Lecture 2 Decision Analysis QM 2 Slides

1DECISION ANALYSIS

Lecture 2

Lecturer : Dr. Dwayne Devonish

MGMT 2012: Introduction to Quantitative Methods

Learning Objectives

Students should be able to:

To outline the key steps of decision-making under uncertainty and risk

To identify various decision-makingmodels and criteria in decision analysis,

To apply these models and criteria toimprove decision-making in organisations

2Making Decisions Decision-making is a critical managerial activitythat occurs virtually everyday.

A managers main role is to make decisions andtake action to direct and guide the operations of anorganisation towards its overall goals.

Decisions can be made under various conditions:certainty (complete information available), risk anduncertainty.

We will focus on decision-making underuncertainty and under risk for this session.

Decision-analysis is a quantitative method that isused to aid in managerial decision-making inorganisations, especially under conditions ofuncertainty and risk.

SIX STEPS TO DECISION MAKING

1. Clearly define the problem at hand.2. List the possible decision alternatives.3. Identify the possible outcomes or

conditions facing the business/industry (i.e.states of nature) circumstances underwhich a decision is made.

4. List the payoffs (e.g. profits/losses) of eachcombination of alternatives and outcomes.

5. Select one of the mathematical decisiontheory models.

6. Apply the model and make your decision.

3DR. GREENS DECISION PROBLEM (SEE APPENDIX FOR EXPANDED SUMMARY)

Define problem To manufacture mahogany work desks.

List alternatives 1. Construct a large new plant

2. A small plant

3. No plant at all

Identify outcomes/ business conditions

The market could be favorable (i.e. high demand) or unfavorable (i.e low demand) for mahogany work desks

List payoffs List the payoff for each state of nature/decision alternative combination create a payoff table (see next slide)

Select a model Decision tables and/or trees can be used to solve the problem

Apply model and make decision

Solutions can be obtained and a sensitivity analysis used to make a decision

Payoff Table of Dr Green Decision Problem

Alternative

State of Nature

Favorable Market ($)

Unfavorable Market ($)

Construct a large plant

200,000 -180,000

Construct a small plant

100,000 -20,000

Do nothing 0 0

4Decision-Making Under Uncertainty Selecting a decision model (step 5) depends onthe amount of risk and uncertainty involved.

Under uncertainty, a manager cannot ascertainthe probability of several outcomes occurring for agiven problem. Consequently, the managersattitude towards uncertainty becomes relevant.Several criteria for decision-making have beendeveloped. The most popular ones are:

Maximax (i.e. optimistic manager)

Maximin (i.e. pessimistic manager)

Equally likelihood criterion (or LaPlace criterion)

Minimax regret

Lets look at these decision criteria:

Maximax Approach

Maximax: Optimistic Approach

Find the alternative that maximizes themaximum payoff for every alternative.

This approach evaluates each decisionalternative in terms of the best payoff that canoccur. The decision maker selects the decisionthat has the largest gain.

Locate the maximum payoff for eachalternative, and then select the alternative withthe maximum number (compare rows).

5Payoff Table of Dr Green Decision Problem

Alternative

State of Nature




200,000 -180,000


100,000 -20,000

Do nothing 0 0

Decision-Making under Maximax

Alternative

State of NatureMaximax




200,000 -180,000 200,000


100,000 -20,000 100,000

Do nothing 0 0 0

The maximum payoffs for each alternative are circled in black.

BEST DECISIONBUILD LARGE

PLANT

6Maximin Approach

Maximin: Pessimistic Approach

Find the alternative that maximizes theminimum payoff for every alternative.

This approach evaluates each decisionalternative in terms of the worst payoffs that canoccur. Then, the decision maker selects thedecision that has the best of the worst payoffs.

Locate the minimum payoffs for eachalternative, and then select the alternative withthe maximum number.

Payoff Table of Dr Green Decision Problem

Alternative

State of Nature




200,000 -180,000


100,000 -20,000

Do nothing 0 0

7Decision-Making under Maximin

Alternative

State of NatureMaximin




200,000 -180,000 -180,000


100,000 -20,000 -20,000

Do nothing 0 0 0

The minimum payoffs for each alternative are circled in black.

BEST DECISIONDO NOTHING

Equally Likelihood or LaPlace Approach

Equally likely: LaPlace Approach

Find the alternative with the highest averagepayoff.

This approach evaluates each decisionalternative in terms of its average payoff. Then,the decision maker selects the alternative thathas the highest average payoff.

Find the average payoff for each alternative,and then select the alternative with the highestaverage.

