Volume of Output (Q)

    Fixed Costs

    Total Costs

    Total Revenues

    Break-Even Point

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    Break-Even Analys is

    in the real world .

    Fixed costsincrease incrementally as outputcapacity increases.

    As capacity increases, periodic expansion of plantand equipment is required, insurance cost andtaxes increase

    Variable Costincrease is curvilinear asoutput production increases.

    As you purchase greater quantities of materials,you usually get quantity discounts.

    Revenueincrease is curvilinear as outputincreases. Quantity discounts are given to larger sales.

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    The Compl icat ions o f

    Non-l ineari ty

    Dollars

    Volume of Output (Q)

    Fixed Costs

    Variable Costs

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    Qis the volume in units

    cis the variable cost per unit

    Fis the total fixed costs

    pis the revenue per unit

    cQis the total variable cost.(Variable cost per unit x Volume)

    Total cost = F+ cQ (Fixed costs + total Variable costs) Total revenue = pQ (Revenue per unit x Volume)

    Break even is where Total Revenue = Totalcosts: pQ = F+ cQ

    Break-Even Analys is(You dont need the formula for exams.)

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    Break-Even Analys is

    can tell you

    ...if a forecast sales volume is sufficient to make

    a profit, or at least cover your costs.

    ...how low your variable cost per unit must be tobreak even, given current product price and

    sales-volume forecast.

    ...what the fixed cost need to be to break even.

    ...how price levels affect the break-even volume.

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    Hosp ital Example

    A hospital is considering a new procedure to be offered,billed at $200 per patient. The fixed cost (F) per year is

    $100,000, with variable costs at $100 per patient.

    How many patients do they need to cover their costs?(I.E. what is the break-even level for this service?)

    Q= F/ (p- c) = 100,000/ (200-100) = 1,000 patien ts

    Where Q= total # of patients; F= fixed costs; p= revenue per unit;

    c= variable costs per patient

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    Using Excel Solver

    Select the Break-Even solver model on the L-Drive(under my name)

    Select MGT 360

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    Using Excel Solver cont.

    Select Excel Solver Models

    Select the Break-Even

    Analysis model.

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    Enabling the Macros

    Mac

    PC

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    Running The Model

    You will get this screen whether you enable themacros or not, but your answer wont be correct if

    you dont enable them.

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    Total Costs

    Total Revenue

    Using the Excel Solver,enter the data requestedin the yellow blocks, andthe answer will appear inthe green block, alongwith the chart.

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    Patients (Q)

    Dollars

    | | | |

    500 1000 1500 2000

    Quantity Total Annual Total Annual

    (patients) Cost ($) Revenue ($)

    (Q) (100,000 + 100Q) (200Q)

    0 100,000 02000 300,000 400,000

    Hosp i tal Examp le(solved using graphical method)

    40,000

    30,000

    20,000

    10,000

    0

    Q tit T t l A l T t l A l

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    40,000

    30,000

    20,000

    10,000

    0

    Patients (Q)

    DOLLARS

    | | | |

    500 1000 1500 2000

    (2000, 40,000)

    Total annual revenues

    Quantity Total Annual Total Annual

    (patients) Cost ($) Revenue ($)

    (Q) (100,000 + 100Q) (200Q)

    0 100,000 02000 300,000 400,000

    Q tit T t l A l T t l A l

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    Quantity Total Annual Total Annual

    (patients) Cost ($) Revenue ($)

    (Q) (100,000 + 100Q) (200Q)

    0 100,000 02000 300,000

    400,000

    Total annual costs

    Patients (Q)

    DOLLARS

    | | | |

    500 1000 1500 2000

    Fixed costs

    (2000, 40,000)

    (2000, 30,000)Total annual revenues

    40,000

    30,000

    20,000

    10,000

    0

    Q tit T t l A l T t l A l

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    Total annual revenues

    Total annual costs

    Patients (Q)

    | | | |

    500 1000 1500 2000

    Fixed costs

    Break-even quantity is 1000 patients

    (2000, 40,000)

    (2000, 30,000)

