09 decision theory l9

7/18/2019 09 Decision Theory L9

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Advanced Engineering

Projects Management

Dr. Nabil I El Sawalhi Assistant Professor of Construction

Management

1 AEPM L9



Decision theory

• Generalized approach to decision making

• Serve as basis for wide range of decision

making

• Degree of certainty about the decision is

important

• This can be from certainty to totaluncertainty which affects the way decision

taken

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Decision theory

• Two approaches for decision theory are:

• A payoff table and decision tree

• They provide structure for the organizinginformation in conductive forms to make

rational decisions.

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What is a Decision?

It is a choice from amongstalternatives

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Decision Making Criteria

• A set of goals or objectives

• A system of priorities

• Numeration of alternative actions• The outcomes associated with each

alternative

• A system of choice criteria.

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Decisions Resources

• Planning

• Organising

• Staffing• Direction

• Control

• Leadership• Communication, etc.

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Decision theory problemcharacteristics

• 1. A list of alternatives

• 2. A list of possible future state of nature

• 3. Payoffs associated with eachalternative/state of nature combination.

• 4. An assessment of the dgree of certianity

of possible future events• 5. A decision criterion.

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List of alternative

• Must be a set of mutually exclusive andcollectively exhaustive decisions that are

available to decision maker.

– For example : a real estate developer mustdecide on a plan for developing a certain

piece of property. After careful consideration

the developer has ruled out to “do nothing”

and is left with the following list of alternatives: – 1. residential proposal 2. commercial

proposal 1 3. commercial proposal 2

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State of nature

• Refers to: a set of possible futureconditions or events, beyond thecontrol of the decision maker, that will

be the primary determinant of theeventual consequence of the decision.

• Ex a real estate developer shop-center

• 1.no shopping center • 2. medium size shopping center

• 3.large shopping center AEPM L9 9



Payoffs

• Payoffs is associated with each decision

alternative and various state of nature

• Payoffs may be:

– Profits

– Revenues

– Costs

– Or other nature of value

• Usually the measure are financially

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Payoffs

• They may be weekly, monthly, annual

• Payoffs are estimated value

• The number of payoffs depend on thenumber of alternative/state of nature

combination.

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Degree of certainty

• Three level of certainty

• 1. complete certain

• 2. complete uncertain• 3. degree of probability “risk” is between

the two extreme cases.

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Three Types of Problems

Certainty Problem

• Situations in which each course of

action is believed by the decisionmaker to result in only one outcome

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Risk Problem

• Situations in which, for each course of

action, the decision maker believes that

alternative outcomes can occur, theprobabilities of which are known or can be

estimated

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• Situations in which, for each course of

action, the decision maker does not know

which outcomes can or will occur

(ambiguous) and thus cannot assignprobabilities to the possible outcome

(variability)

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Uncertainty Problem



Decision criterion

• The process of selecting one alternative

from a list of alternatives is governed by adecision criterion, which embodies the

decision maker‟s attitudes towered the

decision and degree of certainty.

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Decision criterion

• Some decision makers are optimistic

• Others are more pessimistic

• Some wants to maximize gains

• Some wants to reduce loss

• One example of decision criterion is “

Maximize the expected payoffs ” another is

“ Choose the alternative that has the best

possible payoffs ”

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The payoff Table

• The payoff Table is a device a decisionmaker can use to summaries and organize

information relevant to a particular

decision.• It includes”

• List of alternatives

• The possible future state of nature• The payoffs associated with each of

alternative/state of nature combination.

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• If probabilities for the state of nature are

known, these can be listed.

• There is a finite set of discrete decision

alternatives.

• The outcome of a decision is a function of

a single future event.

• Events (states of nature ) are mutually

exclusive and collectively exhaustive.

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S1 S2 S3

a1 v11 v12 v13a2 v21 v22 v23

a3 v31 v32 v33

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The payoff Table

Alternatives

State of nature

a1= the I th alternativeS j = the j th state of natureVij = the value or payoff that will be realized ifalternative I is chosen and event j occurs



– In a Payoff table -

• The rows correspond to the possible

decision alternatives.

• The columns correspond to the

possible future events.

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Payoff or Utility Matrices

• Any problem is represented

by matrices:

• Columns: possible outcome

(O)

• Row : potential course

of action (C or S)

• Cell : represent thepayoff or utility

O2O1

U12U11S1

U22U21S2

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Payoff table for real estate

developer

• Residential

• Commercial 1

• Commercial 2

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Nocentre

Mediumcentre

Largecentre

$4 16 12

5 6 10

-1 4 15

The valuesin the tablerepresentsthe profitsor losses inhundred ofthousand if

theproposedalternativeis chosen



Certainty

Assumptions of certainty• All information is known with certainty

• Complete Knowledge

• Stability

• No-ambiguity

• Enumeration of all strategies• Full knowledge of requirements

• Exactly one payoffs

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DMUC with a single objective

• Example 1.8• Droflas and Partners will launch one of

its heaviest campaigns to promote itssurveying services. The promotionbudget is not yet finalised, but theyknow that some £50,000 will beavailable.

