003-chap2Supp2number2 by fanzhongqing

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									    Chapter 2 Supplement 2: Decision Analysis

                   Second session




                                                operations management
      Quantitative decision-making techniques
      for situations where uncertainty exists




1
    Decision Making Criteria Under Uncertainty

      » Our decision making may differ from others




                                                      operations management
        and also under different circumstances,
        depending upon levels of risk, reward, and
        conditions.

      Example:
      » Win $1 or one chance in 10 of winning $10

      » Win $1M or one chance in 10 of winning $10M

2
    Decision Making Criteria Under Uncertainty




                                                                  operations management
    Maximax criterion            → “high-stakes gambler”
        Choose decision with the maximum of the maximum payoffs


    Maximin criterion             → “risk-averse”
        Choose decision with the maximum of the minimum payoffs


    Minimax regret criterion           → “minimum regret”
        Choose decision with the minimum of the maximum regrets
          for each alternative

3
                       Situation

    » There are two lines, each with a “prize”.




                                                  operations management
      Which line will you chose?

    » Line 1: Fast food
      coupon worth $10

    » Line 2: Restaurant coupon
      worth $100
      OR
      $1 free soft drink coupon

4
                           Payoff Table

    Choice?                        Outcome 1               Outcome 2




                                                                           operations management
    Line 1                 $10 fast food coupon     $10 fast food coupon
    Line 2                 $100 restaurant coupon   $1 soft drink coupon


    Maximax criterion
             Choose decision with the maximum of the maximum
               payoffs

             Line 1 max payoff =
             Line 2 max payoff =
             Maximax →



5
                           Payoff Table

    Choice?                        Outcome 1               Outcome 2




                                                                           operations management
    Line 1                 $10 fast food coupon     $10 fast food coupon
    Line 2                 $100 restaurant coupon   $1 soft drink coupon


    Maximin criterion
             Choose decision with the maximum of the minimum
               payoffs

             Line 1 min payoff =
             Line 2 max payoff =
             Maximin →



6
                           Payoff Table

    Choice?                        Outcome 1               Outcome 2




                                                                           operations management
    Line 1                 $10 fast food coupon     $5 fast food coupon
    Line 2                 $100 restaurant coupon   $1 soft drink coupon


    Minimax regret criterion
             Choose decision with the minimum of the maximum
               regrets for each alternative

             Line 1 max regret =
             Line 2 max regret =
             Minimax regret →



7
        Decision Making with Probabilities


     Risk involves assigning probabilities to states of




                                                           operations management
      nature

     Expected value is a weighted average of
      decision outcomes in which each future state of
      nature is assigned a probability of occurrence




8
             Expected Value




                                        operations management
                        n
            EV (x) =    p(xi)xi
                       i =1

    where
        xi = outcome i
     p(xi) = probability of outcome i


9
               Decision Analysis


     We’ve dealt with states of nature, and




                                              operations management
      probabilities of outcomes…

     What about situations that are far
      more complex? Where there are
      more steps in a situation analysis?


10
           Sequential Decision Trees


      A graphical method for analyzing decision




                                                         operations management
       situations that require a sequence of decisions
       over time
      Decision tree consists of
          Square nodes - indicating decision points

          Circles nodes - indicating states of nature

          Arcs - connecting nodes


11
                 Simple Decision Tree




                                               operations management
                            OUTCOME




     DECISION POINT    ARCS CONNECTING NODES




                            OUTCOME

12
                  Simple Decision Tree




                                                       operations management
                               STATE or OUTCOME “A”
              probability of
               outcome A

     DECISION POINT


             probability of
              outcome B
                                STATE or OUTCOME “B”

13
     Expected Value Class Experiment




                                         operations management
                         EV = 1* $.01
                            = $0.01
        guaranteed
          P=1.00



        3 in a row
          P=⅛

                     3H/T EV = ⅛* $.08
                             = $0.01
14
     Expected Value Class Experiment




                                          operations management
                           EV = 1* $.10
                              = $0.10
        guaranteed
          P=1.00



        3 in a row
          P=⅛

                     3H/T EV = ⅛* $.80
                             = $0.10
15
     Expected Value Class Experiment




                                       operations management
                          EV = $1.00

        guaranteed
          P=1.00



        3 in a row
          P=⅛

                     3H
                          EV = $1.00

16
           Sequential Decision Tree




                                          operations management
                                      C


                    A


 DECISION POINT
                                      D


                    B

17
      Sequential Decision Tree: Education Decisions




                                                  operations management
                                            yes MBA


                         yes     MBA?