    Profits

    Loss

    Quantity Total Annual Total Annual

    (patients) Cost ($) Revenue ($)

    (Q) (100,000 + 100Q) (200Q)

    0 100,000 02000 300,000 400,000

    DOLLARS

    40,000

    30,000

    20,000

    10,000

    0

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    40,000

    30,000

    20,000

    10,000

    0

    Total annual revenues

    Total annual costs

    Patients (Q)

    | | | |

    500 1000 1500 2000

    Fixed costs

    Profits

    Loss

    Sens i tiv i ty Analys is

    Forecast (Q) = 1,500

    pQ(F+ cQ)

    200(1500)[100,000 + 100(1500)]

    = $5,000 profit

    Per-patient cost of theprocedure.

    DOLLARS

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    Two Processes and

    Make-o r-Buy Dec is ions

    Breakeven analysis can be used to choosebetween two different processes

    Also can be used to decide between using an

    internal process or outsourcing that processservice.

    The solution finds the point at which the totalcosts of each of the two processes are equal.

    A forecast of sales (volume level) is thenapplied to see which alternative (process)has the lowest cost for that volume.

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    Two-Process Example

    Process #1 fixed costs for makingwidgets is $12,000, and the variablecost is $1.50 per unit.

    Process #2 fixed costs for makingwidgets is $2400 and the variable costis $2.00 per unit.

    If expected demand is 25,000 widgets,which process is less expensive?

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    Breakeven for

    Two Processes

    For any volume above 19,200units, Process #1 should beused.

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    Q=FmFb

    cbcm

    Q=12,0002,400

    2.01.5

    Breakeven for

    Two Processes

    Q = 19,200

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    An analysis that allows you to rate alternatives byquantifying tangible and/or intangible criteria.

    Criteria are ranked and weighted for eachalternative being evaluated.

    Each score is weighted according to its perceivedimportance to you, with the total weights typicallyequaling 100.

    Thus it measures your preference.

    Alternative with highest sum of the weightedscores is the one you most prefer.

    Preference Matr ix

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    Using the

    Preference Matrix(A hyp othet ical example)

    Problem: Where to go to dinner.

    Possible Criteria:

    Price

    Quality

    Distance

    Atmosphere

    Type of food

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    Weigh t ing the Cri ter ia

    Criteria

    Price

    QualityDistance

    Atmosphere

    Type of food

    Weight

    4

    13

    1

    1

    These are the criteria I selected, and the weights are howimportant each criteria is relative to the other criteria.

    I used a scale of 1-10 (1 being 10% of the weight), but anyscale can be used.

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    Evaluat ingMcDonalds

    Criteria Weight(w)

    Eval.(e)

    Score(w)(e)

    Price 4 10 40

    Quality 1 2 2

    Distance 3 8 24

    Atmosphere 1 2 2

    Type of food 1 5 5

    73

    For simplicity, the valuation scale should be the same as the one for theweights. Evaluations are subjective, and can be individual preference orgroup-consensus.

    The score of 73 is used to compare with the scores from other options.

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    Performance Weights Scores Weighted Scores

    Criterion (A ) (B) (A x B)Market potentialUnit profit marginOperations compatibilityCompetitive advantage

    Investment requirementProject risk

    Thresho ld sco re = 800

    Preference Matr ix(New product evaluation)

    Management decides that a productevaluation must have a total score of atleast 800 to be acceptable.

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    Thresho ld score = 800

    Preference Matr ixEstablishing the criteria weights

    Performance Weights Scores Weighted ScoresCriterion (A ) (B) (A x B)

    Market potential 30

    Unit profit margin 20

    Operations compatibility 20

    Competitive advantage 15

    Investment requirement 10

    Project risk 5

    In this example,the most weight

    is given to aproducts marketpotential.

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    Thresho ld sco re = 800

    Preference Matr ixRating a produ ct

    Performance Weight Score Weighted ScoreCriterion (A ) (B) (A x B)

    Market potential 30 8

    Unit profit margin 20 10

    Operations compatibility 20 6

    Competitive advantage 15 10

    Investment requirement 10 2

    Project risk 5 4

    These are the ratings for one ofthe products being considered.