• The partners want to determine howmuch they should spend for promotionalliterature, and which is the mostappropriate medium for their services.

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• They have created five „publication

strategies‟ with their projected outcomes in

terms of increased commissions.

• The decision criterion to be used in

identifying the optimal strategy is that of

maximum utility. That is the strategy that

yields the maximum utility is the optimumstrategy.

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• Utility for the purposes of this problem wasdefined as the ratio of outcome (i.e.,

increases in value of commissions) to

cost.• Shown below are the strategies and their

respective payoffs

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Strategy Cost

(£10000)

Increase in

commissions

(£10000)

Utility or Pay-off

(Ratio)

S1

1.80 1.78 0.988

S2

2.00 2.02 1.010

S3 2.25 2.42 1.075

S4

2.75 2.68 0.974

S5 3.20 3.24 1.012

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Which is the optimal strategy?

• [Answer = Strategy S3 ]

• The optimal strategy is that strategy whichyields the highest utility or pay-off.

• The pay-off is calculated by dividing thevalue of the increase in commissions by

the cost of the particular strategy.

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NOTE:

• Each strategy results in a unique pay-off;

• There is only one state of nature ;• There is a single measure of performance;

• The optimal strategy is the one that yields

the highest payoff or utility .

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Example 2DMUC with Multiple Objectives

• Droflas & Partners is developing itsannual plan in terms of three objectives:

• Increased Profits;

• Increased Market Share;• Increased Value of Commissions.

• The partners do not regard each of these

objectives with equal emphasis.• They are most interested in increased

market share, followed by commissiongrowth, and then profit.

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• The strength of this interest is currently in

the proportion of 5:3:2 for the three

objectives.

• Droflas have formulated three different

strategies for achieving the stated

objectives, each of which has a different

impact on the three outcomes underconsideration as follows:

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Measures of

Performan

ce (ofThree

Objectives)

ROI

(Profit)

% Increase

(Market

Share)

% Increase

(Commission

Growth)

Weighted or

Composite

Utility(CU)

Weights 0.2 0.5 0.3

Strategy S1 7 4 9 6.1

S2 3 6 7 5.7

S3 5 5 10 6.5

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Note:

• The profit objective could be stated in, andmeasured by, absolute money volume, orpercentage increase, or by return oninvestment (ROI);

• The market share is to be measured interms of percentage of the total market;

• Commission growth could be measured

either in money or percentage terms.• What is the optimal strategy?

• [Answer = Strategy S3]

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UNCERTAINTY

• The condition of being unsure about the possibleoutcome

• It is the variability in relation to performance

measures like cost, duration and quality

• It is associated with ambiguity

• Both of variability and ambiguity are associated

with lack of clarity

• Ambiguity is related to completeness, accuracy,meaning of information, implications.

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Uncertainty Problem

• Three criteria has been suggested for

selecting a course of action:

• MAXIMIN

– (criterion of pessimism)

MAXIMAX

– (optimism)

• MiniMax

– (criterion of regret)

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MaxiMinCriterion of pessimism

• A decision maker who isconfronted with the problemrepresented as follows

1. If (I) select S1, the minimum

gain is 12. If (I) select S2, the minimum

gain is 2

3.There, (I) will select S2because it maximize theminimum gain

O2O1

51S1

32S2

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DECISION MAKING UNDERUNCERTAINTY

• Example 1.• Having decided not to open a Warrington office

Droflas‟ managing partner is then inundatedwith commissions in the Warrington area and is

considering three „new‟ alternative strategies tocope with the work:

• S1: open a new branch office in Warrington;

• S2: merge with a competitor Warrington

practice (SMM perhaps?);• S3: takeover a competitor Warrington practice

(SMM perhaps?).

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• The managing partner has decided

that for the time being only one ofthese three strategies is economicallyfeasible.

• He has also decided that a further

alternative, staff commuting from otheroffices to execute the work, isimpractical.

• Given these options the managingpartner needs to construct aconditional payoff matrix for thisdilemma.

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• After conducting sufficient research, based

upon personal interviews and anticipating

possible reactions of competitors, the

managing partner produces the followingpayoff matrix:

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States of Nature

N1

N2

N3

Strategy S1 15 12 18

S2

9 14 10

S3

13 4 26

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CRITERION OF PESSIMISMThe optimal strategy is the strategy that yields the

„best of the worst‟ outcomes. This is also known as

MAXIMIN.

