2Introduction What makes the difference between good and bad decisions? Good decisions may be defined as:Based on logic,Considered all possible decision alternatives,Examined all available information about future, andApplied decision modeling approach.Bad decisions may be defined as:Not based on logic,Did not use all available information,Did not consider all alternatives, andDid not employ appropriate decision modeling techniques.
3Decision AnalysisA set of quantitative decision-making techniques for decision situations where uncertainty exists
4Decision Theory Elements A set of possible future conditions exists that will have a bearing on the results of the decisionA list of alternatives (courses of action) for the manager to choose fromA known payoff for each alternative under each possible future condition
5Decision Making States of nature Events that may occur in the future Decision maker is uncertain which state of nature will occurDecision maker has no control over the states of nature
6product and service design Decision TheoryDecision Theory represents a general approach to decision making which is suitable for a wide range of operations management decisions, including:capacityplanningproduct and service designlocationplanningequipmentselection
7Five Steps of Decision Making 1. Clearly define the problem at hand.2. List all possible decision alternatives.3. Identify possible future events (states of nature)4. Identify payoff (usually, profit or cost) for eachcombination of alternatives and events.5. Select one of the decision theory modeling techniques, apply decision model, and make decision.
8Thompson Lumber Company (1 of 2) Step 1. Identifies problem as:whether to expand product line by manufacturing and marketing new product which is “backyard storage sheds.”Step 2. Generate decision alternatives available.Decision alternative is defined as course of action or strategy that may be chosen by the decision maker. Alternatives are to construct:(1) a large plant to manufacture storage sheds,(2) a small plant to manufacture storage sheds, or(3) build no plant at all.Step 3. Identify possible future events
9Thompson Lumber Company (2 of 2) Step 4. Express payoff resulting from each possible combination of alternatives and events.Objective is to maximize profits.Step 5. Select decision theory model and apply it to data to help make decision.Type of decision model available depends on the operating environment and the amount of uncertainty and risk involved.
10Payoff TableA method of organizing & illustrating the payoffs from different decisions given various states of natureA payoff is the outcome of the decision
11Payoff TablesPayoff Tables can be constructed when there is a finite set of discrete decision alternatives.In a Payoff Table -The rows correspond to the possible decision alternatives.The columns correspond to the possible future events.Events (States of Nature) are mutually exclusiveThe body of the table contains the payoffs.
12Payoff Table Decision a b 1 Payoff 1a Payoff 1b 2 Payoff 2a Payoff 2b States of NatureDecision a b1 Payoff 1a Payoff 1b2 Payoff 2a Payoff 2b
14Types Of Decision Making Environments Type 1: Decision Making under CertaintyType 2: Decision Making under UncertaintyType 3: Decision Making under Risk.
15Types Of Decision Making Environments Type 1: Decision Making under Certainty. Decision maker knows with certainty the consequence of every decision alternative. (The future state of nature is assumed to be known.)Type 2: Decision Making under Uncertainty. Decision maker has no information about various outcomes. (There is no knowledge about the probability of the states of nature occurring)
16Types Of Decision Making Environments Type 3: Decision Making under Risk. Decision maker has some knowledge regarding the probability of occurrence of each event or state of nature. (There is some knowledge about the probability of the states of nature occurring)
18Decision Making Under Uncertainty- Steps of : Construct a Payoff TableSelect a Decision Making CriterionApply the Criterion to the Payoff TableIdentify the Optimal Solution
19Decision Making Under Uncertainty The decison criteria are based on the decision maker’s attitude toward lifeThese include an individual being pessimistic or optimistic, conservative or aggressive
20Decision Making Criteria Under Uncertainty Criteria for making decisions under uncertainty.Maximax.MaximinEqually likely.Criterion of realism.Minimax regret.First four criteria calculated directly from decision payoff table.Fifth minimax regret criterion requires use of opportunity loss table.