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    Thresho ld score = 800

    Preference Matr ix

    Performance Weight Score Weighted ScoreCriterion (A ) (B) (A x B)

    Total weighted score = 750

    Market potential 30 8 240

    Unit profit margin 20 10 200

    Operations compatibility 20 6 120

    Competitive advantage 15 10 150

    Investment requirement 10 2 20

    Project risk 5 4 20

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    Thresho ld score = 800

    Preference Matr ix

    Performance Weight Score Weighted ScoreCriterion (A ) (B) (A x B)

    Weighted score = 750

    Score does no t meet the

    threshold and is rejected.

    Market potential 30 8 240

    Unit profit margin 20 10 200

    Operations compatibility 20 6 120

    Competitive advantage 15 10 150

    Investment requirement 10 2 20

    Project risk 5 4 20

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    Decision-Making

    Terminology

    Alternatives

    Possible solutions or alternatives to a problem.

    States of Nature(Chance Events) Events effecting the outcome, but which thedecision-maker cannot control.

    EG: What the stock market is going to do.

    Payoffs Profits, losses, costs, etc. that result from

    implementing an alternative.

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    Decis ion-Making

    Contexts Certainty

    Only one state of nature can occur.

    You have complete knowledge about the outcome.

    (Break-even analysis is decision making under certainty.)

    Risk Two or more states of nature

    You know the probabilities of their occurrence

    (Expected-value analysis is decision making under risk.)

    Uncertainty The number of states of nature may be unknown.

    Probabilities of occurrence are unknown.

    (Payoff tables are a good example.)

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    A Cont inuum of

    Awareness

    Decreasing Knowledge about the problem situation

    Certainty Risk Uncertainty

    Only 1 state

    of nature

    More than one

    state of naturewith knownprobabilities

    States of nature

    may be unknown,or a least theirprobabilities areunknown.

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    Payo ff Tab les

    Under Uncertainty

    Bear

    Market

    Level

    Market

    Bull

    Market

    Stock A 400 500 600

    Stock B 200 400 1100

    Stock C 100 500 900

    With uncertainty, you dont know the probabilities for the states of nature.

    States of Nature

    Alternatives

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    Payo ff Tab les

    Under Uncertainty

    Maximax

    The optimists approach Maximin

    The pessimists approach

    Minimax Regret Another pessimistic approach

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    MaximaxApproachPick the best of the best payoffs

    BearMarket

    LevelMarket

    BullMarket

    Stock A 400 500 600

    Stock B 200 400 1100

    Stock C 100 500 900

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    MaximinApproachPick the Best of the Worst payoffs

    BearMarket

    LevelMarket

    BullMarket

    Stock A 400 500 600

    Stock B 200 400 1100

    Stock C 100 500 900

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    Minimax RegretApproachMinimizes the regret you would have from making the wrong choice.

    BearMarket

    LevelMarket

    BullMarket

    Stock A 400 500 600

    Stock B 200 400 1100

    Stock C100 500 900

    Determine the maximum regret, if any, you could have for each payoff.

    0 0

    0

    0

    500

    200 100

    300 200

    R t M t i

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    Regret MatrixCompute total regrets for each alternative

    and select the one with the smallest total regret.

    BearMarket

    LevelMarket

    BullMarket

    Stock A 0 0 500

    Stock B 200 100 0

    Stock C 300 0 200

    500

    300

    500

    Add across each row to get the total regret for each alternative.Pick the alternative that has the LEASTregret.

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    Expected Value Analys isDecision Making Under Risk!

    BearMarket

    LevelMarket

    BullMarket

    Probabilities .2 .6 .2

    Stock A 400 500 600

    Stock B 200 400 1100

    Stock C 100 500 900

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    Expected Value Analys isComputing Expected Values

    Bear

    Market

    Level

    Market

    Bull

    Market

    EV

    Probabilities .2 .6 .2

    Stock A 400x.2 500x.6 600x.2

    =80 =300 =120 500

    Stock B 200x.2 400x.6 1100x.2

    =40 =240 =220 500

    Stock C 100x.2 500x.6 900x.2

    =20 =300 =180 500

    E t d V l A l i

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    Expected Value Analysisusing the Excel Solver

    Why does the solver model pick stock A?(All three have the same expected value!)