States of Nature Worst, or

Minimum

Outcome

N1 N2 N3

Strategy

S1

15 12 18 12

S2 9 14 10 9

S3 13 4 26 4

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CRITERION OF OPTIMISM



CRITERION OF OPTIMISMThe optimal strategy is the strategy that yields the „best of

the best‟ outcomes. Also known as MAXIMAX.

States of Nature Best, or

Maximum

Outcome

N1 N2 N3

Strategy

S1

15 12 18 18

S2 9 14 10 14

S3 13 4 26 26

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COEFFICIENT OF OPTIMISM



COEFFICIENT OF OPTIMISM Assuming that the balance between optimism and

pessimism is 60:40. This creates a coefficient of optimism

of 0.6 then S3 the weighted coefficient of optimism (0.6)solution

Best, or

Maximum

Payoff

Worst, or

Minimum

Payoff

Weighted

Payoff

Weight 0.6 0.4

Strategy S1 18 12 15.6

S2

14 9 12.0

S3 26 4 17.2

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MiniMax criterion (Regret)

1. If (I) select O1, themaximum loss is 2

2. If (I) select O2, the

maximum loss is 5

3. There, (I) select O1

because it minimize the

maximum loss.

O2O1

51S1

32S2

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Regret Criterion

1. If O1 will occur, S2 wouldbe selected

2. But If (I) selected S1 and

O1 did occur, the regret

would be 2-1=1

3. If (I) selected S2 and O1

occur, he would have no

regret (0) and so forth….

O2O1

51S1

32S2

O2O1

01S1

20S2

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CRITERION OF REGRET



CRITERION OF REGRETThe optimal strategy is the strategy that yields the‘minimum of the maximum regret values’ outcome.

Also known as MINIMAX REGRET.The regret or opportunity-loss matrix is:

States of Nature Maximu

Regret

N1 N2 N3

Regret Or Opportunity

Loss

S1

0 2 8 8

S2 6 0 16 16

S3

2 10 0 10

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States of Nature

N1

N2

N3

S1

15 12 18

S2

9 14 10

S3 13 4 26



Minimax = Maximin

• The point at which thisequality happened is theSaddle point

• Saddle point : is the point that

there is no higher value in itscolumn and no lower value inits row

• The corresponding strategies

for saddle point is the best forboth parties (the decisionmaker and the opponent)

O2O1

51S1

32S2

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EQUAL PROBABILITY CRITERION



EQUAL PROBABILITY CRITERIONAlso called the LAPLACE CRITERION, or the Criterionof INSUFFICIENT REASON

States of Nature Expected

Monetary

Value

(EMV)

N1 N2 N3

Probability 1/3 1/3 1/3

Utility or Payoff

Strategy S1

15 12 18 15

S2

9 14 10 11

S3

13 4 26 14.3 49 AEPM L9



Minimax # Maximin

• We don‟t have a Saddlepoint

• Use Mixing strategy

• Select C1 with P1 and C2

with P2 such that

• P1(2)+ P2(3)= P1 (5)+P2(1)

O2O1

52S1

13S2

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DECISION MAKING UNDER



DECISION MAKING UNDERCONFLICT OR COMPETITION

• Assumptions for a 2-person, zero sumgame:

• 2 rational opponents select optimal

strategies;• Both competitors know each other‟s

strategies;

• Payoff matrix is known to eachcompetitor;

• Both competitors choose theirstrategies simultaneously;

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• The loss of one competitor equals exactlythe gain of the other;

• Decision conditions remain unaltered;

• It is a repetitive decision making problem.• The lack of consistency of these

assumptions with conditions for tendering

within the construction industry should beapparent to you.

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Example 1

PURE STRATEGY• Contractor A has three potential strategies

for the execution of a project, A1, A2, A3,and player B has four potential strategies,B1, B2, B3, B4.

• If contractor A adopts strategy A1 andcontractor B adopts strategy B1,

contractor A will gain 8 units (EMV) whilstplayer B will lose 8 units.

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• If contractor A adopts strategy A1 andcontractor B adopts strategy B2,contractor A will gain 9 units whilstcontractor B will lose 9 units.

• All possible combinations of payoffs aregiven in the matrix below:

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Contractor B Minimum

of row

values

B1

B2

B3

B4

Strategy A1 8 12 7 3 3

A2 9 14 10 16 9

A3 7 4 26 5 4Maximum

of column

values

9 14 26 16

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• Applying the criterion of pessimism, the

optimal strategy for Contractor A is

identified by the MAXIMIN outcome.

• The optimal strategy for contractor B is

identified by the MINIMAX outcome.

56AEPM L9

09 decision theory l9

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