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Decision Analysis Part 1 Graduate Program in Business Information Systems Aslı Sencer.

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1 Decision Analysis Part 1 Graduate Program in Business Information Systems Aslı Sencer

2 Analytical Decision Making  Can Help Managers to: Gain deeper insight into the nature of business relationships Gain deeper insight into the nature of business relationships Find better ways to assess values in such relationships; and Find better ways to assess values in such relationships; and See a way of reducing, or at least understanding, uncertainty that surrounds business plans and actions See a way of reducing, or at least understanding, uncertainty that surrounds business plans and actions 2

3 Steps to Analytical DM  Define problem and influencing factors  Establish decision criteria  Select decision-making tool (model)  Identify and evaluate alternatives using decision-making tool (model)  Select best alternative  Implement decision  Evaluate the outcome 3

4 Models  Are less expensive and disruptive than experimenting with the real world system  Allow operations managers to ask “What if” types of questions  Are built for management problems and encourage management input  Force a consistent and systematic approach to the analysis of problems  Require managers to be specific about constraints and goals relating to a problem  Help reduce the time needed in decision making 4

5 Limitations of the Models  They may be expensive and time- consuming to develop and test  Often misused and misunderstood (and feared) because of their mathematical and logical complexity  Tend to downplay the role and value of nonquantifiable information  Often have assumptions that oversimplify the variables of the real world 5

6 The Decision-Making Process ProblemDecision Quantitative Analysis Logic Historical Data Marketing Research Scientific Analysis Modeling Qualitative Analysis Emotions Intuition Personal Experience and Motivation Rumors 6

7  Decision trees  Decision tables Decision Problem Alternatives States of Nature Outcomes Displaying a Decision Problem 7

8 Types of Decision Models  Decision making under uncertainty  Decision making under risk  Decision making under certainty 8

9 Fundamentals of Decision Theory Terms:  Alternative: course of action or choice  State of nature: an occurrence over which the decision maker has no control Symbols used in a decision tree:  A decision node from which one of several alternatives may be selected  A state of nature node out of which one state of nature will occur 9

10 Decision Table States of Nature Alternatives State 1State 2 Alternative 1 Outcome 1Outcome 2 Alternative 2 Outcome 3Outcome 4 10

11 Getz Products Decision Tree 1 2 Unfavorable market Favorable market Construct small plant Construct large plant Do nothing A decision node A state of nature node 11

12 Decision Making under Uncertainty  Maximax - Choose the alternative that maximizes the maximum outcome for every alternative (Optimistic criterion)  Maximin - Choose the alternative that maximizes the minimum outcome for every alternative (Pessimistic criterion)  Equally likely - chose the alternative with the highest average outcome. 12

13 Example: States of Nature Alternatives Favorable Market Unfavorable Market Maximum in Row Minimum in Row Row Average Construct large plant $200,000 -$180,000 $200,000 -$180,000 $10,000 Construct small plant $100,000 -$20,000 $100,000 -$20,000 $40,000 $0 $0 MaximaxMaximin Equally likely Do nothing 13

14 Decision criteria  The maximax choice is to construct a large plant. This is the maximum of the maximum number within each row or alternative.  The maximin choice is to do nothing. This is the maximum of the minimum number within each row or alternative.  The equally likely choice is to construct a small plant. This is the maximum of the average outcomes of each alternative. This approach assumes that all outcomes for any alternative are equally likely. 14

15 Decision Making under Risk  Probabilistic decision situation  States of nature have probabilities of occurrence  Maximum Likelihood Criterion  Maximize Expected Monitary Value (Bayes Decision Rule) 15

16 Maximum Likelihood Criteria  Maximum Likelihood: Identify most likely event, ignore others, and pick act with greatest payoff.  Personal decisions are often made that way.  Collectively, other events may be more likely.  Ignores lots of information. 16

17 Bayes Decision Rule  It is not a perfect criterion because it can lead to the less preferred choice.  Consider the Far-Fetched Lottery decision: Would you gamble? EVENTSProbability ACTS Gamble Don’t Gamble Head.5+$10,000$0 Tail.5 5,

18 The Far-Fetched Lottery Decision Most people prefer not to gamble!  That violates the Bayes decision rule.  But the rule often indicates preferred choices even though it is not perfect. EVENTS Proba- bility ACTS Gamble Don’t Gamble Payoff × Prob. Payoff × Prob Head.5+$5,000$0 Tail.5 2,500 0 Expected Payoff: $2,500 $2,500$0 18

19 Expected Monetary Value N: Number of states of nature k: Number of alternative decisions Xij: Value of Payoff for alternative i in state of nature j, i=1,2,...,k and j=1,2,...,N. Pj: Probability of state of nature j 19

20 Example: 20

21 Decision Making under Certainty  What if Getz knows the state of the nature with certainty?  Then there is no risk for the state of the nature!  A marketing research company requests $65000 for this information 21

22 Questions:  Should Getz hire the firm to make this study?  How much does this information worth?  What is the value of perfect information? 22

23 Expected Value With Perfect Information () Expected Value With Perfect Information (EVPI) EVPI = Expected Payoff - Maximum expected payoff under Certainty with no information Let N: Number of states of nature and k: Number of actions,  EVPI places an upper bound on what one would pay for additional information Maximum expected payoff with no information=Max {EMV i ; i=1,..,k} 23 Expected Payoff under Ceratinty=

24 Example: Expected Value of Perfect Information Construct a large plant Construct a small plant Do nothing 200,000 -$180,000 $0 Favorable Market ($) Unfavorable Market ($) 0.50 EMV $40,000 $100,000-$20,000 $0 $10,000 24