     Stay in school?
                                            no BS/BA


                         no    HS diploma

18
        Decision Analysis: Replace Tire?

     There are two “states of nature: “flat” and “no flat”
        With probabilities of 0.1 and 0.9 respectively




                                                                         operations management
                         new Cost = $50
                   YES

         replace
          tire?
                                 flat   Cost = $50 (tire) + $100 (tow)

                   NO           Probability = 0.1


                                Probability = 0.9

                                no
                                        Cost = $0
                                flat



19
               Decision Analysis: Investment




                                                          operations management
                               Up
                        0.2

      Purchase          0.6
                              Mod
     mutual fund
                         0.2
                              Down          Stock split
 Invest?                             0.2


                        0.2
                               Up
                                      0.8
       Purchase         0.6
       Individual             Mod           No split
         stock           0.2
                              Down


20
               Decision Analysis: Investment




                                                               operations management
                               Probabilities on any “branch”
                        0.2
                                     must sum to 1.0
      Purchase          0.6
     mutual fund
                         0.2

                                            Stock split
 Invest?                          0.2


                        0.2
                                   0.8
       Purchase         0.6
       Individual                          No split
         stock           0.2




21
               Decision Analysis: Investment




                                                             operations management
                               120%   Investment “growths”
                         0.2            at each “leaf” are
                                        “states of nature”
      Purchase           0.6
                 $100          110%
     mutual fund
                          0.2
                               90%       +110% Stock split
 Invest?                              0.2

                               140%
                         0.2
                                       0.8
       Purchase          0.6
       Individual $100         115%         100% No split
         stock            0.2
                               75%


22
               Decision Analysis: Investment




                                                                         operations management
                                      EV = probability x growth x $100
                               120%   EV = (0.2)(1.2)($100)
                         0.2
                                      EV = $24
      Purchase           0.6
                 $100          110%
     mutual fund
                          0.2
                               90%             +110% Stock split
 Invest?                                    0.2

                               140%
                         0.2
                                             0.8
       Purchase          0.6
       Individual $100         115%               100% No split
         stock            0.2
                               75%


23
               Decision Analysis: Investment




                                                                    operations management
                               120%   EV = probabilityGrowth x growth x
                         0.2
                                          probabilitySplit x growthSplit
      Purchase           0.6          EV = (0.2)(1.4)(0.2)(1.1)($100)
                 $100          110%
     mutual fund                      EV = $6.16
                          0.2
                               90%        +110% Stock split
 Invest?                                0.2

                               140%
                         0.2
                                         0.8
       Purchase          0.6
       Individual $100         115%           100% No split
         stock            0.2
                               75%


24
               Decision Analysis: Investment




                                                              operations management
                               120% $24
                         0.2

      Purchase           0.6
                 $100          110% $66
     mutual fund
                          0.2
                               90% $18      +110%$6.16
 Invest?                                  0.2
                                          Stock split
                               140%
                         0.2
                                           0.8
       Purchase          0.6
       Individual $100         115% $69         100% $22.40
         stock            0.2              No split
                               75% $15


25
               Decision Analysis: Investment




                                                                        operations management
                               120% $24
                         0.2

      Purchase           0.6
                 $100          110% $66    $108
     mutual fund
                          0.2
                               90% $18      +110%$6.16
 Invest?                                  0.2
                                          Stock split
                               140%
                         0.2
       Purchase                            0.8                $112.56
                         0.6
       Individual $100         115% $69         100% $22.40
         stock            0.2              No split
                               75% $15


26
        Decision Analysis: Buying a Car

     Situation analysis: Need a car




                                                 operations management
     » Have up to $7,000 to spend
     » Expect to keep it 5 years
     Decisions to be made
     » New or old? What make? Warranty?
     » Whether to / how to finance?
     Caveats
     » This example based on 2005 data
     » Does not factor
       – costs assigned to unreliability
       – benefits assigned to “newness” factor
27
         Decision Analysis: Buying a Car

     States of nature (financial)?




