# Decision Analysis Part 1

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

Analytical Decision Making
Can Help Managers to: Gain deeper insight into the nature of business relationships 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

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

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

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

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

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

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

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

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

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

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.

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

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.

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

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.

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? EVENTS Probability ACTS Gamble Don’t Gamble Head .5 +\$10,000 \$0 Tail -5,000

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 -2,500 Expected Payoff: \$2,500

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

Example: States of Nature Best choice Favorable Market P(0.5)
Alternatives Favorable Market P(0.5) Unfavorable Market P(0.5) Expected value Construct \$200,000 -\$180,000 \$10,000 small plant \$100,000 -\$20,000 \$40,000 Do nothing \$0 Best choice large plant

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

Questions: Should Getz hire the firm to make this study?
How much does this information worth? What is the value of 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, Expected Payoff under Ceratinty= Maximum expected payoff with no information=Max {EMVi; i=1,..,k} EVPI places an upper bound on what one would pay for additional information

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

Expected Value of Perfect Information
Expected Value Under Certainty =(\$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 = \$60,000 So Getz should not be willing to pay more than \$60,000

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%)

Payoff Table Event ACT (choice) Light 0.10 \$25,000 -\$10,000 -\$125,000
(State of nature) Probability ACT (choice) Gears and levers Spring Action Weights and pulleys Light 0.10 \$25,000 -\$10,000 -\$125,000 Moderate 0.70 400,000 440,000 Heavy 0.20 650,000 740,000 750,000

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!

Decision Trees with one set of alternatives and states of nature.
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.

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

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

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

Ex1:Getz Products Decision Tree
Payoffs \$200,000 -\$180,000 \$100,000 -20,000 1 2 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

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?

Ex1:Getz Products Decision Tree
4 7 \$49,200 \$106,400 \$40,000 \$2,400 2 3 5 6 \$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 Fav. Mkt (0.78) Fav. Mkt (0.27) Fav. Mkt (0.5) Unfav. Mkt (0.22) Unfav. Mkt (0.73) Unfav. Mkt (0.5) \$63,600 -\$87,400 \$10,000 Sur. Res. Neg. (.55) Sur. Res. Pos. (.45) 1st decision point 2nd decision point \$49,200

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.

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

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

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

Decision Tree for Ponderosa Record Company

Backward Approach

Optimal Decision Policy
Precision Tree provides excell add-ins. Optimal decision is: Test market If the market is favorable, market nationally 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 0.5

Risk Profile for Ponderosa Record Co.

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)? earnings of success (\$90,000 currently)? test marketing cost (\$15,000 currently)?

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.

References Lapin L.L., Whisler W.D., Quantitative Decision Making, 7e, 2002. Heizer J., Render, B., Operations Management, 7e, 2004. Render, B., Stair R. M., Quantitative Analysis for Management, 8e, 2003. Anderson, D.R., Sweeney D.J, Williams T.A., Statistics for Business and Economics, 8e, 2002. Taha, H., Operations Research, 1997.