21Maximax Criterion (1 of 2) Maximax criterion selects the alternative that maximizes maximum payoff over all alternatives.Is based on the best possible scenario.First locate maximum payoff for each alternative.Select alternative with maximum value.Decision criterion locates alternative with highest possible gain.Called optimistic criterion.Table shows maximax choice is first alternative: "construct large plant."
22Maximax Criterion (2 of 2) Example 1: Thompson Lumber CompanyMaximax criterion selects alternative that maximizes maximum payoff over all alternatives.First alternative, "construct a large plant”, $200,000 payoff is maximum of maximum payoffs for each decision alternative.
23Maximin Criterion (1 of 2) Maximin criterion finds the alternative that maximizes minimum payoff over all alternatives.Is based on the worst-case scenario.First locate minimum payoff for each decision alternative across all states of nature.Select the alternative with the maximum value.Decision criterion locates the alternative that has the least possible loss.Called pessimistic criterion.Maximin choice, "do nothing," is shown in table.$0 payoff is maximum of minimum payoffs for each alternative.
24Maximin Criterion (2 of 2) Example 1. Thompson Lumber CompanyFirst locate minimum payoff for each alternative, and select the alternative with maximum number.
25Equally Likely (Laplace) Criterion (1 of 2) Equally likely, also called Laplace, criterion finds decision alternative with highest average payoff (here the probabilities of each state of nature is assumed to be equal)Calculate average payoff for every alternative.Pick the alternative with maximum average payoff.Assumes all probabilities of occurrence for states of nature are equal.Equally likely choice is the second alternative, "construct a small plant."Strategy shown in table has maximum average payoff ($40,000) over all alternatives.
26Equally Likely (Laplace) Criterion (2 of 2) Example 1. Thompson Lumber CompanyEqually likely criterion finds decision alternative with highest average payoff.Calculate average payoff for every alternative.Pick alternative with maximum average payoff.
27Criterion of Realism (Hurwicz)(1 of 3) Often called weighted average, the criterion of realism (or Hurwicz) decision criterion is a compromise between optimistic and pessimistic decision.Select coefficient of realism, a, with value between 0 and 1.When a is close to 1, decision maker is optimistic about future.When a is close to 0, decision maker is pessimistic about future.
28Criterion of Realism (2 of 3) Formula for criterion of realism =a (maximum payoff for alternative) +(1-a) (minimum payoff for alternative)Assume coefficient of realism a =Best decision would be to construct a large plant.This alternative has highest weighted average payoff: $124,000
29Criterion of Realism (3 of 3) Example 1. Thompson Lumber CompanyCoefficient of realism a = 0.80.$124,000 = (0.80)($200,000) + (0.20)(- $180,000).
30Minimax Regret Criterion (1 of 5) Final decision criterion is based on opportunity loss.Develop opportunity loss (regret) table.Determine opportunity loss of not choosing the best alternative for each state of nature (or the regret by failing to choose the “best” decision)
31Minimax Regret Criterion (2 of 5) Opportunity loss, also called regret for any state of nature, or any column is calculated by subtracting each outcome in column from best outcome in the same column.The alternative with the minimum of the maximum regrets for each alternative is selected.
32Minimax Regret Criterion (3 of 5) Example 1. Thompson Lumber CompanyBest outcome for favorable market is $200,000 as result of first alternative, "construct a large plant."Subtract all payoffs in column from $200,000.Best outcome for unfavorable market is $0 that is the result of third alternative, "do nothing."Subtract all payoffs in column from $0.Table illustrates computations and shows complete opportunity loss table.
33Minimax Regret Criterion (4 of 5) Example 1. Thompson Lumber CompanyTable illustrates computations and shows complete opportunity loss table.
34Minimax Regret Criterion (5 of 5) Example 1. Thompson Lumber CompanyOnce the opportunity loss table has been constructed, locate the maximum opportunity loss within each alternative.Pick the alternative with minimum valueMinimax regret choice is second alternative, "construct a small plant." Regret of $100,000 is minimum of maximum regrets over all alternatives.