8Decision-Making under LaPlace

Alternative

State of NatureAVERAGE

PAYOFFFavorable Market ($)


Construct a large plant 200,000 -180,000 10,000

Construct a small plant 100,000 -20,000 40,000

Do nothing0 0 0

BEST DECISIONBUILD SMALL PLANT

Average pay off = 200,000+-180,000/2

Average pay off = 100,000+-20,000/2

Average pay off = 0 +0/2

Minimax Regret Minimax Regret (or Opportunity Loss)

Approach Opportunity loss or regret refers to thedifference between the optimal (best) profit orpayoff for a given state of nature and the actualpayoff received for a specific decisionalternative i.e. the amount lost by not pickingthe best alternative in a given state of nature.

The decision-maker chooses the alternativethat minimizes the amount of regret/loss.

Step 1: Create an opportunity loss/regret tableby calculating the opportunity loss/regret for notselecting the best decision alternative this isdone by subtracting each payoff in a column(i.e. state of nature) from the best payoff in thatsame column. Hence, you first need to findthe best alternative for each state of nature(in the columns).

9Payoff Table of Dr Green Decision Problem

Alternative

State of Nature




200,000 -180,000


100,000 -20,000

Do nothing 0 0

Regret is the difference between the actualchoice and the best choice for a given state ofnature.

Alternative

State of Nature




200,000 -180,000


100,000 -20,000

Do nothing 0 0

LETS FIRST DETERMINE THE BEST PAY-OFF FOR EACH STATE OF NATURE: SEE RED CIRCLES

Hence, for a favourable market, the best payoff is $200,000, whereas

for unfavourable market the best payoff is $0

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Alternative

State of Nature




200,000-200,000

0- (-180,000)


200,000-100,000

0-(-20,000)

Do nothing 200,000-0 0 - 0

THEN, WE MUST SUBTRACT EACH ACTUAL PAYOFF FOR A GIVEN STATE OF NATURE FROM BEST PAYOFF IN THE SAMESTATE OF NATURE TO CREATE AN OPPORTUNITY LOSS TABLE

SO BEST PAYOFF ACTUAL PAYOFF

Alternative

State of Nature




0 180,000


100,000 20,000

Do nothing 200,000 0

HERE IS OUR OPPORTUNITY LOSS TABLE. STEP 2 = USING THE MINIMAX REGRET CRITERION, WE MUST LOCATE MAXIMUM (WORST) OPPORTUNITY LOSS FOR EACH

ALTERNATIVE.

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Alternative

State of Nature

Worst

RegretFavorable Market ($)



0 180,000 180,000


100,000 20,000 100,000

Do nothing 200,000 0 200,000

THE MAXIMUM (WORST) OPPORTUNITY LOSS FOR EACH ALTERNATIVE IS CIRCLED IN RED. THESE ARE ALSO NOTED IN

THE WORST REGRET COLUMN.

Alternative

State of Nature

Worst

RegretFavorable Market ($)



0 180,000 180,000


100,000 20,000 100,000

Do nothing 200,000 0 200,000

STEP 3: SELECT THE ALTERNATIVE WITH MINIMUM (BEST) WORST REGRET. IN THIS CASE, IT IS CONSTRUCTING THE SMALL

PLANT ($100,000). $100,000 is the smallest loss/ lowest regretamong all losses

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DECISION-MAKING UNDER RISK We have considered decision criteria to be utilisedwhen there is no information about how likely aparticular state of nature will occur.

Decision-making under risk is a decision situation inwhich several possible states of nature may occur,and the probabilities of these states of nature areknown (Render et al., 2009, p.77).

Two popular methods of decision-making under risk is:the Expected Monetary Value (EMV) and ExpectedOpportunity Loss (EOL).

The EMV (or the mean value for an alternative) iscalculated by multiplying the probability of occurrencefor each state of nature by the corresponding payoffand summing them. Lets look at this approach first.

Lets look at last exercise

Alternative

State of Nature




200,000 -180,000


100,000 -20,000

Do nothing 0 0

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SOO.. Suppose John was able to determine that theprobability of favourable market conditions is .60, andthe probability of unfavourable market conditions is .40(hint: probabilities for both conditions must sum to 1).

Given the known probabilities, we can turn to EMVapproach as we are operating under risk.

To determine the best alternative, the EMV approachworks out like this: Payoff x probability

EMV (large plant) = ($200,000)(.6) + (-$180,000)(.4) =

EMV (small plant) = ($100,000)(.6) + (-$20,000)(.4) =

EMV (do nothing) = ($0)(.6) + ($0)(.4) =

You must choose the alternative that generates thehighest EMV.