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    Probabi l i ty Distr ibut ions

    as a measu re of r isk.

    Probabilities

    Expected Payoffs100 200 300 400 500 600 700 800 900 1000 1100

    .1

    .2

    .3

    .4

    .5

    .6

    C

    BA

    Probabilitydistributions for

    the alternatives

    C CB

    B

    BAA

    C A

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    Standard Deviat ion

    as a measu re of r isk

    Alternative

    Stock A

    Stock B

    Stock C

    Standard Deviation

    63.25

    316.93

    252.98

    The lower the standard deviation,the less likely it is that payoffs will deviate from the mean.

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    Coeff ic ien t o f Variat ion

    Standard Deviationonly works as a measureof risk when the expected values you obtain

    are relatively similar.

    Coefficient of Variationmust be used tomeasure risk when the expected values arewidely different.

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    Using Coeff ic ient of Variat ion

    Std. Dev.Expected

    Value

    Coeff. Of

    Variation

    Stock A 63.25 500 0.1265

    Stock B 316.93 500 0.63386

    Stock C 252.98 500 0.50596

    Coefficient of Variation =

    Standard Deviation

    Expected Value

    Since the expected values are the same in this example, there is no need to use Coefficient of Variation.

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    Using Coeffic ien t o f Variat ion

    ExpectedValue

    R.O.IStandardDeviation

    Coefficientof Variation

    X 100 15% 23.5 .235

    Y 100,000 15% 12,600 .126

    Smaller coefficient of variation indicates less risk!

    In this example the Expected Values of the alternatives are widely different, so we need to

    use Coefficient of Variation to make our comparison.

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    Alternatives Low High

    Small facility 200 270Large facility 160 800Do nothing 0 0

    Events(Uncertain Demand)

    MaxiMin Decis ion(another examp le)

    1. Look at the payoffs for each alternative and identify thelowest payoff for each.

    2. Choose the alternative that has the highest of these.(the maximum of the minimums)

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    Events(Uncertain Demand)

    MaxiMaxDecis ion

    1. Look at the payoffs for each alternative and identify thehighest payoff for each.

    2. Choose the alternative that has the highest of these.(the maximum of the maximums)

    Alternatives Low High

    Small facility 200 270Large facility 160 800Do nothing 0 0

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    MiniMax Regret

    Events(Uncertain Demand)

    Look at eachpayoff and ask yourself, If I end up here, doI have any regrets?

    Your regret, if any, is the difference between that payoffand the best choice you could have made with a differentalternative, given the same state of nature (event).

    Alternatives Low High

    Small facility 200 270Large facility 160 800Do nothing 0 0

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    MiniMax Regret

    Events(Uncertain Demand)

    If you chose a small

    facility and demand islow, you have zeroregret. You could nothave done better witha different alternative.

    If you chose a large facility and

    demand is low, you regret you didntbuild a small facility. Your regret is40, which is the difference betweenthe 160 you got and the 200 youcould have gotten.

    Alternatives Low High

    Small facility 200 270Large facility 160 800Do nothing 0 0

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    MiniMax Regret

    Events(Uncertain Demand)

    Alternatives Low High

    Small facility 0 530Large facility 40 0Do nothing 200 800

    EventsTotalRegrets530401000

    Regret MatrixBuilding a large

    facility offers the

    least regret.

    Alternatives Low High

    Small facility 200 270Large facility 160 800Do nothing 0 0

    If you chose a smallfacility and demand ishigh, you forgo thehigher payoff of 800,and thus have a

    regret of 530.

    Expec ted Value

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    Expec ted ValueDecision Making under Risk

    Events

    200*0.4+ 270*0.6= 242

    160*0.4+ 800*0.6= 544

    Multiply each payoff times the probability ofoccurrence its associated event.

    Select the alternative with the highest weighted payoff.