                                                            operations management
     » Expense
        – New cars higher than used cars
     » Depreciation rate
        – New car depreciation higher, varies among makes
     » Repair cost
        – Higher for older vehicles, varies among makes
     » Cost-of-money
        – If auto loan is needed


28
                                       Automobile Depreciation

          1.2
                                                                                 Porsche 911
                                                                                 Honda Civic
           1




                                                                                                    operations management
                                                                                 Chevy Cavalier
                                                                                 Buick Regal
          0.8
                                                                          n          years to 50%
  value




          0.6

                                         3      4                  7                 9
          0.4


          0.2


           0
                2004
                  0      2003
                           1    2002
                                 2     2001
                                        3     2000
                                               4     1999
                                                      5     1998
                                                             6     1997
                                                                    7         1996
                                                                               8      1995
                                                                                       9     1994
                                                                                              10    1993
                                                                                                     11
29 Ref:   http://www.kbb.com/                   years past purchase
         Decision Analysis: Buying a Car

     User choices narrowed to:




                                                                           operations management
     1. 2005 Honda Civic Coupe EX              $18,150
        – 2 door, automatic, 4 cylinder, 1.7 liter VTEC
        – bucket seats, CD, cruise, AC, AB, custom wheels, keyless entry
     2. 1995 Honda Civic Coupe EX                $6,695
        – 84,000 miles
     3. 2005 Chevy Cavalier LS Sport $17,975
        – 2 door, automatic, 4 cylinder, 2.2 liter
        – bucket seats, CD, cruise, AC, AB, custom wheels, keyless entry
     4. 1998 Chevy Cavalier LS Sport             $6,695
        – 72,000 miles




30
         Decision Analysis: Buying a Car

             First two decisions




                                              operations management
                                       new
                              new or
     Honda Civic EX
                               used

                                       used
       which
       make?

                                       new
                             new or
     Chevy Cavalier           used

                                       used

31
                     Decision Analysis: Buying a Car
                        new
 Honda Civic EX   new or
                   used
                       used
     which




                                                                         operations management
     make?
                        new
                                Additional Decision Path for Used Cars
                  new or
       Chevy
                   used
                       used


                                           Y   warranty cost
                              warranty?

        used

                                                 P1      repair cost 1

                                           N

                                                 P2      repair cost 2
32
                 Decision Analysis: Buying a Car

                       Complete Decision Tree




                                                                                          operations management
                                new
                       new or                                        Y   warranty cost
     Honda Civic EX
                        used                       warranty?
                                used
       which
       make?

                                new
                       new or                        Y               N
                                                                                repair costs
      Chevy Cavalier    used
                                       warranty?     warranty cost
                                used




                                                     N           repair costs




33
                                     Auto Depreciation: Honda Civic & Chevy Cavalier

                           20000
                                                                         Honda Civic
                           18000
                                                                         Chevy Cavalier




                                                                                              operations management
                           16000
purchase price (dollars)




                           14000

                           12000

                           10000

                            8000

                            6000

                            4000

                            2000

                                 0
                                      2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993
                                       0    1    2    3    4    5    6    7     8    9   10   11
Ref:                       http://www.kbb.com/
                                                            year of manufacture
34
                        Decision Analysis: Buying a Car
                            new
     Honda Civic EX   new or
                       used
                           used




                                                                         operations management
       which
       make?
                            new
                                     Assumed Repair Costs for Used Cars
                      new or
          Chevy
                       used
                           used