EMV RESULTS

Alternative

State of Nature

EMVFavorable Market ($)



200,000 -180,000

200,000*0.6 +

(-180,000)*0.4 = 48,000


100,000 -20,000

100,000*0.6 +

(-20,000)*0.4 = 52,000

Do nothing 0 00*0.6 + 0*0.4 =

0

Probabilities 0.60 0.40

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EMV RESULTS

Alternative

State of Nature




200,000 -180,000 48,000


100,000 -20,000 52,000

Do nothing 0 0 0


The best decision is to construct a small plant as this generated the highest EMV of $52,000

Expected Opportunity Loss or Regret (EOL)

The EOL approach, like EMV, is used for decision-making under risk conditions based onprobabilities to arrive best decision .

The main difference is that for the EOL, theprobabilities of each state of nature are multipliedby the corresponding regret values for eachdecision alternative.

It is also similar to the Minimax regret criterionsuch that the payoff table must first be convertedfrom payoff values to regret values using theformula: Regret = Best Payoff Actual Payoff(for a given state of nature). This is the first step.

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Lets look at last exercise

Alternatives

States of Nature




200,000 -180,000


100,000 -20,000

Do nothing 0 0

Probabilities .60 .40

Alternative

State of Nature




200,000 -180,000


100,000 -20,000

Do nothing 0 0


LETS FIRST DETERMINE THE BEST PAYOFF FOR EACH STATE OF NATURE: SEE RED CIRCLES

Hence, for a favourable market, the best payoff is $200,000, whereas

for unfavourable market the best payoff is $0

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Alternative

State of Nature




200,000-200,000

0- (-180,000)


200,000-100,000

0-(-20,000)

Do nothing 200,000-0 0 - 0


THEN, WE MUST SUBTRACT EACH ACTUAL PAYOFF FOR A GIVEN STATE OF NATURE FROM BEST PAYOFF IN THE SAMESTATE OF NATURE TO CREATE AN OPPORTUNITY LOSS TABLE

SO BEST PAYOFF ACTUAL PAYOFF

Alternative

State of Nature




0 180,000


100,000 20,000

Do nothing 200,000 0


HERE IS OUR OPPORTUNITY LOSS OR REGRET TABLE.

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EMV RESULTS

Alternative

State of Nature

EOLFavorable Market ($)



0 180,0000*0.6 +

180,000*0.4 = 72,000


100,000 20,000100,000*0.6 +

20,000*0.4 = 68,000

Do nothing 200,000 0200,000*0.6 +

0*0.4 = 120,000


STEP 2: FOR EOL CRITERION, WE MUST (LIKE EMV) MULTIPLY REGRET VALUES FOR EACH ALTERNATIVE BY CORRESPONDING

PROBABILITY OF EACH STATE OF NATUREEOL = Regret x Probability

EOL

Alternative

State of Nature

EOLFavorable Market ($)



0 180,000 72,000


100,000 20,000 68,000

Do nothing 200,000 0 120,000


Now you have expected opportunity loss or regret for each alternative, the best decision is the alternative with least

expected opportunity loss or regret which is to construct small plant (given 68,000 is minimum expected regret or loss)

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Expected Value of Perfect Information (EVPI)

In some situations, it is possible to determine whichstates of nature will actually occur in the future.

In these cases, you would have obtained certain (orperfect) information about those states of natureeither through political means or research analysis(e.g. market or forecast analysis, etc).

If we have that information, we would be able tomake the best decision for a given state of nature(i.e. decision-making under certainty).

Suppose we had to value this perfect information interms of what we would be willing to pay for it, thisvalue is known as expected value of perfectinformation or EVPI.

Expected Value of Perfect Information (EVPI)

EVPI = Expected Value with Perfect Informationminus Maximum Expected Monetary Value (alsocalled the Expected Value without perfect information).

Expected value with perfect information (EVwPI) isthe maximum expected payoff we can obtain if we hadperfect information or certainty before making adecision.

EMV or (expected value without perfect information) isthe value we had computed earlier: the maximum EMVis the maximum expected payoff we obtain if we didnot have complete or perfect information.

When we subtract the two values, we get the EVPI i.e.the maximum you would pay for the perfectinformation.

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EVPI Calculation

EVPI = Expected Value with PerfectInformation minus Maximum ExpectedMonetary Value (also called the ExpectedValue without perfect information).

We have to work out the expected value withperfect information first.