    Alternatives Low High(0.4) (0.6)

    Small facility 200 270Large facility 160 800

    Do nothing 0 0

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    Decis ion Trees are schematic modelsof alternatives available along with their

    possible consequences. They are used in sequential decisionsituations.

    Decision points are represented bysquares.

    Event points (states of nature) arerepresented by circles.

    Dec ision Trees

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    = Event node

    = Decision node

    1stdecision

    Possible2nd decision

    Payoff 1

    Payoff 2

    Payoff 3

    Alternative 3

    Alternative 4

    Alternative 5

    Payoff 1

    Payoff 2

    Payoff 3

    E1& Probabi l i ty

    E2& Probabi l i ty

    E3& Prob abi l ity

    E2& Probabi l i ty

    E3& Probabi l i ty

    Payoff 1

    Payoff 2

    1 2

    Dec ision Trees

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    Buy stock A

    Buy stock B

    Buy stock C

    Bear Market

    Bear Market

    Bear Market

    Level Market

    Level Market

    Level Market

    Bull Market

    Bull Market

    Bull Market

    $400 x .2 = $80

    $500 x .6 = $300

    $600 x .2 = $120

    $200 x .2 = $40

    $400 x .6 = $240

    $1100 x .2 = $220

    $100 x .2 = $20

    $500 x .6 = $300

    $900 x .2 = $180

    .2

    .6

    .2

    .2

    .6

    .2

    .2

    .6

    .2

    $500

    $500

    $500

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    Dec ision Trees

    After drawing a decision tree, we solve it by workingfrom right to left, starting with decisions furthest to theright, and calculating the expected payoff for each of

    its possible paths.

    We pick the alternative for that decision that has thebest expected payoff.

    We saw off, or prune, the branches not chosen bymarking two short lines through them.

    The decision nodes expected payoff is the one

    associated with the single remaining branch.

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    Sample Prob lem

    A retailer must decide whether to build a small or a large facility at a newlocation. Demand can either be low or high, with the probabilitiesestimated to be 0.4and 0.6respectively.

    If a small facility is built and demand is high, the manager may choosenot to expand (payoff = $223,000) or expand (payoff = $270,000) However,if demand is low, there is no reason to expand. (payoff = $200,000)

    If a large facility is built and demand is low, the retailer can do nothing($40,000) or stimulate demand by advertising. Advertising is estimated to

    have a 0.3 chance of a modest response ($20,000) and a 0.7 chance of alarge response ($220,000).

    If a large facility is built and demand is high, the payoff is $800,000.

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    1

    Draw ing the Tree

    There are two choices:Build a small facility orbuild a large facility.

    A retailer must decide whether to builda small or a large facility at a newlocation.

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    Low demand [0.4]

    Dont expand

    Expand

    $200

    $223

    $270

    1

    2

    Draw ing the TreeThe event (state ofnature) in this exampleis demand. It can beeither high or low.

    Demand can either be small or large, with the

    probabilities estimated to be 0.4and 0.6respectively.If a small facility is built and demand is high, themanager may choose not to expand (payoff =$223,000) or expand (payoff = $270,000) However, ifdemand is low, there is no reason to expand. (payoff= $200,000)

    If a large facility is built anddemand is low, the retailer can do

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    1

    Low demand [0.4]

    Dont expand

    Expand

    Do nothing

    Advertise

    $200

    $223

    $270

    $40

    $800

    Modest response [0.3]

    Sizable response [0.7]

    $20

    $220

    High demand [0.6]

    2

    3

    Completed Draw ingThis is the completed tree.

    Now we start pruning itfrom the right. We willbegin with decision #3.

    The state of nature for

    the 3rd

    decision is thepossible response to theadvertising

    If a large facility is builtand demand is high, thepayoff is $800,000.

    nothing ($40,000) or stimulatedemand by advertising.

    Advertising is estimated to have a0.3 chance of a modest response

    ($20,000) and a 0.7 chance of alarge response ($220,000).