25 Expected Value of Perfect Information Expected Value Under Certainty =($200,000* *0.50)= $100,000 =($200,000* *0.50)= $100,000 Max(EMV)= Max{10,000, 40,000, 0}=$40,000 EVPI = Expected Value Under Certainty - Max(EMV) = $100,000 - $40,000 = $100,000 - $40,000 = $60,000 = $60,000 So Getz should not be willing to pay more than $60,000 25

26 Ex: Toy Manufacturer  How to choose among 4 types of tippi-toes?  Demand for tippi-toes is uncertain: Light demand: 25,000 units (10%) Moderate demand: 100,000 units (70%) Heavy demand: 150,000 units (20%) 26

27 Event (State of nature) Probability ACT (choice) Gears and levers Spring Action Weights and pulleys Light0.10$25,000-$10,000-$125,000 Moderate ,000440,000400,000 Heavy ,000740,000750,000 Payoff Table 27

28 Maximum Expected Payoff Criteria ACT (choice) Gears and levers Spring Action Weights and pulleys Expected Payoff $412,500$455,500$417,000 Maximum expected payoff occurs at Spring Action! 28

29  Graphical display of decision process, i.e., alternatives, states of nature, probabilities, payoffs.  Decision tables are convenient for problems with one set of alternatives and states of nature.  With several sets of alternatives and states of nature (sequential decisions), decision trees are used!  EMV criterion is the most commonly used criterion in decision tree analysis. Decision Trees 29

30 Softwares for Decision Tree Analysis  DPL  Tree Plan  Supertree Analysis with less effort. Full color presentations for managers 30

31 Steps of Decision Tree Analysis  Define the problem  Structure or draw the decision tree  Assign probabilities to the states of nature  Estimate payoffs for each possible combination of alternatives and states of nature  Solve the problem by computing expected monetary values for each state-of-nature node 31

32 Decision Tree 1 2 State 1 State 2 State 1 State 2 Alternative 1 Alternative 2 Decision Node Outcome 1 Outcome 2 Outcome 3 Outcome 4 State of Nature Node 32

33 Ex1:Getz Products Decision Tree Payoffs $200,000 -$180,000 $100, , Unfavorable market (0.5) Favorable market (0.5) Construct small plant Construct large plant Do nothing EMV for node 2 = $40,000 EMV for node 1 = $10,000 33

34 A More Complex Decision Tree Let’s say Getz Products has two sequential decisions to make:  Conduct a survey for $10000?  Build a large or small plant or not build? 34

35 Ex1:Getz Products Decision Tree $49,200 $106,400 $40,000 $2, $190,000 -$190,000 $90,000 -$30,000 -$10,000 $190,000 -$190,000 $90,000 -$30,000 -$10,000 $200,000 -$180,000 $100,000 -$20,000 $0 Survey No survey Large plant Small plant No plant Large plant Small plant No plant Large plant Small plant No plant Fav. Mkt (0.78) Fav. Mkt (0.27) Fav. Mkt (0.5) Unfav. Mkt (0.22) Unfav. Mkt (0.73) Unfav. Mkt (0.5) $106,400 $63,600 -$87,400 $2,400 $10,000 $40,000 Sur. Res. Neg. (.55) Sur. Res. Pos. (.45) 1 st decision point 2 nd decision point $49,200 35

36 Resulting Decision  EMV of conducting the survey=$49,200  EMV of not conducting the survey=$40,000 So Getz should conduct the survey! If the survey results are favourable, build large plant. If the survey results are infavourable, build small plant. 36

37 Ex2: Ponderosa Record Company  Decide whether or not to market the recordings of a rock group.  Alternative1: test market 5000 units and if favorable, market units nationally  Alternative2: Market units nationally  Outcome is a complete success (all are sold) or failure 37

38 Ex2: Ponderosa-costs, prices  Fixed payment to group: $5000  Production cost:$5000 and $0.75/cd  Handling, distribution: $0.25/cd  Price of a cd: $2/cd Cost of producing 5,000 cd’s =5,000+5,000+( )5,000=$15,000 Cost of producing 45,000 cd’s =0+5,000+( )45,000=$50,000 Cost of producing 50,000 cd’s =5,000+5,000+( )50,000=$60,000 38

39 Ex2: Ponderosa-Event Probabilities  Without testing P(success)=P(failure)=0.5  With testing P(success|test result is favorable)=0.8 P(failure|test result is favorable)=0.2 P(success|test result is unfavorable)=0.2 P(failure|test result is unfavorable)=0.8 39

40 Decision Tree for Ponderosa Record Company 40

41 Backward Approach 41

42 Optimal Decision Policy  Precision Tree provides excell add-ins.  Optimal decision is: Test market If the market is favorable, market nationally If the market is favorable, market nationally Else, abort Else, abort  Risk Profile Possible outcomes for the opt. soln. $35,000 with probability 0.4 -$55,000 with probability 0.1 -$15,000 with probability

43 Risk Profile for Ponderosa Record Co. 43

44 Sensitivity Analysis The optimal solution depends on many factors. Is the optimal policy robust? Question: -How does $1000 payoff change with respect to a change in success probability (0.8 currently)? success probability (0.8 currently)? earnings of success ($90,000 currently)? earnings of success ($90,000 currently)? test marketing cost ($15,000 currently)? test marketing cost ($15,000 currently)? 44

45 Application Areas of Decision Theory Investments in research and development plant and equipment new buildings and structures Production and Inventory control Aggregate Planning Maintenance Scheduling, etc. 45

46 References  Lapin L.L., Whisler W.D., Quantitative Decision Making, 7e,  Heizer J., Render, B., Operations Management, 7e,  Render, B., Stair R. M., Quantitative Analysis for Management, 8e,  Anderson, D.R., Sweeney D.J, Williams T.A., Statistics for Business and Economics, 8e,  Taha, H., Operations Research,


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