Lets use the last example on the Dr. Green payofftable with probabilities.

Alternatives

States of Nature




200,000 -180,000


100,000 -20,000

Do nothing 0 0


To calculate the EVwPI, Step 1:we must choose the best payoff under

each state nature. You see those values in circles.

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Alternatives

States of Nature




200,000 -180,000


100,000 -20,000

Do nothing 0 0


Step 2: Multiply the best value in each state by correspondingprobability of that state of nature and then sum values.

Favourable Market: 200,000 x .60 + Unfavourable Market: 0 x .40 = 120,000

120,000 is EVwPI

EVPI Calculation EVPI = Expected Value with Perfect

Information (EVwPI) minus MaximumExpected Monetary Value (EMV) (also calledthe Expected Value without perfect information).

EVwPI Max. EMV

So we have the first EV with perfect informationcovered:

EVwPI = 120,000 minus Maximum EMV (fromlast example).

Now remember when we worked out the EMVby multiplying the payoffs for each alternative bycorresponding probabilities of states of nature.

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EMV RESULTS

Alternative

State of Nature




200,000 -180,000

200,000*0.6 +

(-180,000)*0.4 = 48,000


100,000 -20,000

100,000*0.6 +

(-20,000)*0.4 = 52,000

Do nothing 0 00*0.6 + 0*0.4 =

0


EMV RESULTS

Alternative

State of Nature




200,000 -180,000 48,000


100,000 -20,000 52,000

Do nothing 0 0 0


The maximum EMV (without perfect information) was 52,000.

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EVPI Calculation EVPI = Expected Value with Perfect Informationminus Maximum Expected Monetary Value (EMV)(also called the Expected Value without perfectinformation).

So we subtract the two values: EVwPI Max. EMV

EVPI = 120,000 - 52,000 = $68,000

The EVPI is the maximum you will be willing to payfor certain information and that is $68,000 dollars.This is maximum worth of such information.

So if someone had asked you to pay $80,000 forsuch information (i.e. To know exactly what willhappen in the future so you can make a certaindecision), you can decline. You will only pay for suchinformation if it costs less than $68,000.

DECISION ANALYSIS: FINAL NOTE

$68,000 also indicates the additional expectedvalue that can be obtained if perfect informationwere available about the states of nature.

Recall too that $68,000 was the value of EOL; theEOL normally equals the EVPI.

Decision analysis can be conducted manually butadvanced QM software can help decision-makerssolve more complex decision problems.

We will apply manual calculations in tutorials butyou can download the QM software from the coretext (Render et al.) and practise on your own.

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APPENDIX NOTES:Expanded Summary of Decision-Making Steps using Dr. Green Decision Problem Example

Six Steps to Decision-Making1. Clearly define the problem at hand Lets say

Dr. Green wants to determine whether it is moreprofitable to expand his current product line bymanufacturing a new product mahogany workdesks.

2. List the possible decision alternatives (coursesof action that a decision-maker can choose from)- Green has a number of choices: (1) constructa large plant to develop the new products, (2)construct a small plant to develop the newproducts, (3) do nothing (do not worry aboutexpanding the product line)

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Six Steps to Decision-Making 23. Identify the possible states of nature (outcomes)

A state of nature or outcome is a condition orevent that may occur in the future. A decision-maker under uncertainty cannot determine andhas no or little control over which states ofnature will occur. Dr. Green recognises thatthere are two possible outcomes:

The market could be favourable (i.e. highdemand for the product), or

The market could be unfavourable (i.e. lowdemand for the product).

Six Steps to Decision-Making 34. List the payoff or profit of each combination of

alternatives and outcomes Most decisionproblems use profits or losses as a method ofevaluating the consequences of each decisionalternative. These values are presented in payofftable (as shown in earlier slides). Negative valuesare treated as losses, whereas positive values aretreated as profits.

5. Select one of the mathematic decision models There are many criteria that can be used to aiddecision-making. However, the choice of thesecriteria relies on the nature of business/market,decision-maker, and level of risk or uncertainty thatis tolerated.

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Six Steps to Decision-Making 4

6. Apply model and make your decision Once the decision model is applied, theresults are analysed, and the mostplausible decision is selected based onthe models requirements. However, it iscommon for more than one decisioncriterion to be used, and the alternativewhich is supported by most of the criteriais usually considered to be the best one.

END OF LECTURE

Download tutorial assignment foranalysing decision problems.

Read Chapter 3 (Decision Analysis) ofRender et al. text.

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Lecture 2 Decision Analysis QM 2 Slides