35Tom Brown Investment Example for Decision Making Under Uncertainty
36Tom Brown has inherited $1000. Example 2. Tom Brown Investment DecisionTom Brown has inherited $1000.He has decided to invest the money for one year.A broker has suggested five potential investments.Gold.Junk Bond.Growth Stock.Certificate of Deposit.Stock Option Hedge.Tom has to decide how much to invest in each investment.
37The Payoff Table The Stock Option Alternative is dominated by the Example 2. Tom Brown Investment DecisionThe Stock Option Alternative is dominated by theBond Alternative
38Maximax Criterion Example 2. Tom Brown Investment Decision The Optimal decision
39The Maximin Criterion Example 2. Tom Brown Investment Decision The Optimal decision
40Minimax Regret Criterion Example 2. Tom Brown Investment DecisionThe Optimal decisionRegret Table
42Decision Making Under Risk Common for decision maker to have some idea about the probabilities of occurrence of different outcomes or states of nature.Probabilities may be based on decision maker’s personal opinions about future events, or on data obtained from market surveys, expert opinions, etc.When probability of occurrence of each state of nature can be assessed, problem environment is called decision making under risk.
43Expected Monetary Value (1 of 3) Given decision table with conditional values (payoffs) and probability assessments, determine the expected monetary value (EMV) for each alternative.Computed as weighted average of all possible payoffs for each alternative, where weights are probabilities of different states of nature: EMV (alternative i) =(payoff of first state of nature) x (probability of firststate of nature) +(payoff of second state of nature) x (probability of secondstate of nature)(payoff of last state of nature) x (probability of laststate of nature)
44Expected Monetary Value (2 of 3) Example 1. Thompson Lumber CompanyProbability of favorable market is the same as probability of unfavorable market.Each state of nature has a 0.50 probability of occurrence.
45Expected Monetary Value (3 of 3) Example 2. Tom Brown ProblemThe Optimal decision(0.2)(250) + (0.3)(200) + (0.3)(150) + (0.1)(-100) + (0.1)(-150) = 130
46Expected Value of Perfect Information Expected value of perfect information: the difference between the expected payoff under certainty and the expected payoff under riskExpected value of perfect informationExpected payoff under certaintyExpected payoff under risk-=
47Expected Value of Perfect Information Expected value with perfect information is expected or average return, if one has perfect information before decision has to be made.Choose best alternative for each state of nature and multiply its payoff times probability of occurrence of that state of nature:Expected value with perfect information (EV with PI) =(best payoff for first state of nature)x(probability of first state of nature)+ (best payoff for second state of nature)x (probability of second state of nature)(best payoff for last state of nature)x (probability of last state of nature)EVPI = EV with PI - maximum EMVIt is also the smallest expected regret of any decision alternative.
48EV with PI and EVPIBest outcome for state of nature "favorable market" is "build a large plant" with a payoff of $200,000.Best outcome for state of nature "unfavorable market" is "do nothing," with payoff of $0.Expected value with perfect information(EV with PI) = ($200,000)(0.50) + ($0)(0.50)= $ 100,000.If one had perfect information, an average payoff of $100,000 if decision could be repeated many times.Maximum EMV or expected value without perfect information, is $40,000.EVPI = EV with PI - maximum EMV= $100,000 - $40,000 = $60,000.
49Decision TreesAny problem presented in decision table can be graphically illustrated in decision tree.A graphical method for analyzing decision situations that require a sequence of decisions over time (decision situations that cannot be handled by decision tables)Decision tree consists ofSquare nodes - indicating decision pointsCircles nodes - indicating states of natureArcs - connecting nodes
50These nodes are represented using following symbols: = A decision nodeArcs (lines) originating from decision node denote all decision alternatives available at that node.О = A state of nature (or chance) node.Arcs (lines) originating from a chance node denote all states of nature that could occur at that node.