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    Solv ing Decis ion #3

    Low demand [0.4]

    Dont expand

    Expand

    Do nothing

    Advertise

    $200

    $223

    $270

    $40

    $800

    Modest response [0.3]

    Sizable response [0.7]

    $20

    $220

    High demand [0.6]

    1

    2

    3

    0.3x $20 = $6

    0.7x $220 = $154

    $6 + $154 = $160The 40% probabilityof low demand is notyet considered sinceit is the same forboth advertisingstates of nature.

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    Dont expand

    Expand

    Do nothing

    Advertise

    $200

    $223

    $270

    $40

    $800

    $160

    Low demand [0.4]

    Modest response [0.3]

    Sizable response [0.7]

    $20

    $220

    High demand [0.6]

    1

    2

    3

    Solv ing Decis ion #3

    $160

    We eliminate the do

    nothing option since it has a

    lower payoff than doesadvertising.

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    $160

    Modest response [0.3]

    Sizable response [0.7]

    $20

    $220

    Solv ing Decis ion #2

    $160

    Low demand [0.4]

    Dont expand

    Expand

    Do nothing

    Advertise

    $200

    $223

    $270

    $40

    $800

    High demand [0.6]

    1

    2

    3

    $270

    Here there is no state ofnature involved withexpanding or not expanding.They are simply choices if we

    end up with high demand.

    Expanding h as a

    higher expected

    value than n ot

    expanding.

    Low demand expected value of

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    $242

    x 0.4= $80

    x 0.6= $162

    $242

    $160

    $270

    $160

    Low demand [0.4]

    Dont expand

    Expand

    Do nothing

    Advertise

    $200

    $223

    $270

    $40

    $800

    Modest response [0.3]

    Sizable response [0.7]

    $20

    $220

    High demand [0.6]

    1

    2

    3

    Solv ing Decis ion #1p

    $80 is added to the high

    demand expected value of $162

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    So lving Dec is ion #1

    $242

    $160

    $270

    $160

    Low demand [0.4]

    Dont expand

    Expand

    Do nothing

    Advertise

    $200

    $223

    $270

    $40

    $800

    Modest response [0.3]

    Sizable response [0.7]

    $20

    $220

    High demand [0.6]

    1

    2

    3

    x 0.6= $480

    0.4x $160= $64

    $544

    The expected value ofhigh demand for the largefacility ($480) is added tothe expected value of lowdemand for the largefacility ($64).

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    $160

    $270

    $160

    $242

    $544

    Low demand [0.4]

    Dont expand

    Expand

    Do nothing

    Advertise

    $200

    $223

    $270

    $40

    $800

    Modest response [0.3]

    Sizable response [0.7]

    $20

    $220

    High demand [0.6]

    1

    2

    3

    So lving Dec is ion #1

    $544

    The expected value ofbuilding a small facilitycan now be compared tothe expected value of

    building a large facility.

    Ad t f

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    Advantages of

    Decis ion Trees

    Gives structure to a problem situation

    Visual representation of the options

    Forces management to consider eachalternative and compare them

    Optimum courses of action are apparent.

    The only technique for dealing with multiple(sequential) decisions.

    Disadvantages o f

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    Disadvantages o f

    Dec ision Trees

    Many problems are too complex forvisual display

    Complex trees are only computational Subject to estimation errors

    (As with any probabilistic decision tool)

    Only as good as the data used.(True with any model.)

    H k A i t #1

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    Homework Assignment #1Six problems: Due in class next week this time.

    1. Breakeven

    2. Two Processes

    Recommend using the Excel Solver for the above problems.

    3. Preference Matrix4. Payoff Table

    5. Decision-Tree problem #1 (a,b)

    6. Decision-Tree problem #2 (a,b)Do these manually.On the exam you will nothave the use of thecomputer program for analyzing preference matrices, payoff tables ordecision trees. Doing these problems on the computer may NOT adequatelyprepare you for doing the problems on the exams.

    1 Break Even Analysis

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    1. Break Even Analysis

    Mary Williams, owner of Williams Products, is evaluating whether tointroduce a new product line. After thinking through the productionprocess and the costs of raw materials and equipment, she estimates thevariable costs of each unit produced and sold to be $6 and the fixed costsper year at $60,000. (Solver wont provide answers to b, c, or d.)

    a. If the selling price is set at $18 each, how many units must be

    produced and sold for Williams to break even?b. Williams forecasts sales of 10,000 units for the first year if the selling

    price is $14 each. What would be the total contribution to profits fromthis new product during the first year?

    c. If the selling price is set at $12.50, forecast sales is 15,000 units.