                                              Y $1695
                                  warranty?

          used

                                                  P=0.20        $5000

                                              N            repair cost

                                                  P=0.80        $1000
35
                 Decision Analysis: Buying a Car

                                        C = $18,150




                                                                                                operations management
                                 new    D = $7,130                                    C = $6,695
                        new or                                             Y    $1695 D = $1,100
     Honda Civic EX
                         used            I = $7,500       warranty?                  RC = $1,800
                                 used                                                 I = $5,000
       which                            95
       make?
                                        C = $17,975                            P=0.20        $5000
                                 new    D = $10,345
                        new or                              Y   $1695      N            repair cost
      Chevy Cavalier     used
                                         I = $7,500
                                              warranty?
                                 used                                          P=0.80        $1000
                                        98
                                                                P=0.20         $5000
                                                                                       C = $6,695
       C = cost of purchase                                 N            repair cost
                                                                                       D = $2,935
       D = depreciation                                                                RC = $1,800
       I = insurance                                            P=0.80         $1000    I = $5,000
       RC = repair (non-warranty option)
36
                       Sequential Decision Tree

     AC = Expected Accumulated Cost per 5 years (non-financed) after sale of car




                                                                                       operations management
                                  new    AC = 14,630
                         new or                                          Y   AC = $7,795
     Honda Civic EX
                          used                             warranty?
                                  used
       which
       make?

                                  new    AC = $17,845
                                                                         N
      Chevy Cavalier
                         new or                              Y                  AC = $7,900
                          used
                                               warranty?
                                                           AC = $9,735
                                  used




                                                             N         AC = $9,630



37
                        Sequential Decision Tree
     NC = Expected Net Cost per 5 years 5 year loan available at 6% APR after sale




                                                                                       operations management
                                   new    NC = $16,230
                          new or                                         NC = $7,795
     Honda Civic EX
                           used                             warranty?
                                   used
       which
       make?

                                   new    NC = $19,445
                                                             NC =         N
       Chevy Cavalier
                          new or                                                 NC = $7,900
                           used
                                                warranty?   $10,145
                                   used




                                                              N         NC = $10,250



38
           Decision Analysis: Buying a Car

                         Cost* of Vehicle for Five Years




                                                                           operations management
                                New                 Used         Used
                                car              no warranty    warranty
       Honda                 $16,230                  $7,900     $7,795
      Civic EX
       Chevy                 $19,445                  $10,250   $10,145
     Cavalier LS
       Sport

       * depreciation, insurance, financing, repair


39
        Decision Analysis: Life Insurance

     » Decision:
        – Buy whole life insurance




                                                                     operations management
            • Higher cost
            • Provides accumulated cash value
            • Covers until old age
        – Buy term life insurance
            • Lower cost
            • No cash value
            • Limited term
     » States of nature
        – ROI from whole life insurance
        – ROI from “investing the difference” between whole & term
        – ROI from investing the difference in 401K



40
       Decision Analysis: Home Purchase

     » Decision:
        – Rental housing




                                                           operations management
           •   Lower initial cost
           •   Limited term
           •   More flexibility
           •   No tax savings
        – Buy home
           •   Higher initial cost, lower long term cost
           •   Provides accumulated equity
           •   Provides unlimited term living
           •   Potential large tax savings
     » States of nature
        – Home appreciation rates
        – Rental rate increases
        – Mortgage rates

41
                    Rent or Buy Housing?

     States of nature




                                                           operations management
     » Family income of $60,000/year
     » Tax bracket: 50%
     » Condo rental: $2000/month
     » Home purchase: $3000/month, of which $1500 is
       interest payment and deductable at 50% rate
     » Home appreciation
        –   5% chance of no appreciation
        –   25% chance of $10,000 appreciation per year
        –   50% chance of $20,000 appreciation per year
        –   20% chance of $40,000 appreciation per year
     “Long term cost” of home purchase: ~$1400 per month
42

								
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