511 2 Decision Tree State 1 State 2 Outcome 1 Outcome 2 Outcome 3 Alternative 1Alternative 2Decision NodeOutcome 1Outcome 2Outcome 3Outcome 4State of Nature Node
52Decision Tree B State of nature 1 Payoff 1 Decision Point Choose A’1 2Choose A’1Choose A’2Payoff 6Payoff 4Payoff 5Choose A’3Choose A’4Choose A’1Decision PointChance Event
53Decision Tree Thompson Lumber Company Tree usually begins with decision node.Decision is to determine whether to construct large plant, small plant, or no plant.Once the decision is made, one of two possible states of nature (favorable or unfavorable market) will occur.
54Folding Back a Decision Tree Thompson Lumber CompanyIn folding back decision tree, use the following two rules:At each state of nature (or chance) node, compute expected value using probabilities of all possible outcomes at that node and payoffs associated with outcomes.At each decision node, select alternative that yields better expected value or payoff.
55Reduced Decision Tree Thompson Lumber Company Using the rule for decision nodes, select alternative with highest EMV.Corresponds to alternative to build small plant.Resulting EMV is $40,000.
56Decision Trees for Multi-stage Decision Making Problems
57Decision Tree With EMVs Shown Thompson Lumber Company
59Southern Textile Company STATES OF NATUREGood Foreign Poor ForeignDECISION Competitive Conditions Competitive ConditionsExpand $ 800,000 $ 500,000Maintain status quo ,300, ,000Sell now 320, ,000
60Southern Textile Company STATES OF NATUREGood Foreign Poor ForeignDECISION Competitive Conditions Competitive ConditionsExpand $ 800,000 $ 500,000Maintain status quo 1,300, ,000Sell now 320, ,000Maximax SolutionExpand: $800,000Status quo: 1,300,000 MaximumSell: 320,000Decision: Maintain status quo
61Southern Textile Company STATES OF NATUREGood Foreign Poor ForeignDECISION Competitive Conditions Competitive ConditionsExpand $ 800,000 $ 500,000Maintain status quo ,300, ,000Sell now 320, ,000Maximin SolutionExpand: $500,000 MaximumStatus quo: -150,000Sell: 320,000Decision: Expand
63Southern Textile Company STATES OF NATUREGood Foreign Poor ForeignDECISION Competitive Conditions Competitive ConditionsExpand $ 800,000 $ 500,000Maintain status quo ,300, ,000Sell now 320, ,000Hurwicz Criteria = = 0.7Expand: $800,000(0.3) + 500,000(0.7) = $590,000 MaximumStatus quo: 1,300,000(0.3) -150,000(0.7) = 285,000Sell: 320,000(0.3) + 320,000(0.7) = 320,000Decision: Expand
64Southern Textile Company STATES OF NATUREGood Foreign Poor ForeignDECISION Competitive Conditions Competitive ConditionsExpand $ 800,000 $ 500,000Maintain status quo ,300, ,000Sell now 320, ,000Equal Likelihood CriteriaTwo states of nature each weighted 0.50Expand: $800,000(0.5) + 500,000(0.5) = $650,000 MaximumStatus quo: 1,300,000(0.5) -150,000(0.5) = 575,000Sell: 320,000(0.5) + 320,000(0.5) = 320,000Decision: Expand
65Southern Textile Company STATES OF NATUREGood Foreign Poor ForeignDECISION Competitive Conditions Competitive ConditionsExpand $ 800,000 $ 500,000Maintain status quo ,300, ,000Sell now 320, ,000Expected Valuep(good) = p(poor) = 0.30EV(expand) $800,000(0.7) + 500,000(0.3) = $710,000EV(status quo) 1,300,000(0.7) -150,000(0.3) = 865,000 MaximumEV(sell) 320,000(0.7) + 320,000(0.3) = 320,000Decision: Status quo
66EVPI ExampleGood conditions will exist 70% of the time, choose maintain status quo with payoff of $1,300,000Poor conditions will exist 30% of the time, choose expand with payoff of $500,000Expected value given perfect information = $1,300,000 (0.70) + 500,000 (0.30) = $1,060,000 EVPI = $1,060, ,000 = $195,000