    Which pricing strategy ($14 or $12.50) would result in the greater totalcontribution to profits?

    d. What other considerations would be crucial to the final decision aboutmaking and marketing the new product?

    2 Two Processes

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    2. Two ProcessesUse Excel Solver

    Gabriel Manufacturing must implement a manufacturing processthat reduces the amount of toxic by-products. Two processeshave been identified that provide the same level of toxic by-product reduction. The first process would incur $300,000 of

    fixed costs and $600 per unit of variable costs. The secondprocess has fixed costs of $120,000 and variable costs of $900per unit.

    a. What is the break-even quantity beyond which the first

    process is more attractive?b. What is the difference in total cost if the quantity produced

    is 800 units? (You can either estimate this from the solversolution graph, or use the formula given in slide #21.)

    3. Preference Matrix

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    You can use the Solver software or do it on a spreadsheet.

    Axel Express, Inc. collected the following information on two possible

    locations for a new warehouse (1 = poor, 10 = excellent).

    a. Which location, A or B, should be chosen on the basis of the totalweighted score?

    b. If the factors were weighted equally, would the choice change?

    4. Payoff Table

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    yYou can use the Solver software or do it on a spreadsheet, but you

    will need to know how to solve it manually on the test.

    Build-Rite Construction has received favorable publicity from guest

    appearances on a public TV home improvement program. Public TVprogramming decisions seem to be unpredictable, so Build-Rite cannotestimate the probability of continued benefits from its relationship withthe show. Demand for home improvements next year may be either lowor high. But they must decide now whether to hire more employees, do

    nothing, or develop subcontracts with other home improvementcontractors. Build-Rite has developed the following payoff table.

    Alternative Low Moderate High

    Hire ($250,000) $100,000 $625,000

    Subcontract $100,000 $150,000 $415,000

    Do Nothing $ 50,000 $ 80,000 $300,000

    Which alternative is best, according to each of the following criteria?a. Maximin b. Maximax c. Minimax regret

    5 Decision Tree #1

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    5. Decision Tree #1

    A manager is trying to decide whether to buy one machine or two. Ifonly one is purchased, and demand proves to be excessive, the secondmachine can be purchased later. Some sales will be lost, however,because the lead time for producing this type of machine is six months. Inaddition, the cost per machine will be lower if both are purchased at thesame time. The probability of low demand is estimated to be 0.20. The

    after-tax net present value of the benefits from purchasing the twomachines together is $90,000 if demand is low, and $180,000 if demand ishigh.

    If one machine is purchased and demand is low, the net present valueis $120,000. If demand is high, the manager has three options. Doing

    nothing has a net present value of $120,000; subcontracting, $160,000;and buying the second machine, $140,000.

    a. Draw a decision tree for this problem.

    b. How many machines should the company buy initially, and what isthe expected payoff for this alternative?

    Do this manually (no computer).

    6. Decision Tree Problem #2

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    Do this manually (no computer).

    A manager is trying to decide whether to build a small, medium, or large

    facility. Demand can be low, average, or high, with the estimated probabilitiesbeing 0.25, 0.40, and 0.35 respectively.

    A small facility is expected to earn an after-tax, net-present value of$18,000 if demand is low, and $75,000 if demand is medium or high.Expanding a small facility to medium size after demand is established as

    medium or high will only yield an after-tax net profit of $60,000. Expanding itto a large facility if demand is high, nets $125,000.Initially building a medium-sized facility and not expanding it would result

    in a $25,000 loss if demand is low, but net $140,000 in medium demand and$150,000 in high demand. Expanding to a large facility at that point wouldonly net $145,000.

    Building a large facility will net $220,000 if demand is high; $125,000 ifdemand is medium, and is expected to lose $60,000 if demand is low.

    a. Draw an analyze a decision tree